An Integrated Finite Element-based Simulation Framework: From Hole Piercing to Hole Expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaohua; Sun, Xin; Golovashchenko, Segey F.

An integrated finite element-based modeling framework is developed to predict the hole expansion ratio (HER) of AA6111-T4 sheet by considering the piercing-induced damages around the hole edge. Using damage models and parameters calibrated from previously reported tensile stretchability studies, the predicted HER correlates well with experimentally measured HER values for different hole piercing clearances. The hole piercing model shows burrs are not generated on the sheared surface for clearances less than 20%, which corresponds well with the experimental data on pierced holes cross-sections. Finite-element-calculated HER also is not especially sensitive to piercing clearances less than this value. However, as clearancesmore » increase to 30% and further to 40%, the HER values are predicted to be considerably smaller, also consistent with experimental measurements. Upon validation, the integrated modeling framework is used to examine the effects of different hole piercing and hole expansion conditions on the critical HERs for AA6111-T4.« less

Computer program analyzes Buckling Of Shells Of Revolution with various wall construction, BOSOR

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1968-01-01

Computer program performs stability analyses for a wide class of shells without unduly restrictive approximations. The program uses numerical integration, finite difference of finite element techniques to solve with reasonable accuracy almost any buckling problem for shells exhibiting orthotropic behavior.

A Kirchhoff approach to seismic modeling and prestack depth migration

NASA Astrophysics Data System (ADS)

Liu, Zhen-Yue

1993-05-01

The Kirchhoff integral provides a robust method for implementing seismic modeling and prestack depth migration, which can handle lateral velocity variation and turning waves. With a little extra computation cost, the Kirchoff-type migration can obtain multiple outputs that have the same phase but different amplitudes, compared with that of other migration methods. The ratio of these amplitudes is helpful in computing some quantities such as reflection angle. I develop a seismic modeling and prestack depth migration method based on the Kirchhoff integral, that handles both laterally variant velocity and a dip beyond 90 degrees. The method uses a finite-difference algorithm to calculate travel times and WKBJ amplitudes for the Kirchhoff integral. Compared to ray-tracing algorithms, the finite-difference algorithm gives an efficient implementation and single-valued quantities (first arrivals) on output. In my finite difference algorithm, the upwind scheme is used to calculate travel times, and the Crank-Nicolson scheme is used to calculate amplitudes. Moreover, interpolation is applied to save computation cost. The modeling and migration algorithms require a smooth velocity function. I develop a velocity-smoothing technique based on damped least-squares to aid in obtaining a successful migration.

Integrated transient thermal-structural finite element analysis

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Dechaumphai, P.; Wieting, A. R.; Tamma, K. K.

1981-01-01

An integrated thermal structural finite element approach for efficient coupling of transient thermal and structural analysis is presented. Integrated thermal structural rod and one dimensional axisymmetric elements considering conduction and convection are developed and used in transient thermal structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction elasticity solutions and conventional finite element thermal finite element structural analyses.

A symplectic integration method for elastic filaments

NASA Astrophysics Data System (ADS)

Ladd, Tony; Misra, Gaurav

2009-03-01

Elastic rods are a ubiquitous coarse-grained model of semi-flexible biopolymers such as DNA, actin, and microtubules. The Worm-Like Chain (WLC) is the standard numerical model for semi-flexible polymers, but it is only a linearized approximation to the dynamics of an elastic rod, valid for small deflections; typically the torsional motion is neglected as well. In the standard finite-difference and finite-element formulations of an elastic rod, the continuum equations of motion are discretized in space and time, but it is then difficult to ensure that the Hamiltonian structure of the exact equations is preserved. Here we discretize the Hamiltonian itself, expressed as a line integral over the contour of the filament. This discrete representation of the continuum filament can then be integrated by one of the explicit symplectic integrators frequently used in molecular dynamics. The model systematically approximates the continuum partial differential equations, but has the same level of computational complexity as molecular dynamics and is constraint free. Numerical tests show that the algorithm is much more stable than a finite-difference formulation and can be used for high aspect ratio filaments, such as actin. We present numerical results for the deterministic and stochastic motion of single filaments.

Divergence preserving discrete surface integral methods for Maxwell's curl equations using non-orthogonal unstructured grids

NASA Technical Reports Server (NTRS)

Madsen, Niel K.

1992-01-01

Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.

Finite-difference model for 3-D flow in bays and estuaries

USGS Publications Warehouse

Smith, Peter E.; Larock, Bruce E.; ,

1993-01-01

This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.

LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

NASA Technical Reports Server (NTRS)

Ramsey, J. W., Jr.; Taylor, J. T.; Wilson, J. F.; Gray, C. E., Jr.; Leatherman, A. D.; Rooker, J. R.; Allred, J. W.

1976-01-01

The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

Effect of Integration Patterns Around Implant Neck on Stress Distribution in Peri-Implant Bone: A Finite Element Analysis.

PubMed

Han, Jingyun; Sun, Yuchun; Wang, Chao

2017-08-01

To investigate the biomechanical performance of different osseointegration patterns between cortical bone and implants using finite element analysis. Fifteen finite element models were constructed of the mandibular fixed prosthesis supported by implants. Masticatory loads (200 N axial, 100 N oblique, 40 N horizontal) were applied. The cortical bone/implant interface was divided equally into four layers: upper, upper-middle, lower-middle, and lower. The bone stress and implant displacement were calculated for 5 degrees of uniform integration (0, 20%, 40%, 60%, and 100%) and 10 integration patterns. The stress was concentrated in the bone margin and gradually decreased as osseointegration progressed, when the integrated and nonintegrated areas were alternated on the bone-implant surface. Compared with full integration, the integration of only the lower-middle layer or lower half layers significantly decreased von Mises, tensile, and compressive stresses in cortical bone under oblique and horizontal loads, and these patterns did not induce higher stress in the cancellous bone. For the integration of only the upper or upper-middle layer, stress in the cortical and cancellous bones significantly increased and was considerably higher than in the case of nonintegration. In addition, the maximum stress in the cortical bone was sensitive to the quantity of integrated nodes at the bone margin; lower quantity was associated with higher stress. There was no significant difference in the displacement of implants among 15 models. Integration patterns of cortical bone significantly affect stress distribution in peri-implant bone. The integration of only the lower-middle or lower half layers helps to increase the load-bearing capacity of peri-implant bone and decrease the risk of overloading, while upper integration may further increase the risk of bone resorption. © 2016 by the American College of Prosthodontists.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

AN INTEGRATED APPROACH TO CHARACTERIZING BYPASSED OIL IN HETEROGENEOUS AND FRACTURED RESERVOIRS USING PARTITIONING TRACERS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akhil Datta-Gupta

2003-08-01

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have adopted an integrated approach whereby we combine data from multiple sources to minimize the uncertainty and non-uniqueness in the interpreted results. For partitioning interwell tracer tests, these are primarily the distribution of reservoir permeability and oil saturation distribution. A novel approachmore » to multiscale data integration using Markov Random Fields (MRF) has been developed to integrate static data sources from the reservoir such as core, well log and 3-D seismic data. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, the behavior of partitioning tracer tests in fractured reservoirs is investigated using a dual-porosity finite-difference model.« less

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Involution and Difference Schemes for the Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.

In the present paper we consider the Navier-Stokes equations for the two-dimensional viscous incompressible fluid flows and apply to these equations our earlier designed general algorithmic approach to generation of finite-difference schemes. In doing so, we complete first the Navier-Stokes equations to involution by computing their Janet basis and discretize this basis by its conversion into the integral conservation law form. Then we again complete the obtained difference system to involution with eliminating the partial derivatives and extracting the minimal Gröbner basis from the Janet basis. The elements in the obtained difference Gröbner basis that do not contain partial derivatives of the dependent variables compose a conservative difference scheme. By exploiting arbitrariness in the numerical integration approximation we derive two finite-difference schemes that are similar to the classical scheme by Harlow and Welch. Each of the two schemes is characterized by a 5×5 stencil on an orthogonal and uniform grid. We also demonstrate how an inconsistent difference scheme with a 3×3 stencil is generated by an inappropriate numerical approximation of the underlying integrals.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size.

PubMed

Schwalger, Tilo; Deger, Moritz; Gerstner, Wulfram

2017-04-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Dynamic load balancing of applications

DOEpatents

Wheat, Stephen R.

1997-01-01

An application-level method for dynamically maintaining global load balance on a parallel computer, particularly on massively parallel MIMD computers. Global load balancing is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method supports a large class of finite element and finite difference based applications and provides an automatic element management system to which applications are easily integrated.

Static and dynamic behaviour of nonlocal elastic bar using integral strain-based and peridynamic models

NASA Astrophysics Data System (ADS)

Challamel, Noël

2018-04-01

The static and dynamic behaviour of a nonlocal bar of finite length is studied in this paper. The nonlocal integral models considered in this paper are strain-based and relative displacement-based nonlocal models; the latter one is also labelled as a peridynamic model. For infinite media, and for sufficiently smooth displacement fields, both integral nonlocal models can be equivalent, assuming some kernel correspondence rules. For infinite media (or finite media with extended reflection rules), it is also shown that Eringen's differential model can be reformulated into a consistent strain-based integral nonlocal model with exponential kernel, or into a relative displacement-based integral nonlocal model with a modified exponential kernel. A finite bar in uniform tension is considered as a paradigmatic static case. The strain-based nonlocal behaviour of this bar in tension is analyzed for different kernels available in the literature. It is shown that the kernel has to fulfil some normalization and end compatibility conditions in order to preserve the uniform strain field associated with this homogeneous stress state. Such a kernel can be built by combining a local and a nonlocal strain measure with compatible boundary conditions, or by extending the domain outside its finite size while preserving some kinematic compatibility conditions. The same results are shown for the nonlocal peridynamic bar where a homogeneous strain field is also analytically obtained in the elastic bar for consistent compatible kinematic boundary conditions at the vicinity of the end conditions. The results are extended to the vibration of a fixed-fixed finite bar where the natural frequencies are calculated for both the strain-based and the peridynamic models.

A computationally efficient modelling of laminar separation bubbles

NASA Technical Reports Server (NTRS)

Maughmer, Mark D.

1988-01-01

The goal of this research is to accurately predict the characteristics of the laminar separation bubble and its effects on airfoil performance. To this end, a model of the bubble is under development and will be incorporated in the analysis section of the Eppler and Somers program. As a first step in this direction, an existing bubble model was inserted into the program. It was decided to address the problem of the short bubble before attempting the prediction of the long bubble. In the second place, an integral boundary-layer method is believed more desirable than a finite difference approach. While these two methods achieve similar prediction accuracy, finite-difference methods tend to involve significantly longer computer run times than the integral methods. Finally, as the boundary-layer analysis in the Eppler and Somers program employs the momentum and kinetic energy integral equations, a short-bubble model compatible with these equations is most preferable.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

Doi-Peliti path integral methods for stochastic systems with partial exclusion

NASA Astrophysics Data System (ADS)

Greenman, Chris D.

2018-09-01

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

A comparison of VLSI architecture of finite field multipliers using dual, normal or standard basis

NASA Technical Reports Server (NTRS)

Hsu, I. S.; Truong, T. K.; Shao, H. M.; Deutsch, L. J.; Reed, I. S.

1987-01-01

Three different finite field multipliers are presented: (1) a dual basis multiplier due to Berlekamp; (2) a Massy-Omura normal basis multiplier; and (3) the Scott-Tavares-Peppard standard basis multiplier. These algorithms are chosen because each has its own distinct features which apply most suitably in different areas. Finally, they are implemented on silicon chips with nitride metal oxide semiconductor technology so that the multiplier most desirable for very large scale integration implementations can readily be ascertained.

Conformal anomaly of generalized form factors and finite loop integrals

NASA Astrophysics Data System (ADS)

Chicherin, Dmitry; Sokatchev, Emery

2018-04-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ-loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ - 1)-loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.

Wave-vector and polarization dependent impedance model for a hexagonal periodic metasurface exemplified through finite-difference time-domain simulations.

PubMed

Ding, Yi S; He, Yang

2017-08-21

An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

PubMed Central

Gerstner, Wulfram

2017-01-01

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations. PMID:28422957

Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

Dynamic load balancing of applications

DOEpatents

Wheat, S.R.

1997-05-13

An application-level method for dynamically maintaining global load balance on a parallel computer, particularly on massively parallel MIMD computers is disclosed. Global load balancing is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method supports a large class of finite element and finite difference based applications and provides an automatic element management system to which applications are easily integrated. 13 figs.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

Prediction of high-speed rotor noise with a Kirchhoff formula

NASA Technical Reports Server (NTRS)

Purcell, Timothy W.; Strawn, Roger C.; Yu, Yung H.

1987-01-01

A new methodology has been developed to predict the impulsive noise generated by a transonic rotor blade. The formulation uses a full-potential finite-difference method to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far-field. This Kirchhoff formula is written in a blade-fixed coordinate system. It requires initial data across a plane at the sonic radius. This data is provided by the finite-difference solution. Acoustic pressure predictions show excellent agreement with hover experimental data for two hover cases of 0.88 and 0.90 tip Mach number, the latter of which has delocalized transonic flow. These results represent the first successful prediction technique for peak pressure amplitudes using a computational code.

Workshop on the Integration of Finite Element Modeling with Geometric Modeling

NASA Technical Reports Server (NTRS)

Wozny, Michael J.

1987-01-01

The workshop on the Integration of Finite Element Modeling with Geometric Modeling was held on 12 May 1987. It was held to discuss the geometric modeling requirements of the finite element modeling process and to better understand the technical aspects of the integration of these two areas. The 11 papers are presented except for one for which only the abstract is given.

Numerically stable finite difference simulation for ultrasonic NDE in anisotropic composites

NASA Astrophysics Data System (ADS)

Leckey, Cara A. C.; Quintanilla, Francisco Hernando; Cole, Christina M.

2018-04-01

Simulation tools can enable optimized inspection of advanced materials and complex geometry structures. Recent work at NASA Langley is focused on the development of custom simulation tools for modeling ultrasonic wave behavior in composite materials. Prior work focused on the use of a standard staggered grid finite difference type of mathematical approach, by implementing a three-dimensional (3D) anisotropic Elastodynamic Finite Integration Technique (EFIT) code. However, observations showed that the anisotropic EFIT method displays numerically unstable behavior at the locations of stress-free boundaries for some cases of anisotropic materials. This paper gives examples of the numerical instabilities observed for EFIT and discusses the source of instability. As an alternative to EFIT, the 3D Lebedev Finite Difference (LFD) method has been implemented. The paper briefly describes the LFD approach and shows examples of stable behavior in the presence of stress-free boundaries for a monoclinic anisotropy case. The LFD results are also compared to experimental results and dispersion curves.

Reliability analysis of laminated CMC components through shell subelement techniques

NASA Technical Reports Server (NTRS)

Starlinger, Alois; Duffy, Stephen F.; Gyekenyesi, John P.

1992-01-01

An updated version of the integrated design program Composite Ceramics Analysis and Reliability Evaluation of Structures (C/CARES) was developed for the reliability evaluation of ceramic matrix composites (CMC) laminated shell components. The algorithm is now split into two modules: a finite-element data interface program and a reliability evaluation algorithm. More flexibility is achieved, allowing for easy implementation with various finite-element programs. The interface program creates a neutral data base which is then read by the reliability module. This neutral data base concept allows easy data transfer between different computer systems. The new interface program from the finite-element code Matrix Automated Reduction and Coupling (MARC) also includes the option of using hybrid laminates (a combination of plies of different materials or different layups) and allows for variations in temperature fields throughout the component. In the current version of C/CARES, a subelement technique was implemented, enabling stress gradients within an element to be taken into account. The noninteractive reliability function is now evaluated at each Gaussian integration point instead of using averaging techniques. As a result of the increased number of stress evaluation points, considerable improvements in the accuracy of reliability analyses were realized.

Finite element analysis of inviscid subsonic boattail flow

NASA Technical Reports Server (NTRS)

Chima, R. V.; Gerhart, P. M.

1981-01-01

A finite element code for analysis of inviscid subsonic flows over arbitrary nonlifting planar or axisymmetric bodies is described. The code solves a novel primitive variable formulation of the coupled irrotationality and compressible continuity equations. Results for flow over a cylinder, a sphere, and a NACA 0012 airfoil verify the code. Computed subcritical flows over an axisymmetric boattailed afterbody compare well with finite difference results and experimental data. Interative coupling with an integral turbulent boundary layer code shows strong viscous effects on the inviscid flow. Improvements in code efficiency and extensions to transonic flows are discussed.

Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects

NASA Astrophysics Data System (ADS)

Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.

2014-11-01

The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, a high level of scalability can be achieved. By using vertical FDM, an easy method for coupling the dynamics and existing physics packages can be provided. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind-biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative and integral terms. For temporal integration, a time-split, third-order Runge-Kutta (RK3) integration technique was applied. The Euler equations that were used here are in flux form based on the hydrostatic pressure vertical coordinate. The equations are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate was implemented in this model. We validated the model by conducting the widely used standard tests: linear hydrostatic mountain wave, tracer advection, and gravity wave over the Schär-type mountain, as well as density current, inertia-gravity wave, and rising thermal bubble. The results from these tests demonstrated that the model using the horizontal SEM and the vertical FDM is accurate and robust provided sufficient diffusion is applied. The results with various horizontal resolutions also showed convergence of second-order accuracy due to the accuracy of the time integration scheme and that of the vertical direction, although high-order basis functions were used in the horizontal. By using the 2-D slice model, we effectively showed that the combined spatial discretization method of the spectral element and finite difference methods in the horizontal and vertical directions, respectively, offers a viable method for development of an NH dynamical core.

Numerical time-domain electromagnetics based on finite-difference and convolution

NASA Astrophysics Data System (ADS)

Lin, Yuanqu

Time-domain methods posses a number of advantages over their frequency-domain counterparts for the solution of wideband, nonlinear, and time varying electromagnetic scattering and radiation phenomenon. Time domain integral equation (TDIE)-based methods, which incorporate the beneficial properties of integral equation method, are thus well suited for solving broadband scattering problems for homogeneous scatterers. Widespread adoption of TDIE solvers has been retarded relative to other techniques by their inefficiency, inaccuracy and instability. Moreover, two-dimensional (2D) problems are especially problematic, because 2D Green's functions have infinite temporal support, exacerbating these difficulties. This thesis proposes a finite difference delay modeling (FDDM) scheme for the solution of the integral equations of 2D transient electromagnetic scattering problems. The method discretizes the integral equations temporally using first- and second-order finite differences to map Laplace-domain equations into the Z domain before transforming to the discrete time domain. The resulting procedure is unconditionally stable because of the nature of the Laplace- to Z-domain mapping. The first FDDM method developed in this thesis uses second-order Lagrange basis functions with Galerkin's method for spatial discretization. The second application of the FDDM method discretizes the space using a locally-corrected Nystrom method, which accelerates the precomputation phase and achieves high order accuracy. The Fast Fourier Transform (FFT) is applied to accelerate the marching-on-time process in both methods. While FDDM methods demonstrate impressive accuracy and stability in solving wideband scattering problems for homogeneous scatterers, they still have limitations in analyzing interactions between several inhomogenous scatterers. Therefore, this thesis devises a multi-region finite-difference time-domain (MR-FDTD) scheme based on domain-optimal Green's functions for solving sparsely-populated problems. The scheme uses a discrete Green's function (DGF) on the FDTD lattice to truncate the local subregions, and thus reduces reflection error on the local boundary. A continuous Green's function (CGF) is implemented to pass the influence of external fields into each FDTD region which mitigates the numerical dispersion and anisotropy of standard FDTD. Numerical results will illustrate the accuracy and stability of the proposed techniques.

True Concurrent Thermal Engineering Integrating CAD Model Building with Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Panczak, Tim; Ring, Steve; Welch, Mark

1999-01-01

Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.

Investigation for connecting waveguide in off-planar integrated circuits.

PubMed

Lin, Jie; Feng, Zhifang

2017-09-01

The transmission properties of a vertical waveguide connected by different devices in off-planar integrated circuits are designed, investigated, and analyzed in detail by the finite-difference time-domain method. The results show that both guide bandwidth and transmission efficiency can be adjusted effectively by shifting the vertical waveguide continuously. Surprisingly, the wide guide band (0.385[c/a]∼0.407[c/a]) and well transmission (-6  dB) are observed simultaneously in several directions when the vertical waveguide is located at a specific location. The results are very important for all-optical integrated circuits, especially in compact integration.

Optical device terahertz integration in a two-dimensional-three-dimensional heterostructure.

PubMed

Feng, Zhifang; Lin, Jie; Feng, Shuai

2018-01-10

The transmission properties of an off-planar integrated circuit including two wavelength division demultiplexers are designed, simulated, and analyzed in detail by the finite-difference time-domain method. The results show that the wavelength selection for different ports (0.404[c/a] at B 2 port, 0.389[c/a] at B 3 port, and 0.394[c/a] at B 4 port) can be realized by adjusting the parameters. It is especially important that the off-planar integration between two complex devices is also realized. These simulated results give valuable promotions in the all-optical integrated circuit, especially in compact integration.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

A Maple package for computing Gröbner bases for linear recurrence relations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Robertz, Daniel

2006-04-01

A Maple package for computing Gröbner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for example, for automatic generation of difference schemes for linear partial differential equations and for reduction of multiloop Feynman integrals. These two possible applications are illustrated by simple examples of the Laplace equation and a one-loop scalar integral of propagator type.

Long-time asymptotic solution structure of Camassa-Holm equation subject to an initial condition with non-zero reflection coefficient of the scattering data

NASA Astrophysics Data System (ADS)

Chang, Chueh-Hsin; Yu, Ching-Hao; Sheu, Tony Wen-Hann

2016-10-01

In this article, we numerically revisit the long-time solution behavior of the Camassa-Holm equation ut - uxxt + 2ux + 3uux = 2uxuxx + uuxxx. The finite difference solution of this integrable equation is sought subject to the newly derived initial condition with Delta-function potential. Our underlying strategy of deriving a numerical phase accurate finite difference scheme in time domain is to reduce the numerical dispersion error through minimization of the derived discrepancy between the numerical and exact modified wavenumbers. Additionally, to achieve the goal of conserving Hamiltonians in the completely integrable equation of current interest, a symplecticity-preserving time-stepping scheme is developed. Based on the solutions computed from the temporally symplecticity-preserving and the spatially wavenumber-preserving schemes, the long-time asymptotic CH solution characters can be accurately depicted in distinct regions of the space-time domain featuring with their own quantitatively very different solution behaviors. We also aim to numerically confirm that in the two transition zones their long-time asymptotics can indeed be described in terms of the theoretically derived Painlevé transcendents. Another attempt of this study is to numerically exhibit a close connection between the presently predicted finite-difference solution and the solution of the Painlevé ordinary differential equation of type II in two different transition zones.

Finite element area and line integral transforms for generalization of aperture function and geometry in Kirchhoff scalar diffraction theory

NASA Astrophysics Data System (ADS)

Kraus, Hal G.

1993-02-01

Two finite element-based methods for calculating Fresnel region and near-field region intensities resulting from diffraction of light by two-dimensional apertures are presented. The first is derived using the Kirchhoff area diffraction integral and the second is derived using a displaced vector potential to achieve a line integral transformation. The specific form of each of these formulations is presented for incident spherical waves and for Gaussian laser beams. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define apertures of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s), which may be of continuous or discontinuous form. The finite element transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is illustrated in several examples which include secondary obstructions, secondary spider supports, multiple mirror arrays, synthetic aperture arrays, apertures covered by screens, apodization, phase plates, and off-axis apertures. Typically, the finite element line integral transform results in significant gains in computational efficiency over the finite element Kirchhoff transform method, but is also subject to some loss in generality.

Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

NASA Astrophysics Data System (ADS)

Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.

2010-10-01

Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.

Buckling Of Shells Of Revolution /BOSOR/ with various wall constructions

NASA Technical Reports Server (NTRS)

Almroth, B. O.; Bushnell, D.; Sobel, L. H.

1969-01-01

Computer program, using numerical integration and finite difference techniques, solves almost any buckling problem for shells exhibiting orthotropic behavior. Stability analyses can be performed with reasonable accuracy and without unduly restrictive approximations.

An explicit predictor-corrector solver with applications to Burgers' equation

NASA Technical Reports Server (NTRS)

Dey, S. K.; Dey, C.

1983-01-01

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

A computer program for anisotropic shallow-shell finite elements using symbolic integration

NASA Technical Reports Server (NTRS)

Andersen, C. M.; Bowen, J. T.

1976-01-01

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohanty, Subhasish; Majumdar, Saurindranath

Irradiation creep plays a major role in the structural integrity of the graphite components in high temperature gas cooled reactors. Finite element procedures combined with a suitable irradiation creep model can be used to simulate the time-integrated structural integrity of complex shapes, such as the reactor core graphite reflector and fuel bricks. In the present work a comparative study was undertaken to understand the effect of linear and nonlinear irradiation creep on results of finite element based stress analysis. Numerical results were generated through finite element simulations of a typical graphite reflector.

An extension of the finite cell method using boolean operations

NASA Astrophysics Data System (ADS)

Abedian, Alireza; Düster, Alexander

2017-05-01

In the finite cell method, the fictitious domain approach is combined with high-order finite elements. The geometry of the problem is taken into account by integrating the finite cell formulation over the physical domain to obtain the corresponding stiffness matrix and load vector. In this contribution, an extension of the FCM is presented wherein both the physical and fictitious domain of an element are simultaneously evaluated during the integration. In the proposed extension of the finite cell method, the contribution of the stiffness matrix over the fictitious domain is subtracted from the cell, resulting in the desired stiffness matrix which reflects the contribution of the physical domain only. This method results in an exponential rate of convergence for porous domain problems with a smooth solution and accurate integration. In addition, it reduces the computational cost, especially when applying adaptive integration schemes based on the quadtree/octree. Based on 2D and 3D problems of linear elastostatics, numerical examples serve to demonstrate the efficiency and accuracy of the proposed method.

Determination of stresses in gas-turbine disks subjected to plastic flow and creep

NASA Technical Reports Server (NTRS)

Millenson, M B; Manson, S S

1948-01-01

A finite-difference method previously presented for computing elastic stresses in rotating disks is extended to include the computation of the disk stresses when plastic flow and creep are considered. A finite-difference method is employed to eliminate numerical integration and to permit nontechnical personnel to make the calculations with a minimum of engineering supervision. Illustrative examples are included to facilitate explanation of the procedure by carrying out the computations on a typical gas-turbine disk through a complete running cycle. The results of the numerical examples presented indicate that plastic flow markedly alters the elastic-stress distribution.

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.

1995-01-01

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.

Distributed finite-time containment control for double-integrator multiagent systems.

PubMed

Wang, Xiangyu; Li, Shihua; Shi, Peng

2014-09-01

In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.

A finite element-boundary integral method for cavities in a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. However, due to a lack of rigorous mathematical models for conformal antenna arrays, antenna designers resort to measurement and planar antenna concepts for designing non-planar conformal antennas. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We extend this formulation to conformal arrays on large metallic cylinders. In this report, we develop the mathematical formulation. In particular, we discuss the shape functions, the resulting finite elements and the boundary integral equations, and the solution of the conformal finite element-boundary integral system. Some validation results are presented and we further show how this formulation can be applied with minimal computational and memory resources.

Probabilistic Based Modeling and Simulation Assessment

DTIC Science & Technology

2010-06-01

different crash and blast scenarios. With the integration of the high fidelity neck and head model, a methodology to calculate the probability of injury...variability, correlation, and multiple (often competing) failure metrics. Important scenarios include vehicular collisions, blast /fragment impact, and...first area of focus is to develop a methodology to integrate probabilistic analysis into finite element analysis of vehicle collisions and blast . The

Finite-part integration of the generalized Stieltjes transform and its dominant asymptotic behavior for small values of the parameter. I. Integer orders

NASA Astrophysics Data System (ADS)

Tica, Christian D.; Galapon, Eric A.

2018-02-01

The paper addresses the exact evaluation of the generalized Stieltjes transform Sn[f ] =∫0∞f (x ) (ω+x ) -nd x of integral order n = 1, 2, 3, … about ω = 0 from which the asymptotic behavior of Sn[f] for small parameters ω is directly extracted. An attempt to evaluate the integral by expanding the integrand (ω + x)-n about ω = 0 and then naively integrating the resulting infinite series term by term leads to an infinite series whose terms are divergent integrals. Assigning values to the divergent integrals, say, by analytic continuation or by Hadamard's finite part is known to reproduce only some of the correct terms of the expansion but completely misses out a group of terms. Here we evaluate explicitly the generalized Stieltjes transform by means of finite-part integration recently introduced in Galapon [Proc. R. Soc. A 473, 20160567 (2017)]. It is shown that, when f(x) does not vanish or has zero of order m at the origin such that (n - m) ≥ 1, the dominant terms of Sn[f] as ω → 0 come from contributions arising from the poles and branch points of the complex valued function f(z)(ω + z)-n. These dominant terms are precisely the terms missed out by naive term by term integration. Furthermore, it is demonstrated how finite-part integration leads to new series representations of special functions by exploiting their known Stieltjes integral representations. Finally, the application of finite part integration in obtaining asymptotic expansions of the effective diffusivity in the limit of high Peclet number, the Green-Kubo formula for the self-diffusion coefficient, and the antisymmetric part of the diffusion tensor in the weak noise limit is discussed.

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

A Novel Polygonal Finite Element Method: Virtual Node Method

NASA Astrophysics Data System (ADS)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

Numerical Stimulation of Multicomponent Chromatography Using Spreadsheets.

ERIC Educational Resources Information Center

Frey, Douglas D.

1990-01-01

Illustrated is the use of spreadsheet programs for implementing finite difference numerical simulations of chromatography as an instructional tool in a separations course. Discussed are differential equations, discretization and integration, spreadsheet development, computer requirements, and typical simulation results. (CW)

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exac, and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite-element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement.

Gradient corrections to the exchange-correlation free energy

DOE PAGES

Sjostrom, Travis; Daligault, Jerome

2014-10-07

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures abovemore » 10 000 K.« less

Applications of algebraic topology to compatible spatial discretizations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bochev, Pavel Blagoveston; Hyman, James M.

We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups. The latter allows for an elementary calculation of the kernel of the discrete Laplacian. Our framework provides an abstraction that includes examples of compatible finite element, finite volume and finite difference methods. We describe how these methods result from the choice of a reconstructionmore » operator and when they are equivalent.« less

Finite element modeling of frictionally restrained composite interfaces

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

A spectral-finite difference solution of the Navier-Stokes equations in three dimensions

NASA Astrophysics Data System (ADS)

Alfonsi, Giancarlo; Passoni, Giuseppe; Pancaldo, Lea; Zampaglione, Domenico

1998-07-01

A new computational code for the numerical integration of the three-dimensional Navier-Stokes equations in their non-dimensional velocity-pressure formulation is presented. The system of non-linear partial differential equations governing the time-dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral-finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second-order Crank-Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth-order Runge-Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No-slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain.Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors.

Reductions in finite-dimensional integrable systems and special points of classical r-matrices

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2016-12-01

For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.

Numerical Methods for 2-Dimensional Modeling

DTIC Science & Technology

1980-12-01

high-order finite element methods, and a multidimensional version of the method of lines, both utilizing an optimized stiff integrator for the time...integration. The finite element methods have proved disappointing, but the method of lines has provided an unexpectedly large gain in speed. Two...diffusion problems with the same number of unknowns (a 21 x 41 grid), solved by second-order finite element methods, took over seven minutes on the Cray-i

Comparison of mixed-mode stress-intensity factors obtained through displacement correlation, J-integral formulation, and modified crack-closure integral

NASA Astrophysics Data System (ADS)

Bittencourt, Tulio N.; Barry, Ahmabou; Ingraffea, Anthony R.

This paper presents a comparison among stress-intensity factors for mixed-mode two-dimensional problems obtained through three different approaches: displacement correlation, J-integral, and modified crack-closure integral. All mentioned procedures involve only one analysis step and are incorporated in the post-processor page of a finite element computer code for fracture mechanics analysis (FRANC). Results are presented for a closed-form solution problem under mixed-mode conditions. The accuracy of these described methods then is discussed and analyzed in the framework of their numerical results. The influence of the differences among the three methods on the predicted crack trajectory of general problems is also discussed.

Evaluation of Kirkwood-Buff integrals via finite size scaling: a large scale molecular dynamics study

NASA Astrophysics Data System (ADS)

Dednam, W.; Botha, A. E.

2015-01-01

Solvation of bio-molecules in water is severely affected by the presence of co-solvent within the hydration shell of the solute structure. Furthermore, since solute molecules can range from small molecules, such as methane, to very large protein structures, it is imperative to understand the detailed structure-function relationship on the microscopic level. For example, it is useful know the conformational transitions that occur in protein structures. Although such an understanding can be obtained through large-scale molecular dynamic simulations, it is often the case that such simulations would require excessively large simulation times. In this context, Kirkwood-Buff theory, which connects the microscopic pair-wise molecular distributions to global thermodynamic properties, together with the recently developed technique, called finite size scaling, may provide a better method to reduce system sizes, and hence also the computational times. In this paper, we present molecular dynamics trial simulations of biologically relevant low-concentration solvents, solvated by aqueous co-solvent solutions. In particular we compare two different methods of calculating the relevant Kirkwood-Buff integrals. The first (traditional) method computes running integrals over the radial distribution functions, which must be obtained from large system-size NVT or NpT simulations. The second, newer method, employs finite size scaling to obtain the Kirkwood-Buff integrals directly by counting the particle number fluctuations in small, open sub-volumes embedded within a larger reservoir that can be well approximated by a much smaller simulation cell. In agreement with previous studies, which made a similar comparison for aqueous co-solvent solutions, without the additional solvent, we conclude that the finite size scaling method is also applicable to the present case, since it can produce computationally more efficient results which are equivalent to the more costly radial distribution function method.

Restoring a smooth function from its noisy integrals

NASA Astrophysics Data System (ADS)

Goulko, Olga; Prokof'ev, Nikolay; Svistunov, Boris

2018-05-01

Numerical (and experimental) data analysis often requires the restoration of a smooth function from a set of sampled integrals over finite bins. We present the bin hierarchy method that efficiently computes the maximally smooth function from the sampled integrals using essentially all the information contained in the data. We perform extensive tests with different classes of functions and levels of data quality, including Monte Carlo data suffering from a severe sign problem and physical data for the Green's function of the Fröhlich polaron.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Numerical simulation of rarefied gas flow through a slit

NASA Technical Reports Server (NTRS)

Keith, Theo G., Jr.; Jeng, Duen-Ren; De Witt, Kenneth J.; Chung, Chan-Hong

1990-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas from one reservoir to another through a two-dimensional slit. The cases considered are for hard vacuum downstream pressure, finite pressure ratios, and isobaric pressure with thermal diffusion, which are not well established in spite of the simplicity of the flow field. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, three kinds of collision sampling techniques, the time counter (TC) method, the null collision (NC) method, and the no time counter (NTC) method, are used.

The quantum Ising chain with a generalized defect

NASA Astrophysics Data System (ADS)

Grimm, Uwe

1990-08-01

The finite-size scaling properties of the quantum Ising chain with different types of generalized defects are studied. This not only means an alteration of the coupling constant as previously examined, but also an additional arbitrary transformation in the algebra of observables at one site of the chain. One can distinguish between two classes of generalized defects: on the one hand those which do not affect the finite-size integrability of the Ising chain, and on the other hand those that destroy this property. In this context, finite-size integrability is always understood as a synonym for the possibility to write the hamiltonian of the finite chain as a bilinear expression in fermionic operators by means of a Jordan-Wigner transformation. Concerning the first type of defect, an exact solution for the scaling spectrum is obtained for the most universal defect that preserves the global Z2 symmetry of the chain. It is shown that in the continuum limit this yields the same result as for one properly chosen ordinary defect, that is changing the coupling constant only, and thus the finite-size scaling spectra can be described by irreps of a shifted u(1) Kac-Moody algebra. The other type of defect is examined by means of numerical finite-size calculations. In contrast to the first case, these calculations suggest a non-continuous dependence of the scaling dimensions on the defect parameters. A conjecture for the operator content involving only one primary field of a Virasoro algebra with central charge c= {1}/{2} is given.

A reduced-order integral formulation to account for the finite size effect of isotropic square panels using the transfer matrix method.

PubMed

Bonfiglio, Paolo; Pompoli, Francesco; Lionti, Riccardo

2016-04-01

The transfer matrix method is a well-established prediction tool for the simulation of sound transmission loss and the sound absorption coefficient of flat multilayer systems. Much research has been dedicated to enhancing the accuracy of the method by introducing a finite size effect of the structure to be simulated. The aim of this paper is to present a reduced-order integral formulation to predict radiation efficiency and radiation impedance for a panel with equal lateral dimensions. The results are presented and discussed for different materials in terms of radiation efficiency, sound transmission loss, and the sound absorption coefficient. Finally, the application of the proposed methodology for rectangular multilayer systems is also investigated and validated against experimental data.

Finite Difference Model of a Four-Electrode Conductivity Measurement System

DTIC Science & Technology

2016-05-27

for an infinite half space with electrodes placed on the air/media boundary : 1 Less...8) The left hand side of Equation (8) can be converted to a surface integral using Green’s theorem : − � ∇ ∙ �σ���∇ϕ...adjacent to a boundary between two conductivities. The discretized solutions for each face are summed to comprise the surface integral: − � σ

Finite-element numerical modeling of atmospheric turbulent boundary layer

NASA Technical Reports Server (NTRS)

Lee, H. N.; Kao, S. K.

1979-01-01

A dynamic turbulent boundary-layer model in the neutral atmosphere is constructed, using a dynamic turbulent equation of the eddy viscosity coefficient for momentum derived from the relationship among the turbulent dissipation rate, the turbulent kinetic energy and the eddy viscosity coefficient, with aid of the turbulent second-order closure scheme. A finite-element technique was used for the numerical integration. In preliminary results, the behavior of the neutral planetary boundary layer agrees well with the available data and with the existing elaborate turbulent models, using a finite-difference scheme. The proposed dynamic formulation of the eddy viscosity coefficient for momentum is particularly attractive and can provide a viable alternative approach to study atmospheric turbulence, diffusion and air pollution.

Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1998-01-01

We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

New directions in photonics simulation: Lanczos recursion and finite-difference time-domain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hawkins, R.J.; McLeod, R.R.; Kallman, J.S.

1992-06-01

Computational Integrated Photonics (CIP) is the area of computational physics that treats the propagation of light in optical fibers and in integrated optical circuits. The purpose of integrated photonics simulation is to develop the computational tools that will support the design of photonic and optoelectronic integrated devices. CIP has, in general, two thrusts: (1) predictive models of photonic device behavior that can be used reliably to enhance significantly the speed with which designs axe optimized for development applications, and (2) to further our ability to describe the linear and nonlinear processes that occur - and can be exploited - inmore » real photonic devices. Experimental integrated optics has been around for over a decade with much of the work during this period. centered on proof-of-principle devices that could be described using simple analytic and numerical models. Recent advances in material growths, photolithography, and device complexity have conspired to reduce significantly the number of devices that can be designed with simple models and to increase dramatically the interest in CIP. In the area of device design, CIP is viewed as critical to understanding device behavior and to optimization. In the area of propagation physics, CIP is an important tool in the study of nonlinear processes in integrated optical devices and fibers. In this talk I will discuss two of the new directions we have been investigating in CIP: Lanczos recursion and finite-difference time-domain.« less

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations

NASA Technical Reports Server (NTRS)

Candler, Graham V.; Johnson, Heath B.; Nompelis, Ioannis; Subbareddy, Pramod K.; Drayna, Travis W.; Gidzak, Vladimyr; Barnhardt, Michael D.

2015-01-01

Aerothermodynamics and hypersonic flows involve complex multi-disciplinary physics, including finite-rate gas-phase kinetics, finite-rate internal energy relaxation, gas-surface interactions with finite-rate oxidation and sublimation, transition to turbulence, large-scale unsteadiness, shock-boundary layer interactions, fluid-structure interactions, and thermal protection system ablation and thermal response. Many of the flows have a large range of length and time scales, requiring large computational grids, implicit time integration, and large solution run times. The University of Minnesota NASA US3D code was designed for the simulation of these complex, highly-coupled flows. It has many of the features of the well-established DPLR code, but uses unstructured grids and has many advanced numerical capabilities and physical models for multi-physics problems. The main capabilities of the code are described, the physical modeling approaches are discussed, the different types of numerical flux functions and time integration approaches are outlined, and the parallelization strategy is overviewed. Comparisons between US3D and the NASA DPLR code are presented, and several advanced simulations are presented to illustrate some of novel features of the code.

High-efficiency power transfer for silicon-based photonic devices

NASA Astrophysics Data System (ADS)

Son, Gyeongho; Yu, Kyoungsik

2018-02-01

We demonstrate an efficient coupling of guided light of 1550 nm from a standard single-mode optical fiber to a silicon waveguide using the finite-difference time-domain method and propose a fabrication method of tapered optical fibers for efficient power transfer to silicon-based photonic integrated circuits. Adiabatically-varying fiber core diameters with a small tapering angle can be obtained using the tube etching method with hydrofluoric acid and standard single-mode fibers covered by plastic jackets. The optical power transmission of the fundamental HE11 and TE-like modes between the fiber tapers and the inversely-tapered silicon waveguides was calculated with the finite-difference time-domain method to be more than 99% at a wavelength of 1550 nm. The proposed method for adiabatic fiber tapering can be applied in quantum optics, silicon-based photonic integrated circuits, and nanophotonics. Furthermore, efficient coupling within the telecommunication C-band is a promising approach for quantum networks in the future.

Methods for compressible fluid simulation on GPUs using high-order finite differences

NASA Astrophysics Data System (ADS)

Pekkilä, Johannes; Väisälä, Miikka S.; Käpylä, Maarit J.; Käpylä, Petri J.; Anjum, Omer

2017-08-01

We focus on implementing and optimizing a sixth-order finite-difference solver for simulating compressible fluids on a GPU using third-order Runge-Kutta integration. Since graphics processing units perform well in data-parallel tasks, this makes them an attractive platform for fluid simulation. However, high-order stencil computation is memory-intensive with respect to both main memory and the caches of the GPU. We present two approaches for simulating compressible fluids using 55-point and 19-point stencils. We seek to reduce the requirements for memory bandwidth and cache size in our methods by using cache blocking and decomposing a latency-bound kernel into several bandwidth-bound kernels. Our fastest implementation is bandwidth-bound and integrates 343 million grid points per second on a Tesla K40t GPU, achieving a 3 . 6 × speedup over a comparable hydrodynamics solver benchmarked on two Intel Xeon E5-2690v3 processors. Our alternative GPU implementation is latency-bound and achieves the rate of 168 million updates per second.

Finite-dimensional Liouville integrable Hamiltonian systems generated from Lax pairs of a bi-Hamiltonian soliton hierarchy by symmetry constraints

NASA Astrophysics Data System (ADS)

Manukure, Solomon

2018-04-01

We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.

Hybrid codes with finite electron mass

NASA Astrophysics Data System (ADS)

Lipatov, A. S.

This report is devoted to the current status of the hybrid multiscale simulation technique. The different aspects of modeling are discussed. In particular, we consider the different level for description of the plasma model, however, the main attention will be paid to conventional hybrid models. We discuss the main steps of time integration the Vlasov/Maxwell system of equations. The main attention will be paid to the models with finite electron mass. Such model may allow us to explore the plasma system with multiscale phenomena ranging from ion to electron scales. As an application of hybrid modeling technique we consider the simulation of the plasma processes at the collisionless shocks and very shortly ther magnetic field reconnection processes.

Design and Analysis of Enhanced Modulation Response in Integrated Coupled Cavities DBR Lasers Using Photon-Photon Resonance

DOE PAGES

Bardella, Paolo; Chow, Weng; Montrosset, Ivo

2016-01-08

In the last decades, various solutions have been proposed to increase the modulation bandwidth and consequently the transmission bit rate of integrated semiconductor lasers. In this manuscript we discuss a design procedure for a recently proposed laser structure realized with the integration of two DBR lasers. Design guidelines will be proposed and dynamic small and large signal simulations, calculated using a Finite Difference Traveling Wave numerical simulator, will be performed to confirm the design results and the effectiveness of the analyzed integrated configuration to achieve a direct modulation bandwidth up to 80 GHz

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in the generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate an arbitrary finite change of gauge-fixing functions in the path integral.

UXO Discrimination in Cases with Overlapping Signatures

DTIC Science & Technology

2007-03-07

13. APPENDIX B: HFE -BIEM ..........................................................................................................290 - 7...First principals numerical solutions developed were a Hybrid Finite Element – Boundary Integral Equation Method ( HFE -BIEM) body of revolution (BOR...attacks, namely the Method of Auxiliary Sources (MAS) and the Hybrid Finite Element – Boundary Integral Equation Method ( HFE -BIEM). These work

A Strategy for Integrating a Large Finite Element Model: X-33 Lessons Learned

NASA Technical Reports Server (NTRS)

McGhee, David S.

2000-01-01

The X-33 vehicle is an advanced technology demonstrator sponsored by NASA. For the past three years the Structural Dynamics & Loads Group of NASA's Marshall Space Flight Center has had the task of integrating the X-33 vehicle structural finite element model. In that time, five versions of the integrated vehicle model have been produced and a strategy has evolved that would benefit anyone given the task of integrating structural finite element models that have been generated by various modelers and companies. The strategy that has been presented here consists of six decisions that need to be made. These six decisions are: purpose of model, units, common material list, model numbering, interface control, and archive format. This strategy has been proved and expanded from experience on the X-33 vehicle.

Acoustic Parametric Array for Identifying Standoff Targets

NASA Astrophysics Data System (ADS)

Hinders, M. K.; Rudd, K. E.

2010-02-01

An integrated simulation method for investigating nonlinear sound beams and 3D acoustic scattering from any combination of complicated objects is presented. A standard finite-difference simulation method is used to model pulsed nonlinear sound propagation from a source to a scattering target via the KZK equation. Then, a parallel 3D acoustic simulation method based on the finite integration technique is used to model the acoustic wave interaction with the target. Any combination of objects and material layers can be placed into the 3D simulation space to study the resulting interaction. Several example simulations are presented to demonstrate the simulation method and 3D visualization techniques. The combined simulation method is validated by comparing experimental and simulation data and a demonstration of how this combined simulation method assisted in the development of a nonlinear acoustic concealed weapons detector is also presented.

Methods for the calculation of axial wave numbers in lined ducts with mean flow

NASA Technical Reports Server (NTRS)

Eversman, W.

1981-01-01

A survey is made of the methods available for the calculation of axial wave numbers in lined ducts. Rectangular and circular ducts with both uniform and non-uniform flow are considered as are ducts with peripherally varying liners. A historical perspective is provided by a discussion of the classical methods for computing attenuation when no mean flow is present. When flow is present these techniques become either impractical or impossible. A number of direct eigenvalue determination schemes which have been used when flow is present are discussed. Methods described are extensions of the classical no-flow technique, perturbation methods based on the no-flow technique, direct integration methods for solution of the eigenvalue equation, an integration-iteration method based on the governing differential equation for acoustic transmission, Galerkin methods, finite difference methods, and finite element methods.

A finite element-boundary integral method for scattering and radiation by two- and three-dimensional structures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.; Collins, Jeffery D.

1991-01-01

A review of a hybrid finite element-boundary integral formulation for scattering and radiation by two- and three-dimensional composite structures is presented. In contrast to other hybrid techniques involving the finite element method, the proposed one is in principle exact and can be implemented using a low O(N) storage. This is of particular importance for large scale applications and is a characteristic of the boundary chosen to terminate the finite element mesh, usually as close to the structure as possible. A certain class of these boundaries lead to convolutional boundary integrals which can be evaluated via the fast Fourier transform (FFT) without a need to generate a matrix; thus, retaining the O(N) storage requirement. The paper begins with a general description of the method. A number of two- and three-dimensional applications are then given, including numerical computations which demonstrate the method's accuracy, efficiency, and capability.

The Laguerre finite difference one-way equation solver

NASA Astrophysics Data System (ADS)

Terekhov, Andrew V.

2017-05-01

This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing approaches, the integral Laguerre transform instead of Fourier transform is used. After carrying out the approximation of spatial variables it is possible to obtain systems of linear algebraic equations with better computing properties and to reduce computer costs for their solution. High accuracy of calculations is attained at the expense of employing finite difference approximations of higher accuracy order that are based on the dispersion-relationship-preserving method and the Richardson extrapolation in the downward continuation direction. The numerical experiments have verified that as compared to the spectral difference method based on Fourier transform, the new algorithm allows one to calculate wave fields with a higher degree of accuracy and a lower level of numerical noise and artifacts including those for non-smooth velocity models. In the context of solving the geophysical problem the post-stack migration for velocity models of the types Syncline and Sigsbee2A has been carried out. It is shown that the images obtained contain lesser noise and are considerably better focused as compared to those obtained by the known Fourier Finite Difference and Phase-Shift Plus Interpolation methods. There is an opinion that purely finite difference approaches do not allow carrying out the seismic migration procedure with sufficient accuracy, however the results obtained disprove this statement. For the supercomputer implementation it is proposed to use the parallel dichotomy algorithm when solving systems of linear algebraic equations with block-tridiagonal matrices.

A finite element: Boundary integral method for electromagnetic scattering. Ph.D. Thesis Technical Report, Feb. - Sep. 1992

NASA Technical Reports Server (NTRS)

Collins, J. D.; Volakis, John L.

1992-01-01

A method that combines the finite element and boundary integral techniques for the numerical solution of electromagnetic scattering problems is presented. The finite element method is well known for requiring a low order storage and for its capability to model inhomogeneous structures. Of particular emphasis in this work is the reduction of the storage requirement by terminating the finite element mesh on a boundary in a fashion which renders the boundary integrals in convolutional form. The fast Fourier transform is then used to evaluate these integrals in a conjugate gradient solver, without a need to generate the actual matrix. This method has a marked advantage over traditional integral equation approaches with respect to the storage requirement of highly inhomogeneous structures. Rectangular, circular, and ogival mesh termination boundaries are examined for two-dimensional scattering. In the case of axially symmetric structures, the boundary integral matrix storage is reduced by exploiting matrix symmetries and solving the resulting system via the conjugate gradient method. In each case several results are presented for various scatterers aimed at validating the method and providing an assessment of its capabilities. Important in methods incorporating boundary integral equations is the issue of internal resonance. A method is implemented for their removal, and is shown to be effective in the two-dimensional and three-dimensional applications.

Improved accuracy for finite element structural analysis via an integrated force method

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Hopkins, D. A.; Aiello, R. A.; Berke, L.

1992-01-01

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

A generalization of Fatou's lemma for extended real-valued functions on σ-finite measure spaces: with an application to infinite-horizon optimization in discrete time.

PubMed

Kamihigashi, Takashi

2017-01-01

Given a sequence [Formula: see text] of measurable functions on a σ -finite measure space such that the integral of each [Formula: see text] as well as that of [Formula: see text] exists in [Formula: see text], we provide a sufficient condition for the following inequality to hold: [Formula: see text] Our condition is considerably weaker than sufficient conditions known in the literature such as uniform integrability (in the case of a finite measure) and equi-integrability. As an application, we obtain a new result on the existence of an optimal path for deterministic infinite-horizon optimization problems in discrete time.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Methods for analysis of cracks in three-dimensional solids

NASA Technical Reports Server (NTRS)

Raju, I. S.; Newman, J. C., Jr.

1984-01-01

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Radon transport model into a porous ground layer of finite capacity

NASA Astrophysics Data System (ADS)

Parovik, Roman

2017-10-01

The model of radon transfer is considered in a porous ground layer of finite power. With the help of the Laplace integral transformation, a numerical solution of this model is obtained which is based on the construction of a generalized quadrature formula of the highest degree of accuracy for the transition to the original - the function of solving this problem. The calculated curves are constructed and investigated depending on the diffusion and advection coefficients.The work was a mathematical model that describes the effect of the sliding attachment (stick-slip), taking into account hereditarity. This model can be regarded as a mechanical model of earthquake preparation. For such a model was proposed explicit finite- difference scheme, on which were built the waveform and phase trajectories hereditarity effect of stick-slip.

A systematic study of finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2014-09-01

We study systematically finite BRST-BFV transformations in Sp(2)-extended generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

Ignition and structure of a laminar diffusion flame in a compressible mixing layer with finite rate chemistry

NASA Technical Reports Server (NTRS)

Grosch, C. E.; Jackson, T. L.

1991-01-01

The ignition and structure of a reacting compressible mixing layer is considered using finite rate chemistry lying between two streams of reactants with different freestream speeds and temperatures. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. An analysis of both the ignition a diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows to analyze the behavior of these regimes as a function of the parameters of the problem.

Purely numerical approach for analyzing flow to a well intercepting a vertical fracture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Narasimhan, T.N.; Palen, W.A.

1979-03-01

A numerical method, based on an Integral Finite Difference approach, is presented to investigate wells intercepting fractures in general and vertical fractures in particular. Such features as finite conductivity, wellbore storage, damage, and fracture deformability and its influence as permeability are easily handled. The advantage of the numerical approach is that it is based on fewer assumptions than analytic solutions and hence has greater generality. Illustrative examples are given to validate the method against known solutions. New results are presenteed to demonstrate the applicability of the method to problems not apparently considered in the literature so far.

Exploration of Toeplitz-like matrices with unbounded symbols is not a purely academic journey

NASA Astrophysics Data System (ADS)

Böttcher, A.; Garoni, C.; Serra-Capizzano, S.

2017-11-01

It is often asked why Toeplitz-like matrices with unbounded symbols are worth studying. This paper gives an answer by presenting several concrete problems that motivate such studies. It surveys the central results of the theory of Generalized Locally Toeplitz (GLT) sequences in a self-contained tool-kit fashion, and gives a new extension from bounded Riemann integrable functions to unbounded almost everywhere continuous functions. The emergence of unbounded symbols is illustrated by local grid refinements in finite difference and finite element discretizations and also by preconditioning strategies. Bibliography: 40 titles.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

A Novel Multiscale Physics Based Progressive Failure Methodology for Laminated Composite Structures

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Bednarcyk, Brett A.; Collier, Craig S.; Yarrington, Phillip W.

2008-01-01

A variable fidelity, multiscale, physics based finite element procedure for predicting progressive damage and failure of laminated continuous fiber reinforced composites is introduced. At every integration point in a finite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the microscale in two different FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.

A Riemann-Hilbert formulation for the finite temperature Hubbard model

NASA Astrophysics Data System (ADS)

Cavaglià, Andrea; Cornagliotto, Martina; Mattelliano, Massimo; Tateo, Roberto

2015-06-01

Inspired by recent results in the context of AdS/CFT integrability, we reconsider the Thermodynamic Bethe Ansatz equations describing the 1D fermionic Hubbard model at finite temperature. We prove that the infinite set of TBA equations are equivalent to a simple nonlinear Riemann-Hilbert problem for a finite number of unknown functions. The latter can be transformed into a set of three coupled nonlinear integral equations defined over a finite support, which can be easily solved numerically. We discuss the emergence of an exact Bethe Ansatz and the link between the TBA approach and the results by Jüttner, Klümper and Suzuki based on the Quantum Transfer Matrix method. We also comment on the analytic continuation mechanism leading to excited states and on the mirror equations describing the finite-size Hubbard model with twisted boundary conditions.

On the theory of oscillating airfoils of finite span in subsonic compressible flow

NASA Technical Reports Server (NTRS)

Reissner, Eric

1950-01-01

The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

A Strategy for Integrating a Large Finite Element Model Using MSC NASTRAN/PATRAN: X-33 Lessons Learned

NASA Technical Reports Server (NTRS)

McGhee, D. S.

1999-01-01

The X-33 vehicle is an advanced technology demonstrator sponsored by NASA. For the past 3 years the Structural Dynamics and Loads Branch of NASA's Marshall Space Flight Center has had the task of integrating the X-33 vehicle structural finite element model. In that time, five versions of the integrated vehicle model have been produced and a strategy has evolved that would benefit anyone given the task of integrating structural finite element models that have been generated by various modelers and companies. The strategy that has been presented here consists of six decisions that need to be made: purpose of models, units, common materials list, model numbering, interface control, and archive format. This strategy has been proven and expanded from experience on the X-33 vehicle.

Dynamic analysis of suspension cable based on vector form intrinsic finite element method

NASA Astrophysics Data System (ADS)

Qin, Jian; Qiao, Liang; Wan, Jiancheng; Jiang, Ming; Xia, Yongjun

2017-10-01

A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.

DYNAMIC PLANE-STRAIN SHEAR RUPTURE WITH A SLIP-WEAKENING FRICTION LAW CALCULATED BY A BOUNDARY INTEGRAL METHOD.

USGS Publications Warehouse

Andrews, D.J.

1985-01-01

A numerical boundary integral method, relating slip and traction on a plane in an elastic medium by convolution with a discretized Green function, can be linked to a slip-dependent friction law on the fault plane. Such a method is developed here in two-dimensional plane-strain geometry. Spontaneous plane-strain shear ruptures can make a transition from sub-Rayleigh to near-P propagation velocity. Results from the boundary integral method agree with earlier results from a finite difference method on the location of this transition in parameter space. The methods differ in their prediction of rupture velocity following the transition. The trailing edge of the cohesive zone propagates at the P-wave velocity after the transition in the boundary integral calculations. Refs.

Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, John L.

1996-01-01

One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

Interplay of symmetries and other integrability quantifiers in finite-dimensional integrable nonlinear dynamical systems

PubMed Central

Mohanasubha, R.; Chandrasekar, V. K.; Lakshmanan, M.

2016-01-01

In this work, we establish a connection between the extended Prelle–Singer procedure and other widely used analytical methods to identify integrable systems in the case of nth-order nonlinear ordinary differential equations (ODEs). By synthesizing these methods, we bring out the interlink between Lie point symmetries, contact symmetries, λ-symmetries, adjoint symmetries, null forms, Darboux polynomials, integrating factors, the Jacobi last multiplier and generalized λ-symmetries corresponding to the nth-order ODEs. We also prove these interlinks with suitable examples. By exploiting these interconnections, the characteristic quantities associated with different methods can be deduced without solving the associated determining equations. PMID:27436964

Finite element modelling of the foot for clinical application: A systematic review.

PubMed

Behforootan, Sara; Chatzistergos, Panagiotis; Naemi, Roozbeh; Chockalingam, Nachiappan

2017-01-01

Over the last two decades finite element modelling has been widely used to give new insight on foot and footwear biomechanics. However its actual contribution for the improvement of the therapeutic outcome of different pathological conditions of the foot, such as the diabetic foot, remains relatively limited. This is mainly because finite element modelling has only been used within the research domain. Clinically applicable finite element modelling can open the way for novel diagnostic techniques and novel methods for treatment planning/optimisation which would significantly enhance clinical practice. In this context this review aims to provide an overview of modelling techniques in the field of foot and footwear biomechanics and to investigate their applicability in a clinical setting. Even though no integrated modelling system exists that could be directly used in the clinic and considerable progress is still required, current literature includes a comprehensive toolbox for future work towards clinically applicable finite element modelling. The key challenges include collecting the information that is needed for geometry design, the assignment of material properties and loading on a patient-specific basis and in a cost-effective and non-invasive way. The ultimate challenge for the implementation of any computational system into clinical practice is to ensure that it can produce reliable results for any person that belongs in the population for which it was developed. Consequently this highlights the need for thorough and extensive validation of each individual step of the modelling process as well as for the overall validation of the final integrated system. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Interior Fluid Dynamics of Liquid-Filled Projectiles

DTIC Science & Technology

1989-12-01

the Sandia code. The previous codes are primarily based on finite-difference approximations with relatively coarse grid and were designed without...exploits Chorin’s method of artificial compressibility. The steady solution at 11 X 24 X 21 grid points in r, 0, z-direction is obtained by integrating...differences in radial and axial direction and pseudoepectral differencing in the azimuthal direction. Nonuniform grids are introduced for increased

Conservative discretization of the Landau collision integral

DOE PAGES

Hirvijoki, E.; Adams, M. F.

2017-03-28

Here we describe a density, momentum-, and energy-conserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finite-element and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finite-element implementation.

Particle Size Distributions in Atmospheric Clouds

NASA Technical Reports Server (NTRS)

Paoli, Roberto; Shariff, Karim

2003-01-01

In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.

Metriplectic integrators for the Landau collision operator

DOE PAGES

Kraus, Michael; Hirvijoki, Eero

2017-10-02

Here, we present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonicmore » behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.« less

Fast global oscillations in networks of integrate-and-fire neurons with low firing rates.

PubMed

Brunel, N; Hakim, V

1999-10-01

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons --> infinity, the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regions. The results are found to be in good agreement with numerical simulations.

Does the graft-tunnel friction influence knee joint kinematics and biomechanics after anterior cruciate ligament reconstruction? A finite element study.

PubMed

Wan, Chao; Hao, Zhixiu

2018-02-01

Graft tissues within bone tunnels remain mobile for a long time after anterior cruciate ligament (ACL) reconstruction. However, whether the graft-tunnel friction affects the finite element (FE) simulation of the ACL reconstruction is still unclear. Four friction coefficients (from 0 to 0.3) were simulated in the ACL-reconstructed joint model as well as two loading levels of anterior tibial drawer. The graft-tunnel friction did not affect joint kinematics and the maximal principal strain of the graft. By contrast, both the relative graft-tunnel motion and equivalent strain for the bone tunnels were altered, which corresponded to different processes of graft-tunnel integration and bone remodeling, respectively. It implies that the graft-tunnel friction should be defined properly for studying the graft-tunnel integration or bone remodeling after ACL reconstruction using numerical simulation.

Relativistic elliptic matrix tops and finite Fourier transformations

NASA Astrophysics Data System (ADS)

Zotov, A.

2017-10-01

We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.

Finite time control for MIMO nonlinear system based on higher-order sliding mode.

PubMed

Liu, Xiangjie; Han, Yaozhen

2014-11-01

Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Finite element solution for energy conservation using a highly stable explicit integration algorithm

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1972-01-01

Theoretical derivation of a finite element solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete finite element matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the finite element discretization using a highly stable explicit integration procedure with automatic error control features. The finite element algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat element matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.

A class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

System-Integrated Finite Element Analysis of a Full-Scale Helicopter Crash Test with Deployable Energy Absorbers

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Polanco, Michael A.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26-ft/sec and 40-ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test predictions and continuing through post-test validation.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Coupled Aerodynamic and Structural Sensitivity Analysis of a High-Speed Civil Transport

NASA Technical Reports Server (NTRS)

Mason, B. H.; Walsh, J. L.

2001-01-01

An objective of the High Performance Computing and Communication Program at the NASA Langley Research Center is to demonstrate multidisciplinary shape and sizing optimization of a complete aerospace vehicle configuration by using high-fidelity, finite-element structural analysis and computational fluid dynamics aerodynamic analysis. In a previous study, a multi-disciplinary analysis system for a high-speed civil transport was formulated to integrate a set of existing discipline analysis codes, some of them computationally intensive, This paper is an extension of the previous study, in which the sensitivity analysis for the coupled aerodynamic and structural analysis problem is formulated and implemented. Uncoupled stress sensitivities computed with a constant load vector in a commercial finite element analysis code are compared to coupled aeroelastic sensitivities computed by finite differences. The computational expense of these sensitivity calculation methods is discussed.

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

NASA Astrophysics Data System (ADS)

Chróścielewski, Jacek; Schmidt, Rüdiger; Eremeyev, Victor A.

2018-05-01

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

Improved accuracy for finite element structural analysis via a new integrated force method

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Aiello, Robert A.; Berke, Laszlo

1992-01-01

A comparative study was carried out to determine the accuracy of finite element analyses based on the stiffness method, a mixed method, and the new integrated force and dual integrated force methods. The numerical results were obtained with the following software: MSC/NASTRAN and ASKA for the stiffness method; an MHOST implementation method for the mixed method; and GIFT for the integrated force methods. The results indicate that on an overall basis, the stiffness and mixed methods present some limitations. The stiffness method generally requires a large number of elements in the model to achieve acceptable accuracy. The MHOST method tends to achieve a higher degree of accuracy for course models than does the stiffness method implemented by MSC/NASTRAN and ASKA. The two integrated force methods, which bestow simultaneous emphasis on stress equilibrium and strain compatibility, yield accurate solutions with fewer elements in a model. The full potential of these new integrated force methods remains largely unexploited, and they hold the promise of spawning new finite element structural analysis tools.

Computer design of porous active materials at different dimensional scales

NASA Astrophysics Data System (ADS)

Nasedkin, Andrey

2017-12-01

The paper presents a mathematical and computer modeling of effective properties of porous piezoelectric materials of three types: with ordinary porosity, with metallized pore surfaces, and with nanoscale porosity structure. The described integrated approach includes the effective moduli method of composite mechanics, simulation of representative volumes, and finite element method.

Monotonic Derivative Correction for Calculation of Supersonic Flows

ERIC Educational Resources Information Center

Bulat, Pavel V.; Volkov, Konstantin N.

2016-01-01

Aim of the study: This study examines numerical methods for solving the problems in gas dynamics, which are based on an exact or approximate solution to the problem of breakdown of an arbitrary discontinuity (the Riemann problem). Results: Comparative analysis of finite difference schemes for the Euler equations integration is conducted on the…

The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Norrie, D. H.; De Vries, G.

1979-01-01

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

Mixed time integration methods for transient thermal analysis of structures, appendix 5

NASA Technical Reports Server (NTRS)

Liu, W. K.

1982-01-01

Mixed time integration methods for transient thermal analysis of structures are studied. An efficient solution procedure for predicting the thermal behavior of aerospace vehicle structures was developed. A 2D finite element computer program incorporating these methodologies is being implemented. The performance of these mixed time finite element algorithms can then be evaluated employing the proposed example problem.

Finite element-integral simulation of static and flight fan noise radiation from the JT15D turbofan engine

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Horowitz, S. J.

1982-01-01

An iterative finite element integral technique is used to predict the sound field radiated from the JT15D turbofan inlet. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. The velocity potential formulation of the acoustic wave equation was employed in the program. For some single mode JT15D data, the theory and experiment are in good agreement for the far field radiation pattern as well as suppressor attenuation. Also, the computer program is used to simulate flight effects that cannot be performed on a ground static test stand.

Scattering models for some vegetation samples

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.; Antar, Y. M. M.

1987-01-01

The Helmholtz integral equation is presently derived for a scatterer of arbitrary shape, and reduced in order to obtain the far zone-scattered field in terms of the field within the scatterer. Attention is given to the effect of different approaches to field estimation within the scatterer on the backscattering cross section, as illustrated numerically by the cases of a circular disk, a needle, and a finite-length cylinder. A comparison is made of the results obtained by modeling a leaf by means of a circular disk within the Shifrin approximation, and a tree branch by means of a finite-length cylinder, with measurements from a single leaf and a single branch.

Improved finite-element methods for rotorcraft structures

NASA Technical Reports Server (NTRS)

Hinnant, Howard E.

1991-01-01

An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.

Radiation and scattering from printed antennas on cylindrically conformal platforms

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Bindiganavale, Sunil

1994-01-01

The goal was to develop suitable methods and software for the analysis of antennas on cylindrical coated and uncoated platforms. Specifically, the finite element boundary integral and finite element ABC methods were employed successfully and associated software were developed for the analysis and design of wraparound and discrete cavity-backed arrays situated on cylindrical platforms. This work led to the successful implementation of analysis software for such antennas. Developments which played a role in this respect are the efficient implementation of the 3D Green's function for a metallic cylinder, the incorporation of the fast Fourier transform in computing the matrix-vector products executed in the solver of the finite element-boundary integral system, and the development of a new absorbing boundary condition for terminating the finite element mesh on cylindrical surfaces.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Finite Element Model Development and Validation for Aircraft Fuselage Structures

NASA Technical Reports Server (NTRS)

Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.

2000-01-01

The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results. The increased frequency range results in a corresponding increase in the number of modes, modal density and spatial resolution requirements. In this study, conventional modal tests using accelerometers are complemented with Scanning Laser Doppler Velocimetry and Electro-Optic Holography measurements to further resolve the spatial response characteristics. Whenever possible, component and subassembly modal tests are used to validate the finite element models at lower levels of assembly. Normal mode predictions for different finite element representations of components and assemblies are compared with experimental results to assess the most accurate techniques for modeling aircraft fuselage type structures.

Finite BRST-BFV transformations for dynamical systems with second-class constraints

NASA Astrophysics Data System (ADS)

Batalin, Igor A.; Lavrov, Peter M.; Tyutin, Igor V.

2015-06-01

We study finite field-dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

Multiple methods integration for structural mechanics analysis and design

NASA Technical Reports Server (NTRS)

Housner, J. M.; Aminpour, M. A.

1991-01-01

A new research area of multiple methods integration is proposed for joining diverse methods of structural mechanics analysis which interact with one another. Three categories of multiple methods are defined: those in which a physical interface are well defined; those in which a physical interface is not well-defined, but selected; and those in which the interface is a mathematical transformation. Two fundamental integration procedures are presented that can be extended to integrate various methods (e.g., finite elements, Rayleigh Ritz, Galerkin, and integral methods) with one another. Since the finite element method will likely be the major method to be integrated, its enhanced robustness under element distortion is also examined and a new robust shell element is demonstrated.

Proceedings of the 1993 Scientific Conference on Obscuration and Aerosol Research Held in Aberdeen Proving Ground on 22-24 Jun 1993

DTIC Science & Technology

1994-03-01

equation (4.1.27) is not a finite rank integral equation, it suggests that an approxi- mate finite rank integral equation Pf" = Pg + APL(K~p) Pfa 4 \\PNPfa...Harry Salem Richard Farrell Mark Seaver Dennis F Flanigan George Sehmel David Freund Jungshik Shin Robert H Frickel Orazio I Sindoni Edward Fry Michael

The Propagation and Scattering of EM Waves in Electrically Large Ducts

NASA Astrophysics Data System (ADS)

Khan, Saeed Mahmood

The electromagnetic scattering from large arbitrarily shaped ducts with complex termination is studied here by a hybrid technique. The propagation of electromagnetic waves in the duct is analyzed in terms of an approximate modal solution. A finite difference technique is employed for computing the reflection characteristics of the complex terminations. Both solutions are combined using the unimoment method. The analysis here is carried out for monostatic RCS and considers only fields backscattered from inside the cavity. Rim-diffraction has been left out. The procedure offers such advantages as in that it is not necessary to find complicated Green's functions, which may not be readily available, when compared with the integral equation method. Hybridization performed by combining an approximate modal technique with a finite difference one makes the scheme numerically efficient. From a computational EM point of view, it brings together a whole spectrum of techniques associated with high frequency modal analysis, Fourier Methods, Radar Cross Section and Scattering, finite difference solution and the Unimoment Method. The practical application of this technique may range from the study of RCS scattered from jet inlets of radar evasive aircraft to submarine communication waveguides.

Finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems

NASA Astrophysics Data System (ADS)

Xie, Xue-Jun; Zhang, Xing-Hui; Zhang, Kemei

2016-07-01

This paper studies the finite-time state feedback stabilisation of stochastic high-order nonlinear feedforward systems. Based on the stochastic Lyapunov theorem on finite-time stability, by using the homogeneous domination method, the adding one power integrator and sign function method, constructing a ? Lyapunov function and verifying the existence and uniqueness of solution, a continuous state feedback controller is designed to guarantee the closed-loop system finite-time stable in probability.

On Multifunctional Collaborative Methods in Engineering Science

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2001-01-01

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

A 2D Daubechies finite wavelet domain method for transient wave response analysis in shear deformable laminated composite plates

NASA Astrophysics Data System (ADS)

Nastos, C. V.; Theodosiou, T. C.; Rekatsinas, C. S.; Saravanos, D. A.

2018-03-01

An efficient numerical method is developed for the simulation of dynamic response and the prediction of the wave propagation in composite plate structures. The method is termed finite wavelet domain method and takes advantage of the outstanding properties of compactly supported 2D Daubechies wavelet scaling functions for the spatial interpolation of displacements in a finite domain of a plate structure. The development of the 2D wavelet element, based on the first order shear deformation laminated plate theory is described and equivalent stiffness, mass matrices and force vectors are calculated and synthesized in the wavelet domain. The transient response is predicted using the explicit central difference time integration scheme. Numerical results for the simulation of wave propagation in isotropic, quasi-isotropic and cross-ply laminated plates are presented and demonstrate the high spatial convergence and problem size reduction obtained by the present method.

Three-dimensional analysis of chevron-notched specimens by boundary integral method

NASA Technical Reports Server (NTRS)

Mendelson, A.; Ghosn, L.

1983-01-01

The chevron-notched short bar and short rod specimens was analyzed by the boundary integral equations method. This method makes use of boundary surface elements in obtaining the solution. The boundary integral models were composed of linear triangular and rectangular surface segments. Results were obtained for two specimens with width to thickness ratios of 1.45 and 2.00 and for different crack length to width ratios ranging from 0.4 to 0.7. Crack opening displacement and stress intensity factors determined from displacement calculations along the crack front and compliance calculations were compared with experimental values and with finite element analysis.

An Integrated Approach to Characterizing Bypassed Oil in Heterogeneous and Fractured Reservoirs Using Partitioning Tracers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akhil Datta-Gupta

2006-12-31

We explore the use of efficient streamline-based simulation approaches for modeling partitioning interwell tracer tests in hydrocarbon reservoirs. Specifically, we utilize the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. A critical aspect here is the underdetermined and highly ill-posed nature of the associated inverse problems. We have investigated the relative merits of the traditional history matching ('amplitude inversion') and a novel travel time inversion in terms of robustness of the method and convergence behavior of the solution. We show that the traditional amplitude inversion is orders of magnitudemore » more non-linear and the solution here is likely to get trapped in local minimum, leading to inadequate history match. The proposed travel time inversion is shown to be extremely efficient and robust for practical field applications. The streamline approach is generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. The fractures and matrix are treated as separate continua that are connected through a transfer function, as in conventional finite difference simulators for modeling fractured systems. A detailed comparison with a commercial finite difference simulator shows very good agreement. Furthermore, an examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications. We also propose a novel approach to history matching finite-difference models that combines the advantage of the streamline models with the versatility of finite-difference simulation. In our approach, we utilize the streamline-derived sensitivities to facilitate history matching during finite-difference simulation. The use of finite-difference model allows us to account for detailed process physics and compressibility effects. The approach is very fast and avoids much of the subjective judgments and time-consuming trial-and-errors associated with manual history matching. We demonstrate the power and utility of our approach using a synthetic example and two field examples. We have also explored the use of a finite difference reservoir simulator, UTCHEM, for field-scale design and optimization of partitioning interwell tracer tests. The finite-difference model allows us to include detailed physics associated with reactive tracer transport, particularly those related with transverse and cross-streamline mechanisms. We have investigated the potential use of downhole tracer samplers and also the use of natural tracers for the design of partitioning tracer tests. Finally, we discuss several alternative ways of using partitioning interwell tracer tests (PITTs) in oil fields for the calculation of oil saturation, swept pore volume and sweep efficiency, and assess the accuracy of such tests under a variety of reservoir conditions.« less

Efficiency analysis of numerical integrations for finite element substructure in real-time hybrid simulation

NASA Astrophysics Data System (ADS)

Wang, Jinting; Lu, Liqiao; Zhu, Fei

2018-01-01

Finite element (FE) is a powerful tool and has been applied by investigators to real-time hybrid simulations (RTHSs). This study focuses on the computational efficiency, including the computational time and accuracy, of numerical integrations in solving FE numerical substructure in RTHSs. First, sparse matrix storage schemes are adopted to decrease the computational time of FE numerical substructure. In this way, the task execution time (TET) decreases such that the scale of the numerical substructure model increases. Subsequently, several commonly used explicit numerical integration algorithms, including the central difference method (CDM), the Newmark explicit method, the Chang method and the Gui-λ method, are comprehensively compared to evaluate their computational time in solving FE numerical substructure. CDM is better than the other explicit integration algorithms when the damping matrix is diagonal, while the Gui-λ (λ = 4) method is advantageous when the damping matrix is non-diagonal. Finally, the effect of time delay on the computational accuracy of RTHSs is investigated by simulating structure-foundation systems. Simulation results show that the influences of time delay on the displacement response become obvious with the mass ratio increasing, and delay compensation methods may reduce the relative error of the displacement peak value to less than 5% even under the large time-step and large time delay.

A multilevel finite element method for Fredholm integral eigenvalue problems

NASA Astrophysics Data System (ADS)

Xie, Hehu; Zhou, Tao

2015-12-01

In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Gong, J.; Alexanian, A.; Woo, A.

1992-01-01

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.

New Fukui, dual and hyper-dual kernels as bond reactivity descriptors.

PubMed

Franco-Pérez, Marco; Polanco-Ramírez, Carlos-A; Ayers, Paul W; Gázquez, José L; Vela, Alberto

2017-06-21

We define three new linear response indices with promising applications for bond reactivity using the mathematical framework of τ-CRT (finite temperature chemical reactivity theory). The τ-Fukui kernel is defined as the ratio between the fluctuations of the average electron density at two different points in the space and the fluctuations in the average electron number and is designed to integrate to the finite-temperature definition of the electronic Fukui function. When this kernel is condensed, it can be interpreted as a site-reactivity descriptor of the boundary region between two atoms. The τ-dual kernel corresponds to the first order response of the Fukui kernel and is designed to integrate to the finite temperature definition of the dual descriptor; it indicates the ambiphilic reactivity of a specific bond and enriches the traditional dual descriptor by allowing one to distinguish between the electron-accepting and electron-donating processes. Finally, the τ-hyper dual kernel is defined as the second-order derivative of the Fukui kernel and is proposed as a measure of the strength of ambiphilic bonding interactions. Although these quantities have never been proposed, our results for the τ-Fukui kernel and for τ-dual kernel can be derived in zero-temperature formulation of the chemical reactivity theory with, among other things, the widely-used parabolic interpolation model.

Thermodynamic Modelling of Phase Transformation in a Multi-Component System

NASA Astrophysics Data System (ADS)

Vala, J.

2007-09-01

Diffusion in multi-component alloys can be characterized by the vacancy mechanism for substitutional components, by the existence of sources and sinks for vacancies and by the motion of atoms of interstitial components. The description of diffusive and massive phase transformation of a multi-component system is based on the thermodynamic extremal principle by Onsager; the finite thickness of the interface between both phases is respected. The resulting system of partial differential equations of evolution with integral terms for unknown mole fractions (and additional variables in case of non-ideal sources and sinks for vacancies), can be analyzed using the method of lines and the finite difference technique (or, alternatively, the finite element one) together with the semi-analytic and numerical integration formulae and with certain iteration procedure, making use of the spectral properties of linear operators. The original software code for the numerical evaluation of solutions of such systems, written in MATLAB, offers a chance to simulate various real processes of diffusional phase transformation. Some results for the (nearly) steady-state real processes in substitutional alloys have been published yet. The aim of this paper is to demonstrate that the same approach can handle both substitutional and interstitial components even in case of a general system of evolution.

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Theory of BCS-BEC Crossover in Ultracold Fermi Gases: Insights into Thermodynamical and Spectroscopic Experiments

NASA Astrophysics Data System (ADS)

Levin, Kathryn

2009-05-01

In this talk we summarize our theoretical understanding of the atomic Fermi superfluids with an emphasis on understanding current experiments. We compare and contrast different theoretical approaches for dealing with finite temperature, and discuss their respective implications for these trapped gases. Armed with a basic picture of the thermodynamics we turn to a variety of different measurements based on radio frequency spectroscopy, including both momentum integrated and momentum resolved experiments. As recently reviewed in arXiv 0810.1940 and 0810.1938, we show how a broad range of experimental phenomena can be accomodated within our natural extension of the BCS-Leggett ground state to finite temperature, and briefly touch on the applicability of BCS-BEC crossover theory to the high temperature superconductors. Co-authors: Qijin Chen, Yan He and Chih-Chun Chien

A FORTRAN program for calculating nonlinear seismic ground response

USGS Publications Warehouse

Joyner, William B.

1977-01-01

The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.

Benchmarking of Computational Models for NDE and SHM of Composites

NASA Technical Reports Server (NTRS)

Wheeler, Kevin; Leckey, Cara; Hafiychuk, Vasyl; Juarez, Peter; Timucin, Dogan; Schuet, Stefan; Hafiychuk, Halyna

2016-01-01

Ultrasonic wave phenomena constitute the leading physical mechanism for nondestructive evaluation (NDE) and structural health monitoring (SHM) of solid composite materials such as carbon-fiber-reinforced polymer (CFRP) laminates. Computational models of ultrasonic guided-wave excitation, propagation, scattering, and detection in quasi-isotropic laminates can be extremely valuable in designing practically realizable NDE and SHM hardware and software with desired accuracy, reliability, efficiency, and coverage. This paper presents comparisons of guided-wave simulations for CFRP composites implemented using three different simulation codes: two commercial finite-element analysis packages, COMSOL and ABAQUS, and a custom code implementing the Elastodynamic Finite Integration Technique (EFIT). Comparisons are also made to experimental laser Doppler vibrometry data and theoretical dispersion curves.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

The Role of Second Phase Hard Particles on Hole Stretchability of two AA6xxx Alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Xiaohua; Sun, Xin; Golovashchenko, Sergey F.

The hole stretchability of two Aluminum Alloys (AA6111 and AA6022) are studied by using a two stages integrated finite element framework where the edge geometry and edge damages from the hole piercing processes were considered in the subsequent hole expansion processes. Experimentally it has been found that AA6022 has higher hole expansion ratios than those of AA6111. This observation has been nicely captured by finite element simulations. The main cause of differences have been identified to the volume fractions of the random distributed second phase hard particles which play a critical role in determining the fracture strains of the materials.

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

A posteriori error estimation for multi-stage Runge–Kutta IMEX schemes

DOE PAGES

Chaudhry, Jehanzeb H.; Collins, J. B.; Shadid, John N.

2017-02-05

Implicit–Explicit (IMEX) schemes are widely used for time integration methods for approximating solutions to a large class of problems. In this work, we develop accurate a posteriori error estimates of a quantity-of-interest for approximations obtained from multi-stage IMEX schemes. This is done by first defining a finite element method that is nodally equivalent to an IMEX scheme, then using typical methods for adjoint-based error estimation. Furthermore, the use of a nodally equivalent finite element method allows a decomposition of the error into multiple components, each describing the effect of a different portion of the method on the total error inmore » a quantity-of-interest.« less

Geometric integration in Born-Oppenheimer molecular dynamics.

PubMed

Odell, Anders; Delin, Anna; Johansson, Börje; Cawkwell, Marc J; Niklasson, Anders M N

2011-12-14

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: (1) regular time reversible Verlet, (2) second order optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation, accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. © 2011 American Institute of Physics

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Finite-Element Analysis of Crack Arrest Properties of Fiber Reinforced Composites Application in Semi-Elliptical Cracked Pipelines

NASA Astrophysics Data System (ADS)

Wang, Linyuan; Song, Shulei; Deng, Hongbo; Zhong, Kai

2018-04-01

In nowadays, repair method using fiber reinforced composites as the mainstream pipe repair technology, it can provide security for X100 high-grade steel energy long-distance pipelines in engineering. In this paper, analysis of cracked X100 high-grade steel pipe was conducted, simulation analysis was made on structure of pipes and crack arresters (CAs) to obtain the J-integral value in virtue of ANSYS Workbench finite element software and evaluation on crack arrest effects was done through measured elastic-plastic fracture mechanics parameter J-integral and the crack arrest coefficient K, in a bid to summarize effect laws of composite CAs and size of pipes and cracks for repairing CAs. The results indicate that the K value is correlated with laying angle λ, laying length L2/D1, laying thickness T1/T2of CAs, crack depth c/T1 and crack length a/c, and calculate recommended parameters for repairing fiber reinforced composite CAs in terms of two different crack forms.

Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities

NASA Technical Reports Server (NTRS)

Bendiksen, Oddvar O.

1994-01-01

This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.

The effect of loading time on flexible pavement dynamic response: a finite element analysis

NASA Astrophysics Data System (ADS)

Yin, Hao; Solaimanian, Mansour; Kumar, Tanmay; Stoffels, Shelley

2007-12-01

Dynamic response of asphalt concrete (AC) pavements under moving load is a key component for accurate prediction of flexible pavement performance. The time and temperature dependency of AC materials calls for utilizing advanced material characterization and mechanistic theories, such as viscoelasticity and stress/strain analysis. In layered elastic analysis, as implemented in the new Mechanistic-Empirical Pavement Design Guide (MEPDG), the time dependency is accounted for by calculating the loading times at different AC layer depths. In this study, the time effect on pavement response was evaluated by means of the concept of “pseudo temperature.” With the pavement temperature measured from instrumented thermocouples, the time and temperature dependency of AC materials was integrated into one single factor, termed “effective temperature.” Via this effective temperature, pavement responses under a transient load were predicted through finite element analysis. In the finite element model, viscoelastic behavior of AC materials was characterized through relaxation moduli, while the layers with unbound granular material were assumed to be in an elastic mode. The analysis was conducted for two different AC mixtures in a simplified flexible pavement structure at two different seasons. Finite element analysis results reveal that the loading time has a more pronounced impact on pavement response in the summer for both asphalt types. The results indicate that for reasonable prediction of dynamic response in flexible pavements, the effect of the depth-dependent loading time on pavement temperature should be considered.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

The problem of a finite strip compressed between two rough rigid stamps

NASA Technical Reports Server (NTRS)

Gupta, G. D.

1975-01-01

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.

A finite element-boundary integral formulation for scattering by three-dimensional cavity-backed apertures

NASA Technical Reports Server (NTRS)

Jin, Jian-Ming; Volakis, John L.

1990-01-01

A numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is employed to formulate the fields in the cavity region and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.; Woo, Alex C.; Yu, C. Long

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This is due to the lack of rigorous mathematical models for conformal antenna arrays, and as a result the design of conformal arrays is primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. Herewith we shall extend this formulation for conformal arrays on large metallic cylinders. In this we develop the mathematical formulation. In particular we discuss the finite element equations, the shape elements, and the boundary integral evaluation, and it is shown how this formulation can be applied with minimal computation and memory requirements. The implementation shall be discussed in a later report.

A finite element-boundary integral method for conformal antenna arrays on a circular cylinder

NASA Technical Reports Server (NTRS)

Kempel, Leo C.; Volakis, John L.

1992-01-01

Conformal antenna arrays offer many cost and weight advantages over conventional antenna systems. In the past, antenna designers have had to resort to expensive measurements in order to develop a conformal array design. This was due to the lack of rigorous mathematical models for conformal antenna arrays. As a result, the design of conformal arrays was primarily based on planar antenna design concepts. Recently, we have found the finite element-boundary integral method to be very successful in modeling large planar arrays of arbitrary composition in a metallic plane. We are extending this formulation to conformal arrays on large metallic cylinders. In doing so, we will develop a mathematical formulation. In particular, we discuss the finite element equations, the shape elements, and the boundary integral evaluation. It is shown how this formulation can be applied with minimal computation and memory requirements.

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

Finite volume solution of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Loyd, B.; Murman, E. M.

1986-01-01

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

A computational procedure for the dynamics of flexible beams within multibody systems. Ph.D. Thesis Final Technical Report

NASA Technical Reports Server (NTRS)

Downer, Janice Diane

1990-01-01

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Long-term dynamic modeling of tethered spacecraft using nodal position finite element method and symplectic integration

NASA Astrophysics Data System (ADS)

Li, G. Q.; Zhu, Z. H.

2015-12-01

Dynamic modeling of tethered spacecraft with the consideration of elasticity of tether is prone to the numerical instability and error accumulation over long-term numerical integration. This paper addresses the challenges by proposing a globally stable numerical approach with the nodal position finite element method (NPFEM) and the implicit, symplectic, 2-stage and 4th order Gaussian-Legendre Runge-Kutta time integration. The NPFEM eliminates the numerical error accumulation by using the position instead of displacement of tether as the state variable, while the symplectic integration enforces the energy and momentum conservation of the discretized finite element model to ensure the global stability of numerical solution. The effectiveness and robustness of the proposed approach is assessed by an elastic pendulum problem, whose dynamic response resembles that of tethered spacecraft, in comparison with the commonly used time integrators such as the classical 4th order Runge-Kutta schemes and other families of non-symplectic Runge-Kutta schemes. Numerical results show that the proposed approach is accurate and the energy of the corresponding numerical model is conservative over the long-term numerical integration. Finally, the proposed approach is applied to the dynamic modeling of deorbiting process of tethered spacecraft over a long period.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

Examples of finite element mesh generation using SDRC IDEAS

NASA Technical Reports Server (NTRS)

Zapp, John; Volakis, John L.

1990-01-01

IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.

Can we estimate total magnetization directions from aeromagnetic data using Helbig's integrals?

USGS Publications Warehouse

Phillips, J.D.

2005-01-01

An algorithm that implements Helbig's (1963) integrals for estimating the vector components (mx, my, mz) of tile magnetic dipole moment from the first order moments of the vector magnetic field components (??X, ??Y, ??Z) is tested on real and synthetic data. After a grid of total field aeromagnetic data is converted to vector component grids using Fourier filtering, Helbig's infinite integrals are evaluated as finite integrals in small moving windows using a quadrature algorithm based on the 2-D trapezoidal rule. Prior to integration, best-fit planar surfaces must be removed from the component data within the data windows in order to make the results independent of the coordinate system origin. Two different approaches are described for interpreting the results of the integration. In the "direct" method, results from pairs of different window sizes are compared to identify grid nodes where the angular difference between solutions is small. These solutions provide valid estimates of total magnetization directions for compact sources such as spheres or dipoles, but not for horizontally elongated or 2-D sources. In the "indirect" method, which is more forgiving of source geometry, results of the quadrature analysis are scanned for solutions that are parallel to a specified total magnetization direction.

Effects of using a posteriori methods for the conservation of integral invariants. [for weather forecasting

NASA Technical Reports Server (NTRS)

Takacs, Lawrence L.

1988-01-01

The nature and effect of using a posteriori adjustments to nonconservative finite-difference schemes to enforce integral invariants of the corresponding analytic system are examined. The method of a posteriori integral constraint restoration is analyzed for the case of linear advection, and the harmonic response associated with the a posteriori adjustments is examined in detail. The conservative properties of the shallow water system are reviewed, and the constraint restoration algorithm applied to the shallow water equations are described. A comparison is made between forecasts obtained using implicit and a posteriori methods for the conservation of mass, energy, and potential enstrophy in the complete nonlinear shallow-water system.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oler, Kiri J.; Miller, Carl H.

In this paper, we present a methodology for reverse engineering integrated circuits, including a mathematical verification of a scalable algorithm used to generate minimal finite state machine representations of integrated circuits.

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

Flip-chip integration of tilted VCSELs onto a silicon photonic integrated circuit.

PubMed

Lu, Huihui; Lee, Jun Su; Zhao, Yan; Scarcella, Carmelo; Cardile, Paolo; Daly, Aidan; Ortsiefer, Markus; Carroll, Lee; O'Brien, Peter

2016-07-25

In this article we describe a cost-effective approach for hybrid laser integration, in which vertical cavity surface emitting lasers (VCSELs) are passively-aligned and flip-chip bonded to a Si photonic integrated circuit (PIC), with a tilt-angle optimized for optical-insertion into standard grating-couplers. A tilt-angle of 10° is achieved by controlling the reflow of the solder ball deposition used for the electrical-contacting and mechanical-bonding of the VCSEL to the PIC. After flip-chip integration, the VCSEL-to-PIC insertion loss is -11.8 dB, indicating an excess coupling penalty of -5.9 dB, compared to Fibre-to-PIC coupling. Finite difference time domain simulations indicate that the penalty arises from the relatively poor match between the VCSEL mode and the grating-coupler.

Numerical simulations of electrohydrodynamic evolution of thin polymer films

NASA Astrophysics Data System (ADS)

Borglum, Joshua Christopher

Recently developed needleless electrospinning and electrolithography are two successful techniques that have been utilized extensively for low-cost, scalable, and continuous nano-fabrication. Rational understanding of the electrohydrodynamic principles underneath these nano-manufacturing methods is crucial to fabrication of continuous nanofibers and patterned thin films. This research project is to formulate robust, high-efficiency finite-difference Fourier spectral methods to simulate the electrohydrodynamic evolution of thin polymer films. Two thin-film models were considered and refined. The first was based on reduced lubrication theory; the second further took into account the effect of solvent drying and dewetting of the substrate. Fast Fourier Transform (FFT) based spectral method was integrated into the finite-difference algorithms for fast, accurately solving the governing nonlinear partial differential equations. The present methods have been used to examine the dependencies of the evolving surface features of the thin films upon the model parameters. The present study can be used for fast, controllable nanofabrication.

A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a non-orthogonal FDTD method

NASA Astrophysics Data System (ADS)

Ward, A. J.; Pendry, J. B.

2000-06-01

In this paper we present an updated version of our ONYX program for calculating photonic band structures using a non-orthogonal finite difference time domain method. This new version employs the same transparent formalism as the first version with the same capabilities for calculating photonic band structures or causal Green's functions but also includes extra subroutines for the calculation of transmission and reflection coefficients. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwell's equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretization so the technique is ideally suited to handling systems with large and complicated unit cells.

Vibration effect on the Soret-induced convection of ternary mixture in a rectangular cavity heated from below

NASA Astrophysics Data System (ADS)

Lyubimova, T. P.; Zubova, N. A.

2017-06-01

This paper presents the results of numerical simulation of the Soret-induced convection of ternary mixture in the rectangular cavity elongated in horizontal direction in gravity field. The cavity has rigid impermeable boundaries. It is heated from the bellow and undergoes translational linearly polarized vibrations of finite amplitude and frequency in the horizontal direction. The problem is solved by finite difference method in the framework of full unsteady non-linear approach. The procedure of diagonalization of the molecular diffusion coefficient matrix is applied, allowing to eliminate cross-diffusion components in the equations and to reduce the number of the governing parameters. The calculations are performed for model ternary mixture with positive separation ratios of the components. The data on the vibration effect on temporal evolution of instantaneous and average fields and integral characteristics of the flow and heat and mass transfer at different levels of gravity are obtained.

A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

NASA Astrophysics Data System (ADS)

Liu, Zhengguang; Li, Xiaoli

2018-05-01

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

Unsteady transonic flows - Introduction, current trends, applications

NASA Technical Reports Server (NTRS)

Yates, E. C., Jr.

1985-01-01

The computational treatment of unsteady transonic flows is discussed, reviewing the historical development and current techniques. The fundamental physical principles are outlined; the governing equations are introduced; three-dimensional linearized and two-dimensional linear-perturbation theories in frequency domain are described in detail; and consideration is given to frequency-domain FEMs and time-domain finite-difference and integral-equation methods. Extensive graphs and diagrams are included.

Integration of a photonic crystal polarization beam splitter and waveguide bend.

PubMed

Zheng, Wanhua; Xing, Mingxin; Ren, Gang; Johnson, Steven G; Zhou, Wenjun; Chen, Wei; Chen, Lianghui

2009-05-11

In this work, we present the design of an integrated photonic-crystal polarization beam splitter (PC-PBS) and a low-loss photonic-crystal 60 degrees waveguide bend. Firstly, the modal properties of the PC-PBS and the mechanism of the low-loss waveguide bend are investigated by the two-dimensional finite-difference time-domain (FDTD) method, and then the integration of the two devices is studied. It shows that, although the individual devices perform well separately, the performance of the integrated circuit is poor due to the multi-mode property of the PC-PBS. By introducing deformed airhole structures, a single-mode PC-PBS is proposed, which significantly enhance the performance of the circuit with the extinction ratios remaining above 20 dB for both transverse-electric (TE) and transverse-magnetic (TM) polarizations. Both the specific result and the general idea of integration design are promising in the photonic crystal integrated circuits in the future.

Algebraic Bethe ansatz for the two species ASEP with different hopping rates

NASA Astrophysics Data System (ADS)

Cantini, Luigi

2008-03-01

An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved, and the nested algebraic Bethe ansatz is used to derive the Bethe equations for states with arbitrary numbers of particles of each type, generalizing the results of Derrida and Evans [10]. We also present formulae for the total velocity of particles of a given type and their limit given the large size of the system and the finite densities of the particles.

Three-dimensional viscous rotor flow calculations using a viscous-inviscid interaction approach

NASA Technical Reports Server (NTRS)

Chen, Ching S.; Bridgeman, John O.

1990-01-01

A three-dimensional viscous-inviscid interaction analysis was developed to predict the performance of rotors in hover and in forward flight at subsonic and transonic tip speeds. The analysis solves the full-potential and boundary-layer equations by finite-difference numerical procedures. Calculations were made for several different model rotor configurations. The results were compared with predictions from a two-dimensional integral method and with experimental data. The comparisons show good agreement between predictions and test data.

Controlling the sign problem in finite-density quantum field theory

NASA Astrophysics Data System (ADS)

Garron, Nicolas; Langfeld, Kurt

2017-07-01

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

A finite state machine read-out chip for integrated surface acoustic wave sensors

NASA Astrophysics Data System (ADS)

Rakshit, Sambarta; Iliadis, Agis A.

2015-01-01

A finite state machine based integrated sensor circuit suitable for the read-out module of a monolithically integrated SAW sensor on Si is reported. The primary sensor closed loop consists of a voltage controlled oscillator (VCO), a peak detecting comparator, a finite state machine (FSM), and a monolithically integrated SAW sensor device. The output of the system oscillates within a narrow voltage range that correlates with the SAW pass-band response. The period of oscillation is of the order of the SAW phase delay. We use timing information from the FSM to convert SAW phase delay to an on-chip 10 bit digital output operating on the principle of time to digital conversion (TDC). The control inputs of this digital conversion block are generated by a second finite state machine operating under a divided system clock. The average output varies with changes in SAW center frequency, thus tracking mass sensing events in real time. Based on measured VCO gain of 16 MHz/V our system will convert a 10 kHz SAW frequency shift to a corresponding mean voltage shift of 0.7 mV. A corresponding shift in phase delay is converted to a one or two bit shift in the TDC output code. The system can handle alternate SAW center frequencies and group delays simply by adjusting the VCO control and TDC delay control inputs. Because of frequency to voltage and phase to digital conversion, this topology does not require external frequency counter setups and is uniquely suitable for full monolithic integration of autonomous sensor systems and tags.

Thermalization threshold in models of 1D fermions

NASA Astrophysics Data System (ADS)

Mukerjee, Subroto; Modak, Ranjan; Ramswamy, Sriram

2013-03-01

The question of how isolated quantum systems thermalize is an interesting and open one. In this study we equate thermalization with non-integrability to try to answer this question. In particular, we study the effect of system size on the integrability of 1D systems of interacting fermions on a lattice. We find that for a finite-sized system, a non-zero value of an integrability breaking parameter is required to make an integrable system appear non-integrable. Using exact diagonalization and diagnostics such as energy level statistics and the Drude weight, we find that the threshold value of the integrability breaking parameter scales to zero as a power law with system size. We find the exponent to be the same for different models with its value depending on the random matrix ensemble describing the non-integrable system. We also study a simple analytical model of a non-integrable system with an integrable limit to better understand how a power law emerges.

Elevated temperature crack growth

NASA Technical Reports Server (NTRS)

Kim, K. S.; Vanstone, R. H.

1992-01-01

The purpose of this program was to extend the work performed in the base program (CR 182247) into the regime of time-dependent crack growth under isothermal and thermal mechanical fatigue (TMF) loading, where creep deformation also influences the crack growth behavior. The investigation was performed in a two-year, six-task, combined experimental and analytical program. The path-independent integrals for application to time-dependent crack growth were critically reviewed. The crack growth was simulated using a finite element method. The path-independent integrals were computed from the results of finite-element analyses. The ability of these integrals to correlate experimental crack growth data were evaluated under various loading and temperature conditions. The results indicate that some of these integrals are viable parameters for crack growth prediction at elevated temperatures.

Elevated temperature crack growth

NASA Technical Reports Server (NTRS)

Kim, K. S.; Vanstone, R. H.; Malik, S. N.; Laflen, J. H.

1988-01-01

A study was performed to examine the applicability of path-independent (P-I) integrals to crack growth problems in hot section components of gas turbine aircraft engines. Alloy 718 was used and the experimental parameters included combined temperature and strain cycling, thermal gradients, elastic-plastic strain levels, and mean strains. A literature review was conducted of proposed P-I integrals, and those capable of analyzing hot section component problems were selected and programmed into the postprocessor of a finite element code. Detailed elastic-plastic finite element analyses were conducted to simulate crack growth and crack closure of the test specimen, and to evaluate the P-I integrals. It was shown that the selected P-I integrals are very effective for predicting crack growth for isothermal conditions.

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.

1982-01-01

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Analysis of airfoil leading edge separation bubbles

NASA Technical Reports Server (NTRS)

Carter, J. E.; Vatsa, V. N.

1982-01-01

A local inviscid-viscous interaction technique was developed for the analysis of low speed airfoil leading edge transitional separation bubbles. In this analysis an inverse boundary layer finite difference analysis is solved iteratively with a Cauchy integral representation of the inviscid flow which is assumed to be a linear perturbation to a known global viscous airfoil analysis. Favorable comparisons with data indicate the overall validity of the present localized interaction approach. In addition numerical tests were performed to test the sensitivity of the computed results to the mesh size, limits on the Cauchy integral, and the location of the transition region.

A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy

NASA Astrophysics Data System (ADS)

Zhao, Peng; Fan, Engui

2015-04-01

In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.

A model of transverse fuel injection applied to the computation of supersonic combustor flow

NASA Technical Reports Server (NTRS)

Rogers, R. C.

1979-01-01

A two-dimensional, nonreacting flow model of the aerodynamic interaction of a transverse hydrogen jet within a supersonic mainstream has been developed. The model assumes profile shapes of mass flux, pressure, flow angle, and hydrogen concentration and produces downstream profiles of the other flow parameters under the constraints of the integrated conservation equations. These profiles are used as starting conditions for an existing finite difference parabolic computer code for the turbulent supersonic combustion of hydrogen. Integrated mixing and flow profile results obtained from the computer code compare favorably with existing data for the supersonic combustion of hydrogen.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

Average dynamics of a finite set of coupled phase oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dima, Germán C., E-mail: gdima@df.uba.ar; Mindlin, Gabriel B.

2014-06-15

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Average dynamics of a finite set of coupled phase oscillators

PubMed Central

Dima, Germán C.; Mindlin, Gabriel B.

2014-01-01

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate. PMID:24985426

Average dynamics of a finite set of coupled phase oscillators.

PubMed

Dima, Germán C; Mindlin, Gabriel B

2014-06-01

We study the solutions of a dynamical system describing the average activity of an infinitely large set of driven coupled excitable units. We compared their topological organization with that reconstructed from the numerical integration of finite sets. In this way, we present a strategy to establish the pertinence of approximating the dynamics of finite sets of coupled nonlinear units by the dynamics of its infinitely large surrogate.

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martin, Bradley, E-mail: brma7253@colorado.edu; Fornberg, Bengt, E-mail: Fornberg@colorado.edu

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy formore » the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.« less

Computation of rapidly varied unsteady, free-surface flow

USGS Publications Warehouse

Basco, D.R.

1987-01-01

Many unsteady flows in hydraulics occur with relatively large gradients in free surface profiles. The assumption of hydrostatic pressure distribution with depth is no longer valid. These are rapidly-varied unsteady flows (RVF) of classical hydraulics and also encompass short wave propagation of coastal hydraulics. The purpose of this report is to present an introductory review of the Boussinnesq-type differential equations that describe these flows and to discuss methods for their numerical integration. On variable slopes and for large scale (finite-amplitude) disturbances, three independent derivational methods all gave differences in the motion equation for higher order terms. The importance of these higher-order terms for riverine applications must be determined by numerical experiments. Care must be taken in selection of the appropriate finite-difference scheme to minimize truncation error effects and the possibility of diverging (double mode) numerical solutions. It is recommended that practical hydraulics cases be established and tested numerically to demonstrate the order of differences in solution with those obtained from the long wave equations of St. Venant. (USGS)

FDDO and DSMC analyses of rarefied gas flow through 2D nozzles

NASA Technical Reports Server (NTRS)

Chung, Chan-Hong; De Witt, Kenneth J.; Jeng, Duen-Ren; Penko, Paul F.

1992-01-01

Two different approaches, the finite-difference method coupled with the discrete-ordinate method (FDDO), and the direct-simulation Monte Carlo (DSMC) method, are used in the analysis of the flow of a rarefied gas expanding through a two-dimensional nozzle and into a surrounding low-density environment. In the FDDO analysis, by employing the discrete-ordinate method, the Boltzmann equation simplified by a model collision integral is transformed to a set of partial differential equations which are continuous in physical space but are point functions in molecular velocity space. The set of partial differential equations are solved by means of a finite-difference approximation. In the DSMC analysis, the variable hard sphere model is used as a molecular model and the no time counter method is employed as a collision sampling technique. The results of both the FDDO and the DSMC methods show good agreement. The FDDO method requires less computational effort than the DSMC method by factors of 10 to 40 in CPU time, depending on the degree of rarefaction.

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

NASA Technical Reports Server (NTRS)

Gerritsen, Margot; Olsson, Pelle

1996-01-01

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces

NASA Astrophysics Data System (ADS)

Martin, Bradley; Fornberg, Bengt

2017-04-01

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

Evaluation of radiation loading on finite cylindrical shells using the fast Fourier transform: A comparison with direct numerical integration.

PubMed

Liu, S X; Zou, M S

2018-03-01

The radiation loading on a vibratory finite cylindrical shell is conventionally evaluated through the direct numerical integration (DNI) method. An alternative strategy via the fast Fourier transform algorithm is put forward in this work based on the general expression of radiation impedance. To check the feasibility and efficiency of the proposed method, a comparison with DNI is presented through numerical cases. The results obtained using the present method agree well with those calculated by DNI. More importantly, the proposed calculating strategy can significantly save the time cost compared with the conventional approach of straightforward numerical integration.

Effect of analysis parameters on non-linear implicit finite element analysis of marine corroded steel plate

NASA Astrophysics Data System (ADS)

Islam, Muhammad Rabiul; Sakib-Ul-Alam, Md.; Nazat, Kazi Kaarima; Hassan, M. Munir

2017-12-01

FEA results greatly depend on analysis parameters. MSC NASTRAN nonlinear implicit analysis code has been used in large deformation finite element analysis of pitted marine SM490A steel rectangular plate. The effect of two types actual pit shape on parameters of integrity of structure has been analyzed. For 3-D modeling, a proposed method for simulation of pitted surface by probabilistic corrosion model has been used. The result has been verified with the empirical formula proposed by finite element analysis of steel surface generated with different pitted data where analyses have been carried out by the code of LS-DYNA 971. In the both solver, an elasto-plastic material has been used where an arbitrary stress versus strain curve can be defined. In the later one, the material model is based on the J2 flow theory with isotropic hardening where a radial return algorithm is used. The comparison shows good agreement between the two results which ensures successful simulation with comparatively less energy and time.

Technique for evaluation of the strong potential Born approximation for electron capture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sil, N.C.; McGuire, J.H.

1985-04-01

A technique is presented for evaluating differential cross sections in the strong potential Born (SPB) approximation. Our final expression is expressed as a finite sum of one-dimensional integrals, expressible as a finite sum of derivatives of hypergeometric functions.

A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.

PubMed

An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan

2017-01-01

The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.

Implementing Capsule Representation in a Total Hip Dislocation Finite Element Model

PubMed Central

Stewart, Kristofer J; Pedersen, Douglas R; Callaghan, John J; Brown, Thomas D

2004-01-01

Previously validated hardware-only finite element models of THA dislocation have clarified how various component design and surgical placement variables contribute to resisting the propensity for implant dislocation. This body of work has now been enhanced with the incorporation of experimentally based capsule representation, and with anatomic bone structures. The current form of this finite element model provides for large deformation multi-body contact (including capsule wrap-around on bone and/or implant), large displacement interfacial sliding, and large deformation (hyperelastic) capsule representation. In addition, the modular nature of this model now allows for rapid incorporation of current or future total hip implant designs, accepts complex multi-axial physiologic motion inputs, and outputs case-specific component/bone/soft-tissue impingement events. This soft-tissue-augmented finite element model is being used to investigate the performance of various implant designs for a range of clinically-representative soft tissue integrities and surgical techniques. Preliminary results show that capsule enhancement makes a substantial difference in stability, compared to an otherwise identical hardware-only model. This model is intended to help put implant design and surgical technique decisions on a firmer scientific basis, in terms of reducing the likelihood of dislocation. PMID:15296198

A finite nonlinear hyper-viscoelastic model for soft biological tissues.

PubMed

Panda, Satish Kumar; Buist, Martin Lindsay

2018-03-01

Soft tissues exhibit highly nonlinear rate and time-dependent stress-strain behaviour. Strain and strain rate dependencies are often modelled using a hyperelastic model and a discrete (standard linear solid) or continuous spectrum (quasi-linear) viscoelastic model, respectively. However, these models are unable to properly capture the materials characteristics because hyperelastic models are unsuited for time-dependent events, whereas the common viscoelastic models are insufficient for the nonlinear and finite strain viscoelastic tissue responses. The convolution integral based models can demonstrate a finite viscoelastic response; however, their derivations are not consistent with the laws of thermodynamics. The aim of this work was to develop a three-dimensional finite hyper-viscoelastic model for soft tissues using a thermodynamically consistent approach. In addition, a nonlinear function, dependent on strain and strain rate, was adopted to capture the nonlinear variation of viscosity during a loading process. To demonstrate the efficacy and versatility of this approach, the model was used to recreate the experimental results performed on different types of soft tissues. In all the cases, the simulation results were well matched (R 2 ⩾0.99) with the experimental data. Copyright © 2018 Elsevier Ltd. All rights reserved.

Efficient discretization in finite difference method

NASA Astrophysics Data System (ADS)

Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris

2015-04-01

Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.

Benchmark measurements and calculations of a 3-dimensional neutron streaming experiment

NASA Astrophysics Data System (ADS)

Barnett, D. A., Jr.

1991-02-01

An experimental assembly known as the Dog-Legged Void assembly was constructed to measure the effect of neutron streaming in iron and void regions. The primary purpose of the measurements was to provide benchmark data against which various neutron transport calculation tools could be compared. The measurements included neutron flux spectra at four places and integral measurements at two places in the iron streaming path as well as integral measurements along several axial traverses. These data have been used in the verification of Oak Ridge National Laboratory's three-dimensional discrete ordinates code, TORT. For a base case calculation using one-half inch mesh spacing, finite difference spatial differencing, an S(sub 16) quadrature and P(sub 1) cross sections in the MUFT multigroup structure, the calculated solution agreed to within 18 percent with the spectral measurements and to within 24 percent of the integral measurements. Variations on the base case using a fewgroup energy structure and P(sub 1) and P(sub 3) cross sections showed similar agreement. Calculations using a linear nodal spatial differencing scheme and fewgroup cross sections also showed similar agreement. For the same mesh size, the nodal method was seen to require 2.2 times as much CPU time as the finite difference method. A nodal calculation using a typical mesh spacing of 2 inches, which had approximately 32 times fewer mesh cells than the base case, agreed with the measurements to within 34 percent and yet required on 8 percent of the CPU time.

Nanowire nanocomputer as a finite-state machine.

PubMed

Yao, Jun; Yan, Hao; Das, Shamik; Klemic, James F; Ellenbogen, James C; Lieber, Charles M

2014-02-18

Implementation of complex computer circuits assembled from the bottom up and integrated on the nanometer scale has long been a goal of electronics research. It requires a design and fabrication strategy that can address individual nanometer-scale electronic devices, while enabling large-scale assembly of those devices into highly organized, integrated computational circuits. We describe how such a strategy has led to the design, construction, and demonstration of a nanoelectronic finite-state machine. The system was fabricated using a design-oriented approach enabled by a deterministic, bottom-up assembly process that does not require individual nanowire registration. This methodology allowed construction of the nanoelectronic finite-state machine through modular design using a multitile architecture. Each tile/module consists of two interconnected crossbar nanowire arrays, with each cross-point consisting of a programmable nanowire transistor node. The nanoelectronic finite-state machine integrates 180 programmable nanowire transistor nodes in three tiles or six total crossbar arrays, and incorporates both sequential and arithmetic logic, with extensive intertile and intratile communication that exhibits rigorous input/output matching. Our system realizes the complete 2-bit logic flow and clocked control over state registration that are required for a finite-state machine or computer. The programmable multitile circuit was also reprogrammed to a functionally distinct 2-bit full adder with 32-set matched and complete logic output. These steps forward and the ability of our unique design-oriented deterministic methodology to yield more extensive multitile systems suggest that proposed general-purpose nanocomputers can be realized in the near future.

Nanowire nanocomputer as a finite-state machine

PubMed Central

Yao, Jun; Yan, Hao; Das, Shamik; Klemic, James F.; Ellenbogen, James C.; Lieber, Charles M.

2014-01-01

Implementation of complex computer circuits assembled from the bottom up and integrated on the nanometer scale has long been a goal of electronics research. It requires a design and fabrication strategy that can address individual nanometer-scale electronic devices, while enabling large-scale assembly of those devices into highly organized, integrated computational circuits. We describe how such a strategy has led to the design, construction, and demonstration of a nanoelectronic finite-state machine. The system was fabricated using a design-oriented approach enabled by a deterministic, bottom–up assembly process that does not require individual nanowire registration. This methodology allowed construction of the nanoelectronic finite-state machine through modular design using a multitile architecture. Each tile/module consists of two interconnected crossbar nanowire arrays, with each cross-point consisting of a programmable nanowire transistor node. The nanoelectronic finite-state machine integrates 180 programmable nanowire transistor nodes in three tiles or six total crossbar arrays, and incorporates both sequential and arithmetic logic, with extensive intertile and intratile communication that exhibits rigorous input/output matching. Our system realizes the complete 2-bit logic flow and clocked control over state registration that are required for a finite-state machine or computer. The programmable multitile circuit was also reprogrammed to a functionally distinct 2-bit full adder with 32-set matched and complete logic output. These steps forward and the ability of our unique design-oriented deterministic methodology to yield more extensive multitile systems suggest that proposed general-purpose nanocomputers can be realized in the near future. PMID:24469812

Driven Langevin systems: fluctuation theorems and faithful dynamics

NASA Astrophysics Data System (ADS)

Sivak, David; Chodera, John; Crooks, Gavin

2014-03-01

Stochastic differential equations of motion (e.g., Langevin dynamics) provide a popular framework for simulating molecular systems. Any computational algorithm must discretize these equations, yet the resulting finite time step integration schemes suffer from several practical shortcomings. We show how any finite time step Langevin integrator can be thought of as a driven, nonequilibrium physical process. Amended by an appropriate work-like quantity (the shadow work), nonequilibrium fluctuation theorems can characterize or correct for the errors introduced by the use of finite time steps. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. We further show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Finite-size scaling of eigenstate thermalization

NASA Astrophysics Data System (ADS)

Beugeling, W.; Moessner, R.; Haque, Masudul

2014-04-01

According to the eigenstate thermalization hypothesis (ETH), even isolated quantum systems can thermalize because the eigenstate-to-eigenstate fluctuations of typical observables vanish in the limit of large systems. Of course, isolated systems are by nature finite and the main way of computing such quantities is through numerical evaluation for finite-size systems. Therefore, the finite-size scaling of the fluctuations of eigenstate expectation values is a central aspect of the ETH. In this work, we present numerical evidence that for generic nonintegrable systems these fluctuations scale with a universal power law D-1/2 with the dimension D of the Hilbert space. We provide heuristic arguments, in the same spirit as the ETH, to explain this universal result. Our results are based on the analysis of three families of models and several observables for each model. Each family includes integrable members and we show how the system size where the universal power law becomes visible is affected by the proximity to integrability.

Integral finite element analysis of turntable bearing with flexible rings

NASA Astrophysics Data System (ADS)

Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng

2018-03-01

This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling elements is determined by the finite element contact analysis of a single rolling element and the raceway. Based on this, the nonlinear contact between the rolling elements and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral finite element analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other finite element analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Patient-specific bone modeling and analysis: the role of integration and automation in clinical adoption.

PubMed

Zadpoor, Amir A; Weinans, Harrie

2015-03-18

Patient-specific analysis of bones is considered an important tool for diagnosis and treatment of skeletal diseases and for clinical research aimed at understanding the etiology of skeletal diseases and the effects of different types of treatment on their progress. In this article, we discuss how integration of several important components enables accurate and cost-effective patient-specific bone analysis, focusing primarily on patient-specific finite element (FE) modeling of bones. First, the different components are briefly reviewed. Then, two important aspects of patient-specific FE modeling, namely integration of modeling components and automation of modeling approaches, are discussed. We conclude with a section on validation of patient-specific modeling results, possible applications of patient-specific modeling procedures, current limitations of the modeling approaches, and possible areas for future research. Copyright © 2014 Elsevier Ltd. All rights reserved.

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

NASA Astrophysics Data System (ADS)

Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane

2016-12-01

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Cooperative Solutions in Multi-Person Quadratic Decision Problems: Finite-Horizon and State-Feedback Cost-Cumulant Control Paradigm

DTIC Science & Technology

2007-01-01

CONTRACT NUMBER Problems: Finite -Horizon and State-Feedback Cost-Cumulant Control Paradigm (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER...cooperative cost-cumulant control regime for the class of multi-person single-objective decision problems characterized by quadratic random costs and... finite -horizon integral quadratic cost associated with a linear stochastic system . Since this problem formation is parameterized by the number of cost

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

NASA Technical Reports Server (NTRS)

Fisher, Travis C.; Carpenter, Mark H.

2013-01-01

Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

Internal hypersonic flow. [in thin shock layer

NASA Technical Reports Server (NTRS)

Lin, T. C.; Rubin, S. G.

1974-01-01

An approach for studying hypersonic internal flow with the aid of a thin-shock-layer approximation is discussed, giving attention to a comparison of thin-shock-layer results with the data obtained on the basis of the imposition theory or a finite-difference integration of the Euler equations. Relations in the case of strong interaction are considered together with questions of pressure distribution and aspects of the boundary-layer solution.

Integrated thermal disturbance analysis of optical system of astronomical telescope

NASA Astrophysics Data System (ADS)

Yang, Dehua; Jiang, Zibo; Li, Xinnan

2008-07-01

During operation, astronomical telescope will undergo thermal disturbance, especially more serious in solar telescope, which may cause degradation of image quality. As drives careful thermal load investigation and measure applied to assess its effect on final image quality during design phase. Integrated modeling analysis is boosting the process to find comprehensive optimum design scheme by software simulation. In this paper, we focus on the Finite Element Analysis (FEA) software-ANSYS-for thermal disturbance analysis and the optical design software-ZEMAX-for optical system design. The integrated model based on ANSYS and ZEMAX is briefed in the first from an overview of point. Afterwards, we discuss the establishment of thermal model. Complete power series polynomial with spatial coordinates is introduced to present temperature field analytically. We also borrow linear interpolation technique derived from shape function in finite element theory to interface the thermal model and structural model and further to apply the temperatures onto structural model nodes. Thereby, the thermal loads are transferred with as high fidelity as possible. Data interface and communication between the two softwares are discussed mainly on mirror surfaces and hence on the optical figure representation and transformation. We compare and comment the two different methods, Zernike polynomials and power series expansion, for representing and transforming deformed optical surface to ZEMAX. Additionally, these methods applied to surface with non-circular aperture are discussed. At the end, an optical telescope with parabolic primary mirror of 900 mm in diameter is analyzed to illustrate the above discussion. Finite Element Model with most interested parts of the telescope is generated in ANSYS with necessary structural simplification and equivalence. Thermal analysis is performed and the resulted positions and figures of the optics are to be retrieved and transferred to ZEMAX, and thus final image quality is evaluated with thermal disturbance.

On the mechanics of stress analysis of fiber-reinforced composites

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, V.G.

A general mathematical formulation is developed for the three-dimensional inclusion and inhomogeneity problems, which are practically important in many engineering applications such as fiber pullout of reinforced composites, load transfer behavior in the stiffened structural components, and material defects and impurities existing in engineering materials. First, the displacement field (Green's function) for an elastic solid subjected to various distributions of ring loading is derived in closed form using the Papkovich-Neuber displacement potentials and the Hankel transforms. The Green's functions are used to derive the displacement and stress fields due to a finite cylindrical inclusion of prescribed dilatational eigenstrain such asmore » thermal expansion caused by an internal heat source. Unlike an elliptical inclusion, the interior stress field in the cylindrical inclusion is not uniform. Next, the three-dimensional inhomogeneity problem of a cylindrical fiber embedded in an infinite matrix of different material properties is considered to study load transfer of a finite fiber to an elastic medium. By using the equivalent inclusion method, the fiber is modeled as an inclusion with distributed eigenstrains of unknown strength, and the inhomogeneity problem can be treated as an equivalent inclusion problem. The eigenstrains are determined to simulate the disturbance due to the existing fiber. The equivalency of elastic field between inhomogeneity and inclusion problems leads to a set of integral equations. To solve the integral equations, the inclusion domain is discretized into a finite number of sub-inclusions with uniform eigenstrains, and the integral equations are reduced to a set of algebraic equations. The distributions of eigenstrains, interior stress field and axial force along the fiber are presented for various fiber lengths and the ratio of material properties of the fiber relative to the matrix.« less

A time-domain finite element boundary integral approach for elastic wave scattering

NASA Astrophysics Data System (ADS)

Shi, F.; Lowe, M. J. S.; Skelton, E. A.; Craster, R. V.

2018-04-01

The response of complex scatterers, such as rough or branched cracks, to incident elastic waves is required in many areas of industrial importance such as those in non-destructive evaluation and related fields; we develop an approach to generate accurate and rapid simulations. To achieve this we develop, in the time domain, an implementation to efficiently couple the finite element (FE) method within a small local region, and the boundary integral (BI) globally. The FE explicit scheme is run in a local box to compute the surface displacement of the scatterer, by giving forcing signals to excitation nodes, which can lie on the scatterer itself. The required input forces on the excitation nodes are obtained with a reformulated FE equation, according to the incident displacement field. The surface displacements computed by the local FE are then projected, through time-domain BI formulae, to calculate the scattering signals with different modes. This new method yields huge improvements in the efficiency of FE simulations for scattering from complex scatterers. We present results using different shapes and boundary conditions, all simulated using this approach in both 2D and 3D, and then compare with full FE models and theoretical solutions to demonstrate the efficiency and accuracy of this numerical approach.

Some Aspects of Essentially Nonoscillatory (ENO) Formulations for the Euler Equations, Part 3

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1990-01-01

An essentially nonoscillatory (ENO) formulation is described for hyperbolic systems of conservation laws. ENO approaches are based on smart interpolation to avoid spurious numerical oscillations. ENO schemes are a superset of Total Variation Diminishing (TVD) schemes. In the recent past, TVD formulations were used to construct shock capturing finite difference methods. At extremum points of the solution, TVD schemes automatically reduce to being first-order accurate discretizations locally, while away from extrema they can be constructed to be of higher order accuracy. The new framework helps construct essentially non-oscillatory finite difference methods without recourse to local reductions of accuracy to first order. Thus arbitrarily high orders of accuracy can be obtained. The basic general ideas of the new approach can be specialized in several ways and one specific implementation is described based on: (1) the integral form of the conservation laws; (2) reconstruction based on the primitive functions; (3) extension to multiple dimensions in a tensor product fashion; and (4) Runge-Kutta time integration. The resulting method is fourth-order accurate in time and space and is applicable to uniform Cartesian grids. The construction of such schemes for scalar equations and systems in one and two space dimensions is described along with several examples which illustrate interesting aspects of the new approach.

Simulation of a steady-state integrated human thermal system.

NASA Technical Reports Server (NTRS)

Hsu, F. T.; Fan, L. T.; Hwang, C. L.

1972-01-01

The mathematical model of an integrated human thermal system is formulated. The system consists of an external thermal regulation device on the human body. The purpose of the device (a network of cooling tubes held in contact with the surface of the skin) is to maintain the human body in a state of thermoneutrality. The device is controlled by varying the inlet coolant temperature and coolant mass flow rate. The differential equations of the model are approximated by a set of algebraic equations which result from the application of the explicit forward finite difference method to the differential equations. The integrated human thermal system is simulated for a variety of combinations of the inlet coolant temperature, coolant mass flow rate, and metabolic rates.

Photonic crystal ring resonator based optical filters for photonic integrated circuits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robinson, S., E-mail: mail2robinson@gmail.com

In this paper, a two Dimensional (2D) Photonic Crystal Ring Resonator (PCRR) based optical Filters namely Add Drop Filter, Bandpass Filter, and Bandstop Filter are designed for Photonic Integrated Circuits (PICs). The normalized output response of the filters is obtained using 2D Finite Difference Time Domain (FDTD) method and the band diagram of periodic and non-periodic structure is attained by Plane Wave Expansion (PWE) method. The size of the device is minimized from a scale of few tens of millimeters to the order of micrometers. The overall size of the filters is around 11.4 μm × 11.4 μm which ismore » highly suitable of photonic integrated circuits.« less

Directional radiation of Babinet-inverted optical nanoantenna integrated with plasmonic waveguide

NASA Astrophysics Data System (ADS)

Kim, Jineun; Roh, Young-Geun; Cheon, Sangmo; Jeong Kim, Un; Hwang, Sung Woo; Park, Yeonsang; Lee, Chang-Won

2015-07-01

We present a Babinet-inverted optical nanoantenna integrated with a plasmonic waveguide. Using an integrated nanoantenna, we can couple the plasmon guide mode in a metal-insulator-metal (MIM) structure into the resonant antenna feed directly. The resonantly excited feed slot then radiates to free space and generates a magnetic dipole-like far-field pattern. The coupling efficiency of the integrated nanoantenna is calculated as being approximately 19% using a three-dimensional finite-difference time-domain (3D FDTD) simulation. By adding an auxiliary groove structure along with the feed, the radiation direction can be controlled similar to an optical Yagi-Uda antenna. We also determine, both theoretically and experimentally, that groove depth plays a significant role to function groove structure as a reflector or a director. The demonstrated Babinet-inverted optical nanoantenna integrated with a plasmonic waveguide can be used as a “plasmonic via” in plasmonic nanocircuits.

Directional radiation of Babinet-inverted optical nanoantenna integrated with plasmonic waveguide.

PubMed

Kim, Jineun; Roh, Young-Geun; Cheon, Sangmo; Kim, Un Jeong; Hwang, Sung Woo; Park, Yeonsang; Lee, Chang-Won

2015-07-02

We present a Babinet-inverted optical nanoantenna integrated with a plasmonic waveguide. Using an integrated nanoantenna, we can couple the plasmon guide mode in a metal-insulator-metal (MIM) structure into the resonant antenna feed directly. The resonantly excited feed slot then radiates to free space and generates a magnetic dipole-like far-field pattern. The coupling efficiency of the integrated nanoantenna is calculated as being approximately 19% using a three-dimensional finite-difference time-domain (3D FDTD) simulation. By adding an auxiliary groove structure along with the feed, the radiation direction can be controlled similar to an optical Yagi-Uda antenna. We also determine, both theoretically and experimentally, that groove depth plays a significant role to function groove structure as a reflector or a director. The demonstrated Babinet-inverted optical nanoantenna integrated with a plasmonic waveguide can be used as a "plasmonic via" in plasmonic nanocircuits.

Directional radiation of Babinet-inverted optical nanoantenna integrated with plasmonic waveguide

PubMed Central

Kim, Jineun; Roh, Young-Geun; Cheon, Sangmo; Jeong Kim, Un; Hwang, Sung Woo; Park, Yeonsang; Lee, Chang-Won

2015-01-01

We present a Babinet-inverted optical nanoantenna integrated with a plasmonic waveguide. Using an integrated nanoantenna, we can couple the plasmon guide mode in a metal-insulator-metal (MIM) structure into the resonant antenna feed directly. The resonantly excited feed slot then radiates to free space and generates a magnetic dipole-like far-field pattern. The coupling efficiency of the integrated nanoantenna is calculated as being approximately 19% using a three-dimensional finite-difference time-domain (3D FDTD) simulation. By adding an auxiliary groove structure along with the feed, the radiation direction can be controlled similar to an optical Yagi-Uda antenna. We also determine, both theoretically and experimentally, that groove depth plays a significant role to function groove structure as a reflector or a director. The demonstrated Babinet-inverted optical nanoantenna integrated with a plasmonic waveguide can be used as a “plasmonic via” in plasmonic nanocircuits. PMID:26135115

Numerical simulation studies of nano-scale surface plasmon components: waveguides, splitters, and filters

NASA Astrophysics Data System (ADS)

Lin, Xian-Shi; Huang, Xu-Guang

2008-12-01

In this paper, we theoretically and numerically demonstrate a two-dimensional Metal-Dielectric-Metal (MDM) waveguide based on finite-difference time-domain simulation of the propagation characteristics of surface plasmon polaritons (SPPs). For practical applications, we propose a plasmonic Y-branch waveguide based on MDM structure for high integration. The simulation results show that the Y-branch waveguide proposed here makes optical splitter with large branching angle (~180 degree) come true. We also introduce a finite array of periodic tooth structure on one surface of the MDM waveguide which is in a similar way as FBGs or Bragg reflectors, potentially as filters for WDM applications. Our results show that the novel structure not only can realize filtering function of wavelength with a high transmittance over 92%, but also with an ultra-compact size in the length of a few hundred nanometers, in comparison with other grating-like SPPs filters. The MDM waveguide splitters and filters could be utilized to achieve ultra-compact photonic filtering devices for high integration in SPPs-based flat metallic surfaces.

An ultra-accurate numerical method in the design of liquid phononic crystals with hard inclusion

NASA Astrophysics Data System (ADS)

Li, Eric; He, Z. C.; Wang, G.; Liu, G. R.

2017-12-01

The phononics crystals (PCs) are periodic man-made composite materials. In this paper, a mass-redistributed finite element method (MR-FEM) is formulated to study the wave propagation within liquid PCs with hard inclusion. With a perfect balance between stiffness and mass in the MR-FEM model, the dispersion error of longitudinal wave is minimized by redistribution of mass. Such tuning can be easily achieved by adjusting the parameter r that controls the location of integration points of mass matrix. More importantly, the property of mass conservation in the MR-FEM model indicates that the locations of integration points inside or outside the element are immaterial. Four numerical examples are studied in this work, including liquid PCs with cross and circle hard inclusions, different size of inclusion and defect. Compared with standard finite element method, the numerical results have verified the accuracy and effectiveness of MR-FEM. The proposed MR-FEM is a unique and innovative numerical approach with its outstanding features, which has strong potentials to study the stress wave within multi-physics PCs.

Automatic construction of patient-specific finite-element mesh of the spine from IVDs and vertebra segmentations

NASA Astrophysics Data System (ADS)

Castro-Mateos, Isaac; Pozo, Jose M.; Lazary, Aron; Frangi, Alejandro F.

2016-03-01

Computational medicine aims at developing patient-specific models to help physicians in the diagnosis and treatment selection for patients. The spine, and other skeletal structures, is an articulated object, composed of rigid bones (vertebrae) and non-rigid parts (intervertebral discs (IVD), ligaments and muscles). These components are usually extracted from different image modalities, involving patient repositioning. In the case of the spine, these models require the segmentation of IVDs from MR and vertebrae from CT. In the literature, there exists a vast selection of segmentations methods, but there is a lack of approaches to align the vertebrae and IVDs. This paper presents a method to create patient-specific finite element meshes for biomechanical simulations, integrating rigid and non-rigid parts of articulated objects. First, the different parts are aligned in a complete surface model. Vertebrae extracted from CT are rigidly repositioned in between the IVDs, initially using the IVDs location and then refining the alignment using the MR image with a rigid active shape model algorithm. Finally, a mesh morphing algorithm, based on B-splines, is employed to map a template finite-element (volumetric) mesh to the patient-specific surface mesh. This morphing reduces possible misalignments and guarantees the convexity of the model elements. Results show that the accuracy of the method to align vertebrae into MR, together with IVDs, is similar to that of the human observers. Thus, this method is a step forward towards the automation of patient-specific finite element models for biomechanical simulations.

Residual Strength Analyses of Monolithic Structures

NASA Technical Reports Server (NTRS)

Forth, Scott (Technical Monitor); Ambur, Damodar R. (Technical Monitor); Seshadri, B. R.; Tiwari, S. N.

2003-01-01

Finite-element fracture simulation methodology predicts the residual strength of damaged aircraft structures. The methodology uses the critical crack-tip-opening-angle (CTOA) fracture criterion to characterize the fracture behavior of the material. The CTOA fracture criterion assumes that stable crack growth occurs when the crack-tip angle reaches a constant critical value. The use of the CTOA criterion requires an elastic- plastic, finite-element analysis. The critical CTOA value is determined by simulating fracture behavior in laboratory specimens, such as a compact specimen, to obtain the angle that best fits the observed test behavior. The critical CTOA value appears to be independent of loading, crack length, and in-plane dimensions. However, it is a function of material thickness and local crack-front constraint. Modeling the local constraint requires either a three-dimensional analysis or a two-dimensional analysis with an approximation to account for the constraint effects. In recent times as the aircraft industry is leaning towards monolithic structures with the intention of reducing part count and manufacturing cost, there has been a consistent effort at NASA Langley to extend critical CTOA based numerical methodology in the analysis of integrally-stiffened panels.In this regard, a series of fracture tests were conducted on both flat and curved aluminum alloy integrally-stiffened panels. These flat panels were subjected to uniaxial tension and during the test, applied load-crack extension, out-of-plane displacements and local deformations around the crack tip region were measured. Compact and middle-crack tension specimens were tested to determine the critical angle (wc) using three-dimensional code (ZIP3D) and the plane-strain core height (hJ using two-dimensional code (STAGS). These values were then used in the STAGS analysis to predict the fracture behavior of the integrally-stiffened panels. The analyses modeled stable tearing, buckling, and crack branching at the integral stiffener using different values of critical CTOA for different material thicknesses and orientation. Comparisons were made between measured and predicted load-crack extension, out-of-plane displacements and local deformations around the crack tip region. Simultaneously, three-dimensional capabilities to model crack branching and to monitor stable crack growth of multiple cracks in a large thick integrally-stiffened flat panels were implemented in three-dimensional finite element code (ZIP3D) and tested by analyzing the integrally-stiffened panels tested at Alcoa. The residual strength of the panels predicted from STAGS and ZP3D code compared very well with experimental data. In recent times, STAGS software has been updated with new features and now one can have combinations of solid and shell elements in the residual strength analysis of integrally-stiffened panels.

Biomechanical evaluation of different abutment-implant connections - A nonlinear finite element analysis

NASA Astrophysics Data System (ADS)

Ishak, Muhammad Ikman; Shafi, Aisyah Ahmad; Rosli, M. U.; Khor, C. Y.; Zakaria, M. S.; Rahim, Wan Mohd Faizal Wan Abd; Jamalludin, Mohd Riduan

2017-09-01

The success of dental implant surgery is majorly dependent on the stability of prosthesis to anchor to implant body as well as the integration of implant body to bone. The attachment between dental implant body and abutment plays a vital role in attributing to the stability of dental implant system. A good connection between implant body cavity to abutment may minimize the complications of abutment loosening and implant fractures as widely reported in clinical findings. The aim of this paper is to investigate the effect of different abutment-implant connections on stress dispersion within the abutment and implant bodies as well as displacement of implant body via three-dimensional (3-D) finite element analysis (FEA). A 3-D model of mandible was reconstructed from computed tomography (CT) image datasets using an image-processing software with the selected region of interest was the left side covering the second premolar, first molar and second molar regions. The bone was modelled as compact (cortical) and porous (cancellous) structures. Besides, three implant bodies and three generic models of abutment with different types of connections - tapered interference fit (TIF), tapered integrated screwed-in (TIS) and screw retention (SR) were created using computer-aided design (CAD) software and all models were then analysed via 3D FEA software. Occlusal forces of 114.6 N, 17.2 N and 23.4 N were applied in the axial, lingual and mesio-distal directions, respectively, on the top surface of first molar crown. All planes of the mandibular bone model were rigidly fixed. The result exhibited that abutment with TIS connection produced the most favourable stress and displacement outcomes as compared to other attachment types. This is due to the existence of integrated screw at the bottom portion of tapered abutment which increases the motion resistance.

An integrated study of structures, aerodynamics and controls on the forward swept wing X-29A and the oblique wing research aircraft

NASA Technical Reports Server (NTRS)

Dawson, Kenneth S.; Fortin, Paul E.

1987-01-01

The results of an integrated study of structures, aerodynamics, and controls using the STARS program on two advanced airplane configurations are presented. Results for the X-29A include finite element modeling, free vibration analyses, unsteady aerodynamic calculations, flutter/divergence analyses, and an aeroservoelastic controls analysis. Good correlation is shown between STARS results and various other verified results. The tasks performed on the Oblique Wing Research Aircraft include finite element modeling and free vibration analyses.

The Crank Nicolson Time Integrator for EMPHASIS.

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGregor, Duncan Alisdair Odum; Love, Edward; Kramer, Richard Michael Jack

2018-03-01

We investigate the use of implicit time integrators for finite element time domain approxi- mations of Maxwell's equations in vacuum. We discretize Maxwell's equations in time using Crank-Nicolson and in 3D space using compatible finite elements. We solve the system by taking a single step of Newton's method and inverting the Eddy-Current Schur complement allowing for the use of standard preconditioning techniques. This approach also generalizes to more complex material models that can include the Unsplit PML. We present verification results and demonstrate performance at CFL numbers up to 1000.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2017-12-01

Travel time computation is of major interest for a large range of geophysical applications, among which source localization and characterization, phase identification, data windowing and tomography, from decametric scale up to global Earth scale.Ray-tracing tools, being essentially 1D Lagrangian integration along a path, have been used for their efficiency but present some drawbacks, such as a rather difficult control of the medium sampling. Moreover, they do not provide answers in shadow zones. Eikonal solvers, based on an Eulerian approach, have attracted attention in seismology with the pioneering work of Vidale (1988), while such approach has been proposed earlier by Riznichenko (1946). They have been used now for first-arrival travel-time tomography at various scales (Podvin & Lecomte (1991). The framework for solving this non-linear partial differential equation is now well understood and various finite-difference approaches have been proposed, essentially for smooth media. We propose a novel finite element approach which builds a precise solution for strongly heterogeneous anisotropic medium (still in the limit of Eikonal validity). The discontinuous Galerkin method we have developed allows local refinement of the mesh and local high orders of interpolation inside elements. High precision of the travel times and its spatial derivatives is obtained through this formulation. This finite element method also honors boundary conditions, such as complex topographies and absorbing boundaries for mimicking an infinite medium. Applications from travel-time tomography, slope tomography are expected, but also for migration and take-off angles estimation, thanks to the accuracy obtained when computing first-arrival times.References:Podvin, P. and Lecomte, I., 1991. Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 105, 271-284.Riznichenko, Y., 1946. Geometrical seismics of layered media, Trudy Inst. Theor. Geophysics, Vol II, Moscow (in Russian).Vidale, J., 1988. Finite-difference calculation of travel times, Bull. seism. Soc. Am., 78, 2062-2076.

Transit light curves with finite integration time: Fisher information analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Price, Ellen M.; Rogers, Leslie A.

2014-10-10

Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute integration times, and the upcoming Transiting Exoplanet Survey Satellite will record full frame images with a similar integration time. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal to noise. Using the Fisher information matrix technique, we derive analytic approximations for the variances and covariances on the transit parameters obtained from fitting light curvemore » photometry collected with a finite integration time. We find that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters when comparing scenarios with constant total signal to noise (constant total integration time in the absence of read noise). Uncertainties on the transit ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4 for Jupiter-size planets around Sun-like stars for integration times of 30 minutes compared to instantaneously sampled light curves. Similarly, uncertainties on the mid-transit time for Earth and Jupiter-size planets increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are largely unaffected by finite integration times. While correlations among the transit depth, ingress duration, and transit duration all increase in magnitude with longer integration times, the mid-transit time remains uncorrelated with the other parameters. We provide code in Python and Mathematica for predicting the variances and covariances at www.its.caltech.edu/∼eprice.« less

Investigation into discretization methods of the six-parameter Iwan model

NASA Astrophysics Data System (ADS)

Li, Yikun; Hao, Zhiming; Feng, Jiaquan; Zhang, Dingguo

2017-02-01

Iwan model is widely applied for the purpose of describing nonlinear mechanisms of jointed structures. In this paper, parameter identification procedures of the six-parameter Iwan model based on joint experiments with different preload techniques are performed. Four kinds of discretization methods deduced from stiffness equation of the six-parameter Iwan model are provided, which can be used to discretize the integral-form Iwan model into a sum of finite Jenkins elements. In finite element simulation, the influences of discretization methods and numbers of Jenkins elements on computing accuracy are discussed. Simulation results indicate that a higher accuracy can be obtained with larger numbers of Jenkins elements. It is also shown that compared with other three kinds of discretization methods, the geometric series discretization based on stiffness provides the highest computing accuracy.

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

NASA Technical Reports Server (NTRS)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

Strip Yield Model Numerical Application to Different Geometries and Loading Conditions

NASA Technical Reports Server (NTRS)

Hatamleh, Omar; Forman, Royce; Shivakumar, Venkataraman; Lyons, Jed

2006-01-01

A new numerical method based on the strip-yield analysis approach was developed for calculating the Crack Tip Opening Displacement (CTOD). This approach can be applied for different crack configurations having infinite and finite geometries, and arbitrary applied loading conditions. The new technique adapts the boundary element / dislocation density method to obtain crack-face opening displacements at any point on a crack, and succeeds by obtaining requisite values as a series of definite integrals, the functional parts of each being evaluated exactly in a closed form.

Flat bases of invariant polynomials and P-matrices of E{sub 7} and E{sub 8}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Talamini, Vittorino

2010-02-15

Let G be a compact group of linear transformations of a Euclidean space V. The G-invariant C{sup {infinity}} functions can be expressed as C{sup {infinity}} functions of a finite basic set of G-invariant homogeneous polynomials, sometimes called an integrity basis. The mathematical description of the orbit space V/G depends on the integrity basis too: it is realized through polynomial equations and inequalities expressing rank and positive semidefiniteness conditions of the P-matrix, a real symmetric matrix determined by the integrity basis. The choice of the basic set of G-invariant homogeneous polynomials forming an integrity basis is not unique, so it ismore » not unique the mathematical description of the orbit space too. If G is an irreducible finite reflection group, Saito et al. [Commun. Algebra 8, 373 (1980)] characterized some special basic sets of G-invariant homogeneous polynomials that they called flat. They also found explicitly the flat basic sets of invariant homogeneous polynomials of all the irreducible finite reflection groups except of the two largest groups E{sub 7} and E{sub 8}. In this paper the flat basic sets of invariant homogeneous polynomials of E{sub 7} and E{sub 8} and the corresponding P-matrices are determined explicitly. Using the results here reported one is able to determine easily the P-matrices corresponding to any other integrity basis of E{sub 7} or E{sub 8}. From the P-matrices one may then write down the equations and inequalities defining the orbit spaces of E{sub 7} and E{sub 8} relatively to a flat basis or to any other integrity basis. The results here obtained may be employed concretely to study analytically the symmetry breaking in all theories where the symmetry group is one of the finite reflection groups E{sub 7} and E{sub 8} or one of the Lie groups E{sub 7} and E{sub 8} in their adjoint representations.« less

Ground motion simulations in Marmara (Turkey) region from 3D finite difference method

NASA Astrophysics Data System (ADS)

Aochi, Hideo; Ulrich, Thomas; Douglas, John

2016-04-01

In the framework of the European project MARSite (2012-2016), one of the main contributions from our research team was to provide ground-motion simulations for the Marmara region from various earthquake source scenarios. We adopted a 3D finite difference code, taking into account the 3D structure around the Sea of Marmara (including the bathymetry) and the sea layer. We simulated two moderate earthquakes (about Mw4.5) and found that the 3D structure improves significantly the waveforms compared to the 1D layer model. Simulations were carried out for different earthquakes (moderate point sources and large finite sources) in order to provide shake maps (Aochi and Ulrich, BSSA, 2015), to study the variability of ground-motion parameters (Douglas & Aochi, BSSA, 2016) as well as to provide synthetic seismograms for the blind inversion tests (Diao et al., GJI, 2016). The results are also planned to be integrated in broadband ground-motion simulations, tsunamis generation and simulations of triggered landslides (in progress by different partners). The simulations are freely shared among the partners via the internet and the visualization of the results is diffused on the project's homepage. All these simulations should be seen as a reference for this region, as they are based on the latest knowledge that obtained during the MARSite project, although their refinement and validation of the model parameters and the simulations are a continuing research task relying on continuing observations. The numerical code used, the models and the simulations are available on demand.

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1991-01-01

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program.

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Raju, I. S.

1992-01-01

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program.

TAP 2: A finite element program for thermal analysis of convectively cooled structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1980-01-01

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Finite element methodology for integrated flow-thermal-structural analysis

NASA Technical Reports Server (NTRS)

Thornton, Earl A.; Ramakrishnan, R.; Vemaganti, G. R.

1988-01-01

Papers entitled, An Adaptive Finite Element Procedure for Compressible Flows and Strong Viscous-Inviscid Interactions, and An Adaptive Remeshing Method for Finite Element Thermal Analysis, were presented at the June 27 to 29, 1988, meeting of the AIAA Thermophysics, Plasma Dynamics and Lasers Conference, San Antonio, Texas. The papers describe research work supported under NASA/Langley Research Grant NsG-1321, and are submitted in fulfillment of the progress report requirement on the grant for the period ending February 29, 1988.

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.

1986-01-01

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

seismo-live: Training in Computational Seismology using Jupyter Notebooks

NASA Astrophysics Data System (ADS)

Igel, H.; Krischer, L.; van Driel, M.; Tape, C.

2016-12-01

Practical training in computational methodologies is still underrepresented in Earth science curriculae despite the increasing use of sometimes highly sophisticated simulation technologies in research projects. At the same time well-engineered community codes make it easy to return simulation-based results yet with the danger that the inherent traps of numerical solutions are not well understood. It is our belief that training with highly simplified numerical solutions (here to the equations describing elastic wave propagation) with carefully chosen elementary ingredients of simulation technologies (e.g., finite-differencing, function interpolation, spectral derivatives, numerical integration) could substantially improve this situation. For this purpose we have initiated a community platform (www.seismo-live.org) where Python-based Jupyter notebooks can be accessed and run without and necessary downloads or local software installations. The increasingly popular Jupyter notebooks allow combining markup language, graphics, equations with interactive, executable python codes. We demonstrate the potential with training notebooks for the finite-difference method, pseudospectral methods, finite/spectral element methods, the finite-volume and the discontinuous Galerkin method. The platform already includes general Python training, introduction to the ObsPy library for seismology as well as seismic data processing and noise analysis. Submission of Jupyter notebooks for general seismology are encouraged. The platform can be used for complementary teaching in Earth Science courses on compute-intensive research areas.

Probabilistic structural analysis methods for select space propulsion system components

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Cruse, T. A.

1989-01-01

The Probabilistic Structural Analysis Methods (PSAM) project developed at the Southwest Research Institute integrates state-of-the-art structural analysis techniques with probability theory for the design and analysis of complex large-scale engineering structures. An advanced efficient software system (NESSUS) capable of performing complex probabilistic analysis has been developed. NESSUS contains a number of software components to perform probabilistic analysis of structures. These components include: an expert system, a probabilistic finite element code, a probabilistic boundary element code and a fast probability integrator. The NESSUS software system is shown. An expert system is included to capture and utilize PSAM knowledge and experience. NESSUS/EXPERT is an interactive menu-driven expert system that provides information to assist in the use of the probabilistic finite element code NESSUS/FEM and the fast probability integrator (FPI). The expert system menu structure is summarized. The NESSUS system contains a state-of-the-art nonlinear probabilistic finite element code, NESSUS/FEM, to determine the structural response and sensitivities. A broad range of analysis capabilities and an extensive element library is present.

SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)

EPA Science Inventory

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...

An Analysis of Heavy-Ion Single Event Effects for a Variety of Finite State-Machine Mitigation Strategies

NASA Technical Reports Server (NTRS)

Berg, Melanie D.; Label, Kenneth A.; Kim, Hak; Phan, Anthony; Seidleck, Christina

2014-01-01

Finite state-machines (FSMs) are used to control operational flow in application specific integrated circuits (ASICs) and field programmable gate array (FPGA) devices. Because of their ease of interpretation, FSMs simplify the design and verification process and consequently are significant components in a synchronous design.

Hypercube matrix computation task

NASA Technical Reports Server (NTRS)

Calalo, Ruel H.; Imbriale, William A.; Jacobi, Nathan; Liewer, Paulett C.; Lockhart, Thomas G.; Lyzenga, Gregory A.; Lyons, James R.; Manshadi, Farzin; Patterson, Jean E.

1988-01-01

A major objective of the Hypercube Matrix Computation effort at the Jet Propulsion Laboratory (JPL) is to investigate the applicability of a parallel computing architecture to the solution of large-scale electromagnetic scattering problems. Three scattering analysis codes are being implemented and assessed on a JPL/California Institute of Technology (Caltech) Mark 3 Hypercube. The codes, which utilize different underlying algorithms, give a means of evaluating the general applicability of this parallel architecture. The three analysis codes being implemented are a frequency domain method of moments code, a time domain finite difference code, and a frequency domain finite elements code. These analysis capabilities are being integrated into an electromagnetics interactive analysis workstation which can serve as a design tool for the construction of antennas and other radiating or scattering structures. The first two years of work on the Hypercube Matrix Computation effort is summarized. It includes both new developments and results as well as work previously reported in the Hypercube Matrix Computation Task: Final Report for 1986 to 1987 (JPL Publication 87-18).

A study of infrasound propagation based on high-order finite difference solutions of the Navier-Stokes equations.

PubMed

Marsden, O; Bogey, C; Bailly, C

2014-03-01

The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described.

Hierarchical nonlinear dynamics of human attention.

PubMed

Rabinovich, Mikhail I; Tristan, Irma; Varona, Pablo

2015-08-01

Attention is the process of focusing mental resources on a specific cognitive/behavioral task. Such brain dynamics involves different partially overlapping brain functional networks whose interconnections change in time according to the performance stage, and can be stimulus-driven or induced by an intrinsically generated goal. The corresponding activity can be described by different families of spatiotemporal discrete patterns or sequential dynamic modes. Since mental resources are finite, attention modalities compete with each other at all levels of the hierarchy, from perception to decision making and behavior. Cognitive activity is a dynamical process and attention possesses some universal dynamical characteristics. Thus, it is time to apply nonlinear dynamical theory for the description and prediction of hierarchical attentional tasks. Such theory has to include the analyses of attentional control stability, the time cost of attention switching, the finite capacity of informational resources in the brain, and the normal and pathological bifurcations of attention sequential dynamics. In this paper we have integrated today's knowledge, models and results in these directions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Rolling Element Bearing Stiffness Matrix Determination (Presentation)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Y.; Parker, R.

2014-01-01

Current theoretical bearing models differ in their stiffness estimates because of different model assumptions. In this study, a finite element/contact mechanics model is developed for rolling element bearings with the focus of obtaining accurate bearing stiffness for a wide range of bearing types and parameters. A combined surface integral and finite element method is used to solve for the contact mechanics between the rolling elements and races. This model captures the time-dependent characteristics of the bearing contact due to the orbital motion of the rolling elements. A numerical method is developed to determine the full bearing stiffness matrix corresponding tomore » two radial, one axial, and two angular coordinates; the rotation about the shaft axis is free by design. This proposed stiffness determination method is validated against experiments in the literature and compared to existing analytical models and widely used advanced computational methods. The fully-populated stiffness matrix demonstrates the coupling between bearing radial, axial, and tilting bearing deflections.« less

Improved Boundary Layer Module (BLM) for the Solid Performance Program (SPP)

NASA Astrophysics Data System (ADS)

Coats, D. E.; Cebeci, T.

1982-03-01

The requirements for a replacement to the Bartz boundary layer code, the standard method of computing the performance loss due to viscous effects by the solid performance program, were discussed by the propulsion community along with four nationally recognized boundary layer experts. A consensus was reached regarding the preferred features for the analysis of the replacement code. The major points that were agreed upon are: (1) finite difference methods are preferred over integral methods; (2) a single equation eddy viscosity model was considered to be adequate for the purpose of computing performance loss; (3) a variable grid capability in both coordinate directions would be required; (4) a proven finite difference algorithm which is not stability restricted should be used, that is, an implicit numerical scheme would be required; and (5) the replacement code should be able to compute both turbulent and laminar flows. The program should treat mass addition at the wall as well as being able to calculate a stagnation point starting line.

A solution to neural field equations by a recurrent neural network method

NASA Astrophysics Data System (ADS)

Alharbi, Abir

2012-09-01

Neural field equations (NFE) are used to model the activity of neurons in the brain, it is introduced from a single neuron 'integrate-and-fire model' starting point. The neural continuum is spatially discretized for numerical studies, and the governing equations are modeled as a system of ordinary differential equations. In this article the recurrent neural network approach is used to solve this system of ODEs. This consists of a technique developed by combining the standard numerical method of finite-differences with the Hopfield neural network. The architecture of the net, energy function, updating equations, and algorithms are developed for the NFE model. A Hopfield Neural Network is then designed to minimize the energy function modeling the NFE. Results obtained from the Hopfield-finite-differences net show excellent performance in terms of accuracy and speed. The parallelism nature of the Hopfield approaches may make them easier to implement on fast parallel computers and give them the speed advantage over the traditional methods.

Moisture Transport in Composites during Repair Work,

DTIC Science & Technology

1983-09-01

4 * FINITE DIFFERENCE EQUATIONS. .. . . .. . .. .. .. .. .. 6 INI I A ANBOUNAAYYCONDITIONS................ 7 REASONABLE FIRST...DURING DRYING AND CURING . . . ........ 9 5 CONVERGENCE OF FINITE DIFFERENCE METHOD USING DIFFERENT At . . .. 12 6 CONVERGENCE OF FDA METHOD FOR SAME At...transport we will use a finite difference approach, changing the Fickian equation to a finite number of linear algebraic equations that can be solved by

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

A Second Order Semi-Discrete Cosserat Rod Model Suitable for Dynamic Simulations in Real Time

NASA Astrophysics Data System (ADS)

Lang, Holger; Linn, Joachim

2009-09-01

We present an alternative approach for a semi-discrete viscoelastic Cosserat rod model that allows both fast dynamic computations within milliseconds and accurate results compared to detailed finite element solutions. The model is able to represent extension, shearing, bending and torsion. For inner dissipation, a consistent damping potential from Antman is chosen. The continuous equations of motion, which consist a system of nonlinear hyperbolic partial differential algebraic equations, are derived from a two dimensional variational principle. The semi-discrete balance equations are obtained by spatial finite difference schemes on a staggered grid and standard index reduction techniques. The right-hand side of the model and its Jacobian can be chosen free of higher algebraic (e.g. root) or transcendent (e.g. trigonometric or exponential) functions and is therefore extremely cheap to evaluate numerically. For the time integration of the system, we use well established stiff solvers. As our model yields computational times within milliseconds, it is suitable for interactive manipulation. It reflects structural mechanics solutions sufficiently correct, as comparison with detailed finite element results shows.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

MSC products for the simulation of tire behavior

NASA Technical Reports Server (NTRS)

Muskivitch, John C.

1995-01-01

The modeling of tires and the simulation of tire behavior are complex problems. The MacNeal-Schwendler Corporation (MSC) has a number of finite element analysis products that can be used to address the complexities of tire modeling and simulation. While there are many similarities between the products, each product has a number of capabilities that uniquely enable it to be used for a specific aspect of tire behavior. This paper discusses the following programs: (1) MSC/NASTRAN - general purpose finite element program for linear and nonlinear static and dynamic analysis; (2) MSC/ADAQUS - nonlinear statics and dynamics finite element program; (3) MSC/PATRAN AFEA (Advanced Finite Element Analysis) - general purpose finite element program with a subset of linear and nonlinear static and dynamic analysis capabilities with an integrated version of MSC/PATRAN for pre- and post-processing; and (4) MSC/DYTRAN - nonlinear explicit transient dynamics finite element program.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Seakeeping with the semi-Lagrangian particle finite element method

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio

2017-07-01

The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

Tiny surface plasmon resonance sensor integrated on silicon waveguide based on vertical coupling into finite metal-insulator-metal plasmonic waveguide.

PubMed

Lee, Dong-Jin; Yim, Hae-Dong; Lee, Seung-Gol; O, Beom-Hoan

2011-10-10

We propose a tiny surface plasmon resonance (SPR) sensor integrated on a silicon waveguide based on vertical coupling into a finite thickness metal-insulator-metal (f-MIM) plasmonic waveguide structure acting as a Fabry-Perot resonator. The resonant characteristics of vertically coupled f-MIM plasmonic waveguides are theoretically investigated and optimized. Numerical results show that the SPR sensor with a footprint of ~0.0375 μm2 and a sensitivity of ~635 nm/RIU can be designed at a 1.55 μm transmission wavelength.

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

Nano-islands integrated evanescence-based lab-on-a-chip on silica-on-silicon and polydimethylsiloxane hybrid platform for detection of recombinant growth hormone

PubMed Central

Ozhikandathil, J.; Packirisamy, M.

2012-01-01

Integration of nano-materials in optical microfluidic devices facilitates the realization of miniaturized analytical systems with enhanced sensing abilities for biological and chemical substances. In this work, a novel method of integration of gold nano-islands in a silica-on-silicon-polydimethylsiloxane microfluidic device is reported. The device works based on the nano-enhanced evanescence technique achieved by interacting the evanescent tail of propagating wave with the gold nano-islands integrated on the core of the waveguide resulting in the modification of the propagating UV-visible spectrum. The biosensing ability of the device is investigated by finite-difference time-domain simulation with a simplified model of the device. The performance of the proposed device is demonstrated for the detection of recombinant growth hormone based on antibody-antigen interaction. PMID:24106526

STARS: An integrated general-purpose finite element structural, aeroelastic, and aeroservoelastic analysis computer program

NASA Technical Reports Server (NTRS)

Gupta, Kajal K.

1991-01-01

The details of an integrated general-purpose finite element structural analysis computer program which is also capable of solving complex multidisciplinary problems is presented. Thus, the SOLIDS module of the program possesses an extensive finite element library suitable for modeling most practical problems and is capable of solving statics, vibration, buckling, and dynamic response problems of complex structures, including spinning ones. The aerodynamic module, AERO, enables computation of unsteady aerodynamic forces for both subsonic and supersonic flow for subsequent flutter and divergence analysis of the structure. The associated aeroservoelastic analysis module, ASE, effects aero-structural-control stability analysis yielding frequency responses as well as damping characteristics of the structure. The program is written in standard FORTRAN to run on a wide variety of computers. Extensive graphics, preprocessing, and postprocessing routines are also available pertaining to a number of terminals.

A combined finite element-boundary element formulation for solution of axially symmetric bodies

NASA Technical Reports Server (NTRS)

Collins, Jeffrey D.; Volakis, John L.

1991-01-01

A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.

Comparison of finite-difference schemes for analysis of shells of revolution. [stress and free vibration analysis

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.

Stress and Fracture Analyses Under Elastic-plastic and Creep Conditions: Some Basic Developments and Computational Approaches

NASA Technical Reports Server (NTRS)

Reed, K. W.; Stonesifer, R. B.; Atluri, S. N.

1983-01-01

A new hybrid-stress finite element algorith, suitable for analyses of large quasi-static deformations of inelastic solids, is presented. Principal variables in the formulation are the nominal stress-rate and spin. A such, a consistent reformulation of the constitutive equation is necessary, and is discussed. The finite element equations give rise to an initial value problem. Time integration has been accomplished by Euler and Runge-Kutta schemes and the superior accuracy of the higher order schemes is noted. In the course of integration of stress in time, it has been demonstrated that classical schemes such as Euler's and Runge-Kutta may lead to strong frame-dependence. As a remedy, modified integration schemes are proposed and the potential of the new schemes for suppressing frame dependence of numerically integrated stress is demonstrated. The topic of the development of valid creep fracture criteria is also addressed.

Solfatara volcano subsurface imaging: two different approaches to process and interpret multi-variate data sets

NASA Astrophysics Data System (ADS)

Bernardinetti, Stefano; Bruno, Pier Paolo; Lavoué, François; Gresse, Marceau; Vandemeulebrouck, Jean; Revil, André

2017-04-01

The need to reduce model uncertainty and produce a more reliable geophysical imaging and interpretations is nowadays a fundamental task required to geophysics techniques applied in complex environments such as Solfatara Volcano. The use of independent geophysical methods allows to obtain many information on the subsurface due to the different sensitivities of the data towards parameters such as compressional and shearing wave velocities, bulk electrical conductivity, or density. The joint processing of these multiple physical properties can lead to a very detailed characterization of the subsurface and therefore enhance our imaging and our interpretation. In this work, we develop two different processing approaches based on reflection seismology and seismic P-wave tomography on one hand, and electrical data acquired over the same line, on the other hand. From these data, we obtain an image-guided electrical resistivity tomography and a post processing integration of tomographic results. The image-guided electrical resistivity tomography is obtained by regularizing the inversion of the electrical data with structural constraints extracted from a migrated seismic section using image processing tools. This approach enables to focus the reconstruction of electrical resistivity anomalies along the features visible in the seismic section, and acts as a guide for interpretation in terms of subsurface structures and processes. To integrate co-registrated P-wave velocity and electrical resistivity values, we apply a data mining tool, the k-means algorithm, to individuate relationships between the two set of variables. This algorithm permits to individuate different clusters with the objective to minimize the sum of squared Euclidean distances within each cluster and maximize it between clusters for the multivariate data set. We obtain a partitioning of the multivariate data set in a finite number of well-correlated clusters, representative of the optimum clustering of our geophysical variables (P-wave velocities and electrical resistivities). The result is an integrated tomography that shows a finite number of homogeneous geophysical facies, and therefore permits to highlight the main geological features of the subsurface.

Large deflection elastic-plastic dynamic response of stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Stricklin, J. A.; Haisler, W. E.; Vonriesemann, W. A.; Leick, R. D.; Hunsaker, B.; Saczalski, K. J.

1972-01-01

The formulation and check out porblems for a computer code DYNAPLAS, which analyzes the large deflection elastic-plastic dynamic response of stiffened shells of revolution, are presented. The formulation for special discretization is by the finite element method with finite differences being used for the evaluation of the pseudo forces due to material and geometric nonlinearities. Time integration is by the Houbolt method. The stiffeners may be due to concentrated or distributed eccentric rings and spring supports at arbitrary angles around the circumference of the elements. Check out porblems include the comparison of solutions from DYNAPLAS with experimental and other computer solutions for rings, conical and cylindrical shells and a curved panel. A hypothetical submarine including stiffeners and missile tube is studied under a combination of hydrostatic and dynamically applied asymmetrical pressure loadings.

Optics and Nonlinear Buckling Mechanics in Large-Area, Highly Stretchable Arrays of Plasmonic Nanostructures.

PubMed

Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A

2015-06-23

Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body.

NESSUS/NASTRAN Interface

NASA Technical Reports Server (NTRS)

Millwater, Harry; Riha, David

1996-01-01

The NESSUS and NASTRAN computer codes were successfully integrated. The enhanced NESSUS code will use NASTRAN for the structural Analysis and NESSUS for the probabilistic analysis. Any quantities in the NASTRAN bulk data input can be random variables. Any NASTRAN result that is written to the output2 file can be returned to NESSUS as the finite element result. The interfacing between NESSUS and NASTRAN is handled automatically by NESSUS. NESSUS and NASTRAN can be run on different machines using the remote host option.

Extended observability of linear time-invariant systems under recurrent loss of output data

NASA Technical Reports Server (NTRS)

Luck, Rogelio; Ray, Asok; Halevi, Yoram

1989-01-01

Recurrent loss of sensor data in integrated control systems of an advanced aircraft may occur under different operating conditions that include detected frame errors and queue saturation in computer networks, and bad data suppression in signal processing. This paper presents an extension of the concept of observability based on a set of randomly selected nonconsecutive outputs in finite-dimensional, linear, time-invariant systems. Conditions for testing extended observability have been established.

Verlet scheme non-conservativeness for simulation of spherical particles collisional dynamics and method of its compensation

NASA Astrophysics Data System (ADS)

Savin, Andrei V.; Smirnov, Petr G.

2018-05-01

Simulation of collisional dynamics of a large ensemble of monodisperse particles by the method of discrete elements is considered. Verle scheme is used for integration of the equations of motion. Non-conservativeness of the finite-difference scheme is discovered depending on the time step, which is equivalent to a pure-numerical energy source appearance in the process of collision. Compensation method for the source is proposed and tested.

FDTD Modeling and Counteraction to Scintillation Effects in the lonosphere

DTIC Science & Technology

2014-04-05

collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT...for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A, 23 (3), pp. 713-722, 2006. [21] Coe, R. L. and E. J...Seibel, “Improved near-field calculations using vectorial diffraction integrals in the finite-difference time-domain method,” J. Opt. Soc. Am. A, 28

Finite-size corrections in simulation of dipolar fluids

NASA Astrophysics Data System (ADS)

Belloni, Luc; Puibasset, Joël

2017-12-01

Monte Carlo simulations of dipolar fluids are performed at different numbers of particles N = 100-4000. For each size of the cubic cell, the non-spherically symmetric pair distribution function g(r,Ω) is accumulated in terms of projections gmnl(r) onto rotational invariants. The observed N dependence is in very good agreement with the theoretical predictions for the finite-size corrections of different origins: the explicit corrections due to the absence of fluctuations in the number of particles within the canonical simulation and the implicit corrections due to the coupling between the environment around a given particle and that around its images in the neighboring cells. The latter dominates in fluids of strong dipolar coupling characterized by low compressibility and high dielectric constant. The ability to clean with great precision the simulation data from these corrections combined with the use of very powerful anisotropic integral equation techniques means that exact correlation functions both in real and Fourier spaces, Kirkwood-Buff integrals, and bridge functions can be derived from box sizes as small as N ≈ 100, even with existing long-range tails. In the presence of dielectric discontinuity with the external medium surrounding the central box and its replica within the Ewald treatment of the Coulombic interactions, the 1/N dependence of the gmnl(r) is shown to disagree with the, yet well-accepted, prediction of the literature.

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method.

PubMed

Sasaki, Akira; Kojo, Masashi; Hirose, Kikuji; Goto, Hidekazu

2011-11-02

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

Manifesting enhanced cancellations in supergravity: integrands versus integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bern, Zvi; Enciso, Michael; Parra-Martinez, Julio

2017-05-25

We have found examples of `enhanced ultraviolet cancellations' with no known standard-symmetry explanation in a variety of supergravity theories. Furthermore, by examining one- and two-loop examples in four- and five-dimensional half-maximal supergravity, we argue that enhanced cancellations in general cannot be exhibited prior to integration. In light of this, we explore reorganizations of integrands into parts that are manifestly finite and parts that have poor power counting but integrate to zero due to integral identities. At two loops we find that in the large loop-momentum limit the required integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry outmore » a nontrivial check at four loops showing that the identities generated in this way are a complete set. We propose that at L loops the combination of Lorentz and SL(L) symmetry is sufficient for displaying enhanced cancellations when they happen, whenever the theory is known to be ultraviolet finite up to (L - 1) loops.« less

A total variation diminishing finite difference algorithm for sonic boom propagation models

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1993-01-01

It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.

Customized shaping of vibration modes by acoustic metamaterial synthesis

NASA Astrophysics Data System (ADS)

Xu, Jiawen; Li, Shilong; Tang, J.

2018-04-01

Acoustic metamaterials have attractive potential in elastic wave guiding and attenuation over specific frequency ranges. The vast majority of related investigations are on transient waves. In this research we focus on stationary wave manipulation, i.e., shaping of vibration modes. Periodically arranged piezoelectric transducers shunted with inductive circuits are integrated to a beam structure to form a finite-length metamaterial beam. We demonstrate for the first time that, under a given operating frequency of interest, we can facilitate a metamaterial design such that this frequency becomes a natural frequency of the integrated system. Moreover, the vibration mode corresponding to this natural frequency can be customized and shaped to realize tailored/localized response distribution. This is fundamentally different from previous practices of utilizing geometry modification and/or feedback control to achieve mode tailoring. The metamaterial design is built upon the combinatorial effects of the bandgap feature and the effective resonant cavity feature, both attributed to the dynamic characteristics of the metamaterial beam. Analytical investigations based on unit-cell dynamics and modal analysis of the metamaterial beam are presented to reveal the underlying mechanism. Case illustrations are validated by finite element analyses. Owing to the online tunability of circuitry integrated, the proposed mode shaping technique can be online adjusted to fit specific requirements. The customized shaping of vibration modes by acoustic metamaterial synthesis has potential applications in vibration suppression, sensing enhancement and energy harvesting.

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

Universal entanglement spectra of gapped one-dimensional field theories

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Ludwig, Andreas W. W.; Ryu, Shinsei

2017-03-01

We discuss the entanglement spectrum of the ground state of a (1+1)-dimensional system in a gapped phase near a quantum phase transition. In particular, in proximity to a quantum phase transition described by a conformal field theory (CFT), the system is represented by a gapped Lorentz invariant field theory in the "scaling limit" (correlation length ξ much larger than microscopic "lattice" scale "a "), and can be thought of as a CFT perturbed by a relevant perturbation. We show that for such (1+1) gapped Lorentz invariant field theories in infinite space, the low-lying entanglement spectrum obtained by tracing out, say, left half-infinite space, is precisely equal to the physical spectrum of the unperturbed gapless, i.e., conformal field theory defined on a finite interval of length Lξ=ln(ξ /a ) with certain boundary conditions. In particular, the low-lying entanglement spectrum of the gapped theory is the finite-size spectrum of a boundary conformal field theory, and is always discrete and universal. Each relevant perturbation, and thus each gapped phase in proximity to the quantum phase transition, maps into a particular boundary condition. A similar property has been known to hold for Baxter's corner transfer matrices in a very special class of fine-tuned, namely, integrable off-critical lattice models, for the entire entanglement spectrum and independent of the scaling limit. In contrast, our result applies to completely general gapped Lorentz invariant theories in the scaling limit, without the requirement of integrability, for the low-lying entanglement spectrum. While the entanglement spectrum of the ground state of a gapped theory on a finite interval of length 2 R with suitable boundary conditions, bipartitioned into two equal pieces, turns out to exhibit a crossover between the finite-size spectra of the same CFT with in general different boundary conditions as the system size R crosses the correlation length from the "critical regime'' R ≪ξ to the "gapped regime'' R ≫ξ , the physical spectrum on a finite interval of length R with the same boundary conditions, on the other hand, is known to undergo a dramatic reorganization during the same crossover from being discrete to being continuous.

Method for calculating the aerodynamic loading on an oscillating finite wing in subsonic and sonic flow

NASA Technical Reports Server (NTRS)

Runyan, Harry L; Woolston, Donald S

1957-01-01

A method is presented for calculating the loading on a finite wing oscillating in subsonic or sonic flow. The method is applicable to any plan form and may be used for determining the loading on deformed wings. The procedure is approximate and requires numerical integration over the wing surface.

FDTD simulation of EM wave propagation in 3-D media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, T.; Tripp, A.C.

1996-01-01

A finite-difference, time-domain solution to Maxwell`s equations has been developed for simulating electromagnetic wave propagation in 3-D media. The algorithm allows arbitrary electrical conductivity and permittivity variations within a model. The staggered grid technique of Yee is used to sample the fields. A new optimized second-order difference scheme is designed to approximate the spatial derivatives. Like the conventional fourth-order difference scheme, the optimized second-order scheme needs four discrete values to calculate a single derivative. However, the optimized scheme is accurate over a wider wavenumber range. Compared to the fourth-order scheme, the optimized scheme imposes stricter limitations on the time stepmore » sizes but allows coarser grids. The net effect is that the optimized scheme is more efficient in terms of computation time and memory requirement than the fourth-order scheme. The temporal derivatives are approximated by second-order central differences throughout. The Liao transmitting boundary conditions are used to truncate an open problem. A reflection coefficient analysis shows that this transmitting boundary condition works very well. However, it is subject to instability. A method that can be easily implemented is proposed to stabilize the boundary condition. The finite-difference solution is compared to closed-form solutions for conducting and nonconducting whole spaces and to an integral-equation solution for a 3-D body in a homogeneous half-space. In all cases, the finite-difference solutions are in good agreement with the other solutions. Finally, the use of the algorithm is demonstrated with a 3-D model. Numerical results show that both the magnetic field response and electric field response can be useful for shallow-depth and small-scale investigations.« less

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

Prediction of Path Deviation in Robot Based Incremental Sheet Metal Forming by Means of a New Solid-Shell Finite Element Technology and a Finite Elastoplastic Model with Combined Hardening

NASA Astrophysics Data System (ADS)

Kiliclar, Yalin; Laurischkat, Roman; Vladimirov, Ivaylo N.; Reese, Stefanie

2011-08-01

The presented project deals with a robot based incremental sheet metal forming process, which is called roboforming and has been developed at the Chair of Production Systems. It is characterized by flexible shaping using a freely programmable path-synchronous movement of two industrial robots. The final shape is produced by the incremental infeed of the forming tool in depth direction and its movement along the part contour in lateral direction. However, the resulting geometries formed in roboforming deviate several millimeters from the reference geometry. This results from the compliance of the involved machine structures and the springback effects of the workpiece. The project aims to predict these deviations caused by resiliences and to carry out a compensative path planning based on this prediction. Therefore a planning tool is implemented which compensates the robots's compliance and the springback effects of the sheet metal. The forming process is simulated by means of a finite element analysis using a material model developed at the Institute of Applied Mechanics (IFAM). It is based on the multiplicative split of the deformation gradient in the context of hyperelasticity and combines nonlinear kinematic and isotropic hardening. Low-order finite elements used to simulate thin sheet structures, such as used for the experiments, have the major problem of locking, a nonphysical stiffening effect. For an efficient finite element analysis a special solid-shell finite element formulation based on reduced integration with hourglass stabilization has been developed. To circumvent different locking effects, the enhanced assumed strain (EAS) and the assumed natural strain (ANS) concepts are included in this formulation. Having such powerful tools available we obtain more accurate geometries.

The reality of artificial viscosity

DOE PAGES

Margolin, L. G.

2018-02-24

Artificial viscosity is used in the computer simulation of high Reynolds number flows and is one of the oldest numerical artifices. In this work, I will describe the origin and the interpretation of artificial viscosity as a physical phenomenon. The basis of this interpretation is the finite scale theory, which describes the evolution of integral averages of the fluid solution over finite (length) scales. I will outline the derivation of finite scale Navier–Stokes equations and highlight the particular properties of the equations that depend on the finite scales. Those properties include enslavement, inviscid dissipation, and a law concerning the partitionmore » of total flux of conserved quantities into advective and diffusive components.« less

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2016-04-01

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

The reality of artificial viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L. G.

Artificial viscosity is used in the computer simulation of high Reynolds number flows and is one of the oldest numerical artifices. In this work, I will describe the origin and the interpretation of artificial viscosity as a physical phenomenon. The basis of this interpretation is the finite scale theory, which describes the evolution of integral averages of the fluid solution over finite (length) scales. I will outline the derivation of finite scale Navier–Stokes equations and highlight the particular properties of the equations that depend on the finite scales. Those properties include enslavement, inviscid dissipation, and a law concerning the partitionmore » of total flux of conserved quantities into advective and diffusive components.« less

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

PubMed

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

DAMAGE ASSESSMENT OF RC BEAMS BY NONLINEAR FINITE ELEMENT ANALYSES

NASA Astrophysics Data System (ADS)

Saito, Shigehiko; Maki, Takeshi; Tsuchiya, Satoshi; Watanabe, Tadatomo

This paper presents damage assessment schemes by using 2-dimensional nonlinear finite element analyses. The second strain invariant of deviatoric strain tensor and consumed strain energy are calculated by local strain at each integration po int of finite elements. Those scalar values are averaged over certain region. The produced nonlocal values are used for indices to verify structural safety by confirming which the ultimate limit state for failure is reached or not. Flexural and shear failure of reinforced concrete beams are estimated by us ing the proposed indices.

Analysis of Large Quasistatic Deformations of Inelastic Solids by a New Stress Based Finite Element Method. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Reed, Kenneth W.

1992-01-01

A new hybrid stress finite element algorithm suitable for analyses of large quasistatic deformation of inelastic solids is presented. Principal variables in the formulation are the nominal stress rate and spin. The finite element equations which result are discrete versions of the equations of compatibility and angular momentum balance. Consistent reformulation of the constitutive equation and accurate and stable time integration of the stress are discussed at length. Examples which bring out the feasibility and performance of the algorithm conclude the work.

A mixed shear flexible finite element for the analysis of laminated plates

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1984-01-01

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.

Reliability analysis of laminated CMC components through shell subelement techniques

NASA Technical Reports Server (NTRS)

Starlinger, A.; Duffy, S. F.; Gyekenyesi, J. P.

1992-01-01

An updated version of the integrated design program C/CARES (composite ceramic analysis and reliability evaluation of structures) was developed for the reliability evaluation of CMC laminated shell components. The algorithm is now split in two modules: a finite-element data interface program and a reliability evaluation algorithm. More flexibility is achieved, allowing for easy implementation with various finite-element programs. The new interface program from the finite-element code MARC also includes the option of using hybrid laminates and allows for variations in temperature fields throughout the component.

Solid/FEM integration at SNLA

NASA Technical Reports Server (NTRS)

Chavez, Patrick F.

1987-01-01

The effort at Sandia National Labs. on the methodologies and techniques being used to generate strict hexahedral finite element meshes from a solid model is described. The functionality of the modeler is used to decompose the solid into a set of nonintersecting meshable finite element primitives. The description of the decomposition is exported, via a Boundary Representative format, to the meshing program which uses the information for complete finite element model specification. Particular features of the program are discussed in some detail along with future plans for development which includes automation of the decomposition using artificial intelligence techniques.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Numerical calculations of velocity and pressure distribution around oscillating airfoils

NASA Technical Reports Server (NTRS)

Bratanow, T.; Ecer, A.; Kobiske, M.

1974-01-01

An analytical procedure based on the Navier-Stokes equations was developed for analyzing and representing properties of unsteady viscous flow around oscillating obstacles. A variational formulation of the vorticity transport equation was discretized in finite element form and integrated numerically. At each time step of the numerical integration, the velocity field around the obstacle was determined for the instantaneous vorticity distribution from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints, using the Lagrangian Multiplier Technique, at each time step of the numerical integration. The procedure was then applied for determining pressures around obstacles oscillating in unsteady flow. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

On the superposition principle in interference experiments.

PubMed

Sinha, Aninda; H Vijay, Aravind; Sinha, Urbasi

2015-05-14

The superposition principle is usually incorrectly applied in interference experiments. This has recently been investigated through numerics based on Finite Difference Time Domain (FDTD) methods as well as the Feynman path integral formalism. In the current work, we have derived an analytic formula for the Sorkin parameter which can be used to determine the deviation from the application of the principle. We have found excellent agreement between the analytic distribution and those that have been earlier estimated by numerical integration as well as resource intensive FDTD simulations. The analytic handle would be useful for comparing theory with future experiments. It is applicable both to physics based on classical wave equations as well as the non-relativistic Schrödinger equation.

Meshfree Modeling of Munitions Penetration in Soils

DTIC Science & Technology

2017-04-01

discretization ...................... 8 Figure 2. Nodal smoothing domain for the modified stabilized nonconforming nodal integration...projectile ............................................................................................... 36 Figure 17. Discretization for the...List of Acronyms DEM: discrete element methods FEM: finite element methods MSNNI: modified stabilized nonconforming nodal integration RK

The behavior of integral abutment bridges.

DOT National Transportation Integrated Search

1999-01-01

This report presents findings of a literature review, a field trip, and a finite element analysis pertaining to integral bridges. The purpose of the report is to identify problems and uncertainties, and to gain insight into the interactions between t...

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study.

PubMed

Zhan, He-qing; Xia, Ling; Shou, Guo-fa; Zang, Yun-liang; Liu, Feng; Crozier, Stuart

2014-03-01

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies.

Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study*

PubMed Central

Zhan, He-qing; Xia, Ling; Shou, Guo-fa; Zang, Yun-liang; Liu, Feng; Crozier, Stuart

2014-01-01

In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. Fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies. PMID:24599687

Simulation of silicon thin-film solar cells for oblique incident waves

NASA Astrophysics Data System (ADS)

Jandl, Christine; Hertel, Kai; Pflaum, Christoph; Stiebig, Helmut

2011-05-01

To optimize the quantum efficiency (QE) and short-circuit current density (JSC) of silicon thin-film solar cells, one has to study the behavior of sunlight in these solar cells. Simulations are an adequate and economic method to analyze the optical properties of light caused by absorption and reflection. To this end a simulation tool is developed to take several demands into account. These include the analysis of perpendicular and oblique incident waves under E-, H- and circularly polarized light. Furthermore, the topology of the nanotextured interfaces influences the efficiency and therefore also the short-circuit current density. It is well known that a rough transparent conductive oxide (TCO) layer increases the efficiency of solar cells. Therefore, it is indispensable that various roughness profiles at the interfaces of the solar cell layers can be modeled in such a way that atomic force microscope (AFM) scan data can be integrated. Numerical calculations of Maxwell's equations based on the finite integration technique (FIT) and Finite Difference Time Domain (FDTD) method are necessary to incorporate all these requirements. The simulations are performed in parallel on high performance computers (HPC) to meet the large computational requirements.

A comparative study of finite element and finite difference methods for Cauchy-Riemann type equations

NASA Technical Reports Server (NTRS)

Fix, G. J.; Rose, M. E.

1983-01-01

A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.

Adapting Surface Ground Motion Relations to Underground conditions: A case study for the Sudbury Neutrino Observatory in Sudbury, Ontario, Canada

NASA Astrophysics Data System (ADS)

Babaie Mahani, A.; Eaton, D. W.

2013-12-01

Ground Motion Prediction Equations (GMPEs) are widely used in Probabilistic Seismic Hazard Assessment (PSHA) to estimate ground-motion amplitudes at Earth's surface as a function of magnitude and distance. Certain applications, such as hazard assessment for caprock integrity in the case of underground storage of CO2, waste disposal sites, and underground pipelines, require subsurface estimates of ground motion; at present, such estimates depend upon theoretical modeling and simulations. The objective of this study is to derive correction factors for GMPEs to enable estimation of amplitudes in the subsurface. We use a semi-analytic approach along with finite-difference simulations of ground-motion amplitudes for surface and underground motions. Spectral ratios of underground to surface motions are used to calculate the correction factors. Two predictive methods are used. The first is a semi-analytic approach based on a quarter-wavelength method that is widely used for earthquake site-response investigations; the second is a numerical approach based on elastic finite-difference simulations of wave propagation. Both methods are evaluated using recordings of regional earthquakes by broadband seismometers installed at the surface and at depths of 1400 m and 2100 m in the Sudbury Neutrino Observatory, Canada. Overall, both methods provide a reasonable fit to the peaks and troughs observed in the ratios of real data. The finite-difference method, however, has the capability to simulate ground motion ratios more accurately than the semi-analytic approach.

Low speed airfoil design and analysis

NASA Technical Reports Server (NTRS)

Eppler, R.; Somers, D. M.

1979-01-01

A low speed airfoil design and analysis program was developed which contains several unique features. In the design mode, the velocity distribution is not specified for one but many different angles of attack. Several iteration options are included which allow the trailing edge angle to be specified while other parameters are iterated. For airfoil analysis, a panel method is available which uses third-order panels having parabolic vorticity distributions. The flow condition is satisfied at the end points of the panels. Both sharp and blunt trailing edges can be analyzed. The integral boundary layer method with its laminar separation bubble analog, empirical transition criterion, and precise turbulent boundary layer equations compares very favorably with other methods, both integral and finite difference. Comparisons with experiment for several airfoils over a very wide Reynolds number range are discussed. Applications to high lift airfoil design are also demonstrated.

Broadband enhancement of single photon emission and polarization dependent coupling in silicon nitride waveguides.

PubMed

Bisschop, Suzanne; Guille, Antoine; Van Thourhout, Dries; Hens, Zeger; Brainis, Edouard

2015-06-01

Single-photon (SP) sources are important for a number of optical quantum information processing applications. We study the possibility to integrate triggered solid-state SP emitters directly on a photonic chip. A major challenge consists in efficiently extracting their emission into a single guided mode. Using 3D finite-difference time-domain simulations, we investigate the SP emission from dipole-like nanometer-sized inclusions embedded into different silicon nitride (SiNx) photonic nanowire waveguide designs. We elucidate the effect of the geometry on the emission lifetime and the polarization of the emitted SP. The results show that highly efficient and polarized SP sources can be realized using suspended SiNx slot-waveguides. Combining this with the well-established CMOS-compatible processing technology, fully integrated and complex optical circuits for quantum optics experiments can be developed.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.

PubMed

Chen, Qiang; Ren, Xuemei; Na, Jing

2015-09-01

In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Binary neutron star merger simulations with different initial orbital frequency and equation of state

NASA Astrophysics Data System (ADS)

Maione, F.; De Pietri, R.; Feo, A.; Löffler, F.

2016-09-01

We present results from three-dimensional general relativistic simulations of binary neutron star coalescences and mergers using public codes. We considered equal mass models where the baryon mass of the two neutron stars is 1.4{M}⊙ , described by four different equations of state (EOS) for the cold nuclear matter (APR4, SLy, H4, and MS1; all parametrized as piecewise polytropes). We started the simulations from four different initial interbinary distances (40,44.3,50, and 60 km), including up to the last 16 orbits before merger. That allows us to show the effects on the gravitational wave (GW) phase evolution, radiated energy and angular momentum due to: the use of different EOS, the orbital eccentricity present in the initial data and the initial separation (in the simulation) between the two stars. Our results show that eccentricity has a major role in the discrepancy between numerical and analytical waveforms until the very last few orbits, where ‘tidal’ effects and missing high-order post-Newtonian coefficients also play a significant role. We test different methods for extrapolating the GW signal extracted at finite radii to null infinity. We show that an effective procedure for integrating the Newman-Penrose {\\psi }4 signal to obtain the GW strain h is to apply a simple high-pass digital filter to h after a time domain integration, where only the two physical motivated integration constants are introduced. That should be preferred to the more common procedures of introducing additional integration constants, integrating in the frequency domain or filtering {\\psi }4 before integration.

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology. Appendix C -- Finite Element Models Solution Database File, Appendix D -- Benchmark Finite Element Models Solution Database File

NASA Technical Reports Server (NTRS)

Allen, Phillip A.; Wells, Douglas N.

2013-01-01

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

NASA Technical Reports Server (NTRS)

Stein, M.; Housner, J. D.

1978-01-01

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Integral Equations and Scattering Solutions for a Square-Well Potential.

ERIC Educational Resources Information Center

Bagchi, B.; Seyler, R. G.

1979-01-01

Derives Green's functions and integral equations for scattering solutions subject to a variety of boundary conditions. Exact solutions are obtained for the case of a finite spherical square-well potential, and properties of these solutions are discussed. (Author/HM)

A finite element boundary integral formulation for radiation and scattering by cavity antennas using tetrahedral elements

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.; Chatterjee, A.; Jin, J. M.

1992-01-01

A hybrid finite element boundary integral formulation is developed using tetrahedral and/or triangular elements for discretizing the cavity and/or aperture of microstrip antenna arrays. The tetrahedral elements with edge based linear expansion functions are chosen for modeling the volume region and triangular elements are used for discretizing the aperture. The edge based expansion functions are divergenceless thus removing the requirement to introduce a penalty term and the tetrahedral elements permit greater geometrical adaptability than the rectangular bricks. The underlying theory and resulting expressions are discussed in detail together with some numerical scattering examples for comparison and demonstration.

On high-order perturbative calculations at finite density

DOE PAGES

Ghisoiu, Ioan; Gorda, Tyler; Kurkela, Aleksi; ...

2016-12-01

We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes — aresult reminiscent of a previously proposed “naive real-time formalism” for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbativemore » orders.« less

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

NASA Astrophysics Data System (ADS)

Zuchowski, Loïc; Brun, Michael; De Martin, Florent

2018-05-01

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

Asynchronous variational integration using continuous assumed gradient elements.

PubMed

Wolff, Sebastian; Bucher, Christian

2013-03-01

Asynchronous variational integration (AVI) is a tool which improves the numerical efficiency of explicit time stepping schemes when applied to finite element meshes with local spatial refinement. This is achieved by associating an individual time step length to each spatial domain. Furthermore, long-term stability is ensured by its variational structure. This article presents AVI in the context of finite elements based on a weakened weak form (W2) Liu (2009) [1], exemplified by continuous assumed gradient elements Wolff and Bucher (2011) [2]. The article presents the main ideas of the modified AVI, gives implementation notes and a recipe for estimating the critical time step.

Coupled NASTRAN/boundary element formulation for acoustic scattering

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Henderson, Francis M.; Schuetz, Luise S.

1987-01-01

A coupled finite element/boundary element capability is described for calculating the sound pressure field scattered by an arbitrary submerged 3-D elastic structure. Structural and fluid impedances are calculated with no approximation other than discretization. The surface fluid pressures and normal velocities are first calculated by coupling a NASTRAN finite element model of the structure with a discretized form of the Helmholtz surface integral equation for the exterior field. Far field pressures are then evaluated from the surface solution using the Helmholtz exterior integral equation. The overall approach is illustrated and validated using a known analytic solution for scattering from submerged spherical shells.

Magnitude of finite-nucleus-size effects in relativistic density functional computations of indirect NMR nuclear spin-spin coupling constants.

PubMed

Autschbach, Jochen

2009-09-14

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

Simplicial Palatini action

NASA Astrophysics Data System (ADS)

Khatsymovsky, V. M.

2018-01-01

We consider the piecewise flat spacetime and a simplicial analog of the Palatini form of the general relativity (GR) action where the discrete Christoffel symbols are given on the tetrahedra as variables that are independent of the metric. Excluding these variables with the help of the equations of motion gives exactly the Regge action. This paper continues our previous work. Now, we include the parity violation term and the analog of the Barbero-Immirzi parameter introduced in the orthogonal connection form of GR. We consider the path integral and the functional integration over the connection. The result of the latter (for certain limiting cases of some parameters) is compared with the earlier found result of the functional integration over the connection for the analogous orthogonal connection representation of Regge action. These results, mainly as some measures on the lengths/areas, are discussed for the possibility of the diagram technique where the perturbative diagrams for the Regge action calculated using the measure obtained are finite. This finiteness is due to these measures providing elementary lengths being mostly bounded and separated from zero, just as the finiteness of a theory on a lattice with an analogous probability distribution of spacings.

Vorticity dipoles and a theoretical model of a finite force at the moving contact line singularity

NASA Astrophysics Data System (ADS)

Zhang, Peter; Devoria, Adam; Mohseni, Kamran

2017-11-01

In the well known works of Moffatt (1964) and Huh & Scriven (1971), an infinite force was reported at the moving contact line (MCL) and attributed to a non-integrable stress along the fluid-solid boundary. In our recent investigation of the boundary driven wedge, a model of the MCL, we find that the classical solution theoretically predicts a finite force at the contact line if the forces applied by the two boundaries that make up the corner are taken into consideration. Mathematically, this force can be obtained by the complex contour integral of the holomorphic vorticity-pressure function given by G = μω + ip . Alternatively, this force can also be found using a carefully defined real integral that incorporates the two boundaries. Motivated by this discovery, we have found that the rate of change in circulation, viscous energy dissipation, and viscous energy flux is also finite per unit contact line length. The analysis presented demonstrates that despite a singular stress and a relatively simple geometry, the no-slip semi-infinite wedge is capable of capturing some physical quantities of interest. Furthermore, this result provides a foundation for other challenging topics such as dynamic contact angle.

Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence.

PubMed

Soltwisch, Victor; Hönicke, Philipp; Kayser, Yves; Eilbracht, Janis; Probst, Jürgen; Scholze, Frank; Beckhoff, Burkhard

2018-03-29

The geometry of a Si3N4 lamellar grating was investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. While simple layered systems are usually treated with the matrix formalism to determine the X-ray standing-wave field, this approach fails for laterally structured surfaces. Maxwell solvers based on finite elements are often used to model electrical field strengths for any 2D or 3D structures in the optical spectral range. We show that this approach can also be applied in the field of X-rays. The electrical field distribution obtained with the Maxwell solver can subsequently be used to calculate the fluorescence intensities in full analogy to the X-ray standing-wave field obtained by the matrix formalism. Only the effective 1D integration for the layer system has to be replaced by a 2D integration of the finite elements, taking into account the local excitation conditions. We will show that this approach is capable of reconstructing the geometric line shape of a structured surface with high elemental sensitivity. This combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.

The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions

NASA Technical Reports Server (NTRS)

Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan

1995-01-01

The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.

Development and Application of Compatible Discretizations of Maxwell's Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, D; Koning, J; Rieben, R

We present the development and application of compatible finite element discretizations of electromagnetics problems derived from the time dependent, full wave Maxwell equations. We review the H(curl)-conforming finite element method, using the concepts and notations of differential forms as a theoretical framework. We chose this approach because it can handle complex geometries, it is free of spurious modes, it is numerically stable without the need for filtering or artificial diffusion, it correctly models the discontinuity of fields across material boundaries, and it can be very high order. Higher-order H(curl) and H(div) conforming basis functions are not unique and we havemore » designed an extensible C++ framework that supports a variety of specific instantiations of these such as standard interpolatory bases, spectral bases, hierarchical bases, and semi-orthogonal bases. Virtually any electromagnetics problem that can be cast in the language of differential forms can be solved using our framework. For time dependent problems a method-of-lines scheme is used where the Galerkin method reduces the PDE to a semi-discrete system of ODE's, which are then integrated in time using finite difference methods. For time integration of wave equations we employ the unconditionally stable implicit Newmark-Beta method, as well as the high order energy conserving explicit Maxwell Symplectic method; for diffusion equations, we employ a generalized Crank-Nicholson method. We conclude with computational examples from resonant cavity problems, time-dependent wave propagation problems, and transient eddy current problems, all obtained using the authors massively parallel computational electromagnetics code EMSolve.« less

Mixed Integer PDE Constrained Optimization for the Control of a Wildfire Hazard

DTIC Science & Technology

2017-01-01

are nodes suitable for extinguishing the fire. We introduce a discretization of the time horizon [0, T] by the set of time T := {0, At,..., ntZ\\t = T...of the constraints and objective with a discrete counterpart. The PDE is replaced by a linear system obtained from a convergent finite difference...method [5] and the integral is replaced by a quadrature formula. The domain is discretized by replacing 17 with an equidistant grid of length Ax

Time-Domain Computation Of Electromagnetic Fields In MMICs

NASA Technical Reports Server (NTRS)

Lansing, Faiza S.; Rascoe, Daniel L.

1995-01-01

Maxwell's equations solved on three-dimensional, conformed orthogonal grids by finite-difference techniques. Method of computing frequency-dependent electrical parameters of monolithic microwave integrated circuit (MMIC) involves time-domain computation of propagation of electromagnetic field in response to excitation by single pulse at input terminal, followed by computation of Fourier transforms to obtain frequency-domain response from time-domain response. Parameters computed include electric and magnetic fields, voltages, currents, impedances, scattering parameters, and effective dielectric constants. Powerful and efficient means for analyzing performance of even complicated MMIC.

On Leighton's comparison theorem

NASA Astrophysics Data System (ADS)

Ghatasheh, Ahmed; Weikard, Rudi

2017-06-01

We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.

Numerical calculations of two dimensional, unsteady transonic flows with circulation

NASA Technical Reports Server (NTRS)

Beam, R. M.; Warming, R. F.

1974-01-01

The feasibility of obtaining two-dimensional, unsteady transonic aerodynamic data by numerically integrating the Euler equations is investigated. An explicit, third-order-accurate, noncentered, finite-difference scheme is used to compute unsteady flows about airfoils. Solutions for lifting and nonlifting airfoils are presented and compared with subsonic linear theory. The applicability and efficiency of the numerical indicial function method are outlined. Numerically computed subsonic and transonic oscillatory aerodynamic coefficients are presented and compared with those obtained from subsonic linear theory and transonic wind-tunnel data.

Active Vibration damping of Smart composite beams based on system identification technique

NASA Astrophysics Data System (ADS)

Bendine, Kouider; Satla, Zouaoui; Boukhoulda, Farouk Benallel; Nouari, Mohammed

2018-03-01

In the present paper, the active vibration control of a composite beam using piezoelectric actuator is investigated. The space state equation is determined using system identification technique based on the structure input output response provided by ANSYS APDL finite element package. The Linear Quadratic (LQG) control law is designed and integrated into ANSYS APDL to perform closed loop simulations. Numerical examples for different types of excitation loads are presented to test the efficiency and the accuracy of the proposed model.

Sensitivities Kernels of Seismic Traveltimes and Amplitudes for Quality Factor and Boundary Topography

NASA Astrophysics Data System (ADS)

Hsieh, M.; Zhao, L.; Ma, K.

2010-12-01

Finite-frequency approach enables seismic tomography to fully utilize the spatial and temporal distributions of the seismic wavefield to improve resolution. In achieving this goal, one of the most important tasks is to compute efficiently and accurately the (Fréchet) sensitivity kernels of finite-frequency seismic observables such as traveltime and amplitude to the perturbations of model parameters. In scattering-integral approach, the Fréchet kernels are expressed in terms of the strain Green tensors (SGTs), and a pre-established SGT database is necessary to achieve practical efficiency for a three-dimensional reference model in which the SGTs must be calculated numerically. Methods for computing Fréchet kernels for seismic velocities have long been established. In this study, we develop algorithms based on the finite-difference method for calculating Fréchet kernels for the quality factor Qμ and seismic boundary topography. Kernels for the quality factor can be obtained in a way similar to those for seismic velocities with the help of the Hilbert transform. The effects of seismic velocities and quality factor on either traveltime or amplitude are coupled. Kernels for boundary topography involve spatial gradient of the SGTs and they also exhibit interesting finite-frequency characteristics. Examples of quality factor and boundary topography kernels will be shown for a realistic model for the Taiwan region with three-dimensional velocity variation as well as surface and Moho discontinuity topography.

Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.; Broduer, Steve (Technical Monitor)

2001-01-01

Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.

Differentiable representations of finite dimensional Lie groups in rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Wickramasekara, Sujeewa

The inceptive motivation for introducing rigged Hilbert spaces (RHS) in quantum physics in the mid 1960's was to provide the already well established Dirac formalism with a proper mathematical context. It has since become clear, however, that this mathematical framework is lissome enough to accommodate a class of solutions to the dynamical equations of quantum physics that includes some which are not possible in the normative Hilbert space theory. Among the additional solutions, in particular, are those which describe aspects of scattering and decay phenomena that have eluded the orthodox quantum physics. In this light, the RHS formulation seems to provide a mathematical rubric under which various phenomenological observations and calculational techniques, commonly known in the study of resonance scattering and decay as ``effective theories'' (e.g., the Wigner- Weisskopf method), receive a unified theoretical foundation. These observations lead to the inference that a theory founded upon the RHS mathematics may prove to be of better utility and value in understanding quantum physical phenomena. This dissertation primarily aims to contribute to the general formalism of the RHS theory of quantum mechanics by undertaking a study of differentiable representations of finite dimensional Lie groups. In particular, it is shown that a finite dimensional operator Lie algebra G in a rigged Hilbert space can be always integrated, provided one parameter integrability holds true for the elements of any basis for G . This result differs from and extends the well known integration theorem of E. Nelson and the subsequent works of others on unitary representations in that it does not require any assumptions on the existence of analytic vectors. Also presented here is a construction of a particular rigged Hilbert space of Hardy class functions that appears useful in formulating a relativistic version of the RHS theory of resonances and decay. As a contexture for the construction, a synopsis of the new relativistic theory is presented.

Challenges in Integrating Nondestructive Evaluation and Finite Element Methods for Realistic Structural Analysis

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali; Baaklini, George Y.; Zagidulin, Dmitri; Rauser, Richard W.

2000-01-01

Capabilities and expertise related to the development of links between nondestructive evaluation (NDE) and finite element analysis (FEA) at Glenn Research Center (GRC) are demonstrated. Current tools to analyze data produced by computed tomography (CT) scans are exercised to help assess the damage state in high temperature structural composite materials. A utility translator was written to convert velocity (an image processing software) STL data file to a suitable CAD-FEA type file. Finite element analyses are carried out with MARC, a commercial nonlinear finite element code, and the analytical results are discussed. Modeling was established by building MSC/Patran (a pre and post processing finite element package) generated model and comparing it to a model generated by Velocity in conjunction with MSC/Patran Graphics. Modeling issues and results are discussed in this paper. The entire process that outlines the tie between the data extracted via NDE and the finite element modeling and analysis is fully described.

An expert system for integrated structural analysis and design optimization for aerospace structures

NASA Technical Reports Server (NTRS)

1992-01-01

The results of a research study on the development of an expert system for integrated structural analysis and design optimization is presented. An Object Representation Language (ORL) was developed first in conjunction with a rule-based system. This ORL/AI shell was then used to develop expert systems to provide assistance with a variety of structural analysis and design optimization tasks, in conjunction with procedural modules for finite element structural analysis and design optimization. The main goal of the research study was to provide expertise, judgment, and reasoning capabilities in the aerospace structural design process. This will allow engineers performing structural analysis and design, even without extensive experience in the field, to develop error-free, efficient and reliable structural designs very rapidly and cost-effectively. This would not only improve the productivity of design engineers and analysts, but also significantly reduce time to completion of structural design. An extensive literature survey in the field of structural analysis, design optimization, artificial intelligence, and database management systems and their application to the structural design process was first performed. A feasibility study was then performed, and the architecture and the conceptual design for the integrated 'intelligent' structural analysis and design optimization software was then developed. An Object Representation Language (ORL), in conjunction with a rule-based system, was then developed using C++. Such an approach would improve the expressiveness for knowledge representation (especially for structural analysis and design applications), provide ability to build very large and practical expert systems, and provide an efficient way for storing knowledge. Functional specifications for the expert systems were then developed. The ORL/AI shell was then used to develop a variety of modules of expert systems for a variety of modeling, finite element analysis, and design optimization tasks in the integrated aerospace structural design process. These expert systems were developed to work in conjunction with procedural finite element structural analysis and design optimization modules (developed in-house at SAT, Inc.). The complete software, AutoDesign, so developed, can be used for integrated 'intelligent' structural analysis and design optimization. The software was beta-tested at a variety of companies, used by a range of engineers with different levels of background and expertise. Based on the feedback obtained by such users, conclusions were developed and are provided.

An expert system for integrated structural analysis and design optimization for aerospace structures

NASA Astrophysics Data System (ADS)

1992-04-01

The results of a research study on the development of an expert system for integrated structural analysis and design optimization is presented. An Object Representation Language (ORL) was developed first in conjunction with a rule-based system. This ORL/AI shell was then used to develop expert systems to provide assistance with a variety of structural analysis and design optimization tasks, in conjunction with procedural modules for finite element structural analysis and design optimization. The main goal of the research study was to provide expertise, judgment, and reasoning capabilities in the aerospace structural design process. This will allow engineers performing structural analysis and design, even without extensive experience in the field, to develop error-free, efficient and reliable structural designs very rapidly and cost-effectively. This would not only improve the productivity of design engineers and analysts, but also significantly reduce time to completion of structural design. An extensive literature survey in the field of structural analysis, design optimization, artificial intelligence, and database management systems and their application to the structural design process was first performed. A feasibility study was then performed, and the architecture and the conceptual design for the integrated 'intelligent' structural analysis and design optimization software was then developed. An Object Representation Language (ORL), in conjunction with a rule-based system, was then developed using C++. Such an approach would improve the expressiveness for knowledge representation (especially for structural analysis and design applications), provide ability to build very large and practical expert systems, and provide an efficient way for storing knowledge. Functional specifications for the expert systems were then developed. The ORL/AI shell was then used to develop a variety of modules of expert systems for a variety of modeling, finite element analysis, and design optimization tasks in the integrated aerospace structural design process. These expert systems were developed to work in conjunction with procedural finite element structural analysis and design optimization modules (developed in-house at SAT, Inc.). The complete software, AutoDesign, so developed, can be used for integrated 'intelligent' structural analysis and design optimization. The software was beta-tested at a variety of companies, used by a range of engineers with different levels of background and expertise. Based on the feedback obtained by such users, conclusions were developed and are provided.

Conservative properties of finite difference schemes for incompressible flow

NASA Technical Reports Server (NTRS)

Morinishi, Youhei

1995-01-01

The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.

Nilpotent symmetries in supergroup field cosmology

NASA Astrophysics Data System (ADS)

Upadhyay, Sudhaker

2015-06-01

In this paper, we study the gauge invariance of the third quantized supergroup field cosmology which is a model for multiverse. Further, we propose both the infinitesimal (usual) as well as the finite superfield-dependent BRST symmetry transformations which leave the effective theory invariant. The effects of finite superfield-dependent BRST transformations on the path integral (so-called void functional in the case of third quantization) are implemented. Within the finite superfield-dependent BRST formulation, the finite superfield-dependent BRST transformations with specific parameter switch the void functional from one gauge to another. We establish this result for the most general gauge with the help of explicit calculations which holds for all possible sets of gauge choices at both the classical and the quantum levels.

Engineering studies on joint bar integrity, part II : finite element analysis

DOT National Transportation Integrated Search

2014-04-02

This paper is the second in a two-part series describing : research sponsored by the Federal Railroad Administration : (FRA) to study the structural integrity of joint bars. In Part I, : observations from field surveys of joint bar inspections : cond...

Finite element modelling of creep crack growth in 316 stainless and 9Cr-1Mo steels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishnaswamy, P.; Brust, F.W.

1994-09-01

The failure behavior of steels under sustained and cyclic loads has been addressed. The constitutive behavior of the two steels have been represented by the conventional strain-hardening law and the Murakami-Ohno model for reversed and cyclic loads. The laws have been implemented into the research finite element code FVP. Post processors for FVP to calculate various path independent integral fracture parameters have been written. Compact tension C(T) specimens have been tested under sustained and cyclic loads with both the load point displacement and crack growth monitored during the tests. FE models with extremely refined meshes for the C(T) specimens weremore » prepared and the experiment simulated numerically. Results from this analysis focus on the differences between the various constitutive models as well as the fracture parameters in characterizing the creep crack growth of the two steels.« less

Isolation and Connectivity in Random Geometric Graphs with Self-similar Intensity Measures

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.

2018-05-01

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson distributed, and the probability of no isolated nodes is equal to the probability the whole graph is connected. Here we examine these properties for several self-similar node distributions, including smooth and fractal, uniform and nonuniform, and finitely ramified or otherwise. We show that nonuniformity can break the Poisson distribution property, but it strengthens the link between isolation and connectivity. It also stretches out the connectivity transition. Finite ramification is another mechanism for lack of connectivity. The same considerations apply to fractal distributions as smooth, with some technical differences in evaluation of the integrals and analytical arguments.

Finite volume model for two-dimensional shallow environmental flow

USGS Publications Warehouse

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

A two-dimensional numerical simulation of a supersonic, chemically reacting mixing layer

NASA Technical Reports Server (NTRS)

Drummond, J. Philip

1988-01-01

Research has been undertaken to achieve an improved understanding of physical phenomena present when a supersonic flow undergoes chemical reaction. A detailed understanding of supersonic reacting flows is necessary to successfully develop advanced propulsion systems now planned for use late in this century and beyond. In order to explore such flows, a study was begun to create appropriate physical models for describing supersonic combustion, and to develop accurate and efficient numerical techniques for solving the governing equations that result from these models. From this work, two computer programs were written to study reacting flows. Both programs were constructed to consider the multicomponent diffusion and convection of important chemical species, the finite rate reaction of these species, and the resulting interaction of the fluid mechanics and the chemistry. The first program employed a finite difference scheme for integrating the governing equations, whereas the second used a hybrid Chebyshev pseudospectral technique for improved accuracy.

Elasto visco-plastic flow with special attention to boundary conditions

NASA Technical Reports Server (NTRS)

Shimazaki, Y.; Thompson, E. G.

1981-01-01

A simple but nontrivial steady-state creeping elasto visco-plastic (Maxwell fluid) radial flow problem is analyzed, with special attention given to the effects of the boundary conditions. Solutions are obtained through integration of a governing equation on stress using the Runge-Kutta method for initial value problems and finite differences for boundary value problems. A more general approach through the finite element method, an approach that solves for the velocity field rather than the stress field and that is applicable to a wide range of problems, is presented and tested using the radial flow example. It is found that steady-state flows of elasto visco-plastic materials are strongly influenced by the state of stress of material as it enters the region of interest. The importance of this boundary or initial condition in analyses involving materials coming into control volumes from unusual stress environments is emphasized.

The Ablowitz–Ladik system on a finite set of integers

NASA Astrophysics Data System (ADS)

Xia, Baoqiang

2018-07-01

We show how to solve initial-boundary value problems for integrable nonlinear differential–difference equations on a finite set of integers. The method we employ is the discrete analogue of the unified transform (Fokas method). The implementation of this method to the Ablowitz–Ladik system yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem, which has a jump matrix with explicit -dependence involving certain functions referred to as spectral functions. Some of these functions are defined in terms of the initial value, while the remaining spectral functions are defined in terms of two sets of boundary values. These spectral functions are not independent but satisfy an algebraic relation called global relation. We analyze the global relation to characterize the unknown boundary values in terms of the given initial and boundary values. We also discuss the linearizable boundary conditions.

Thermal form-factor approach to dynamical correlation functions of integrable lattice models

NASA Astrophysics Data System (ADS)

Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Kozlowski, Karol K.; Suzuki, Junji

2017-11-01

We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function.

The application of an atomistic J-integral to a ductile crack.

PubMed

Zimmerman, Jonathan A; Jones, Reese E

2013-04-17

In this work we apply a Lagrangian kernel-based estimator of continuum fields to atomic data to estimate the J-integral for the emission dislocations from a crack tip. Face-centered cubic (fcc) gold and body-centered cubic (bcc) iron modeled with embedded atom method (EAM) potentials are used as example systems. The results of a single crack with a K-loading compare well to an analytical solution from anisotropic linear elastic fracture mechanics. We also discovered that in the post-emission of dislocations from the crack tip there is a loop size-dependent contribution to the J-integral. For a system with a finite width crack loaded in simple tension, the finite size effects for the systems that were feasible to compute prevented precise agreement with theory. However, our results indicate that there is a trend towards convergence.

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

NASA Astrophysics Data System (ADS)

Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

Finite-size effects on the radiative energy loss of a fast parton in hot and dense strongly interacting matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caron-Huot, Simon; Gale, Charles

2010-12-15

We consider finite-size effects on the radiative energy loss of a fast parton moving in a finite-temperature, strongly interacting medium, using the light-cone path integral formalism put forward by B. G. Zakharov [JETP Lett. 63, 952 (1996); 65, 615 (1997)]. We present a convenient reformulation of the problem that makes possible its exact numerical analysis. This is done by introducing the concept of a radiation rate in the presence of finite-size effects. This effectively extends the finite-temperature approach of Arnold, Moore, and Yaffe [J. High Energy Phys. 11 (2001) 057; 12 (2001) 009; 06 (2001) 030] (AMY) to include interferencemore » between vacuum and medium radiation. We compare results with those obtained in the regime considered by AMY, with those obtained at leading order in an opacity expansion, and with those obtained deep in the Landau-Pomeranchuk-Migdal regime.« less

Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

PubMed

Wang, Yujuan; Song, Yongduan; Ren, Wei

2017-07-06

This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

Finite-time stabilization for a class of nonholonomic feedforward systems subject to inputs saturation.

PubMed

Gao, Fangzheng; Yuan, Ye; Wu, Yuqiang

2016-09-01

This paper studies the problem of finite-time stabilization by state feedback for a class of uncertain nonholonomic systems in feedforward-like form subject to inputs saturation. Under the weaker homogeneous condition on systems growth, a saturated finite-time control scheme is developed by exploiting the adding a power integrator method, the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed saturated controller guarantees that the states of closed-loop system are regulated to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of saturated finite-time control for vertical wheel on rotating table is solved. Simulation results are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Focal shift and the axial optical coordinate for high-aperture systems of finite Fresnel number.

PubMed

Sheppard, Colin J R; Török, Peter

2003-11-01

Analytic expressions are given for the on-axis intensity predicted by the Rayleigh-Sommerfeld and Kirchhoff diffraction integrals for a scalar optical system of high numerical aperture and finite value of Fresnel number. A definition of the axial optical coordinate is introduced that is valid for finite values of Fresnel number, for high-aperture systems, and for observation points distant from the focus. The focal shift effect is reexamined. For the case when the focal shift is small, explicit expressions are given for the focal shift and the axial peak in intensity.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Finite Element Model Development For Aircraft Fuselage Structures

NASA Technical Reports Server (NTRS)

Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.

2000-01-01

The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results.

Practical aspects of prestack depth migration with finite differences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marxen, Olaf, E-mail: olaf.marxen@vki.ac.be; Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse; Magin, Thierry E.

2013-12-15

A new numerical method is presented here that allows to consider chemically reacting gases during the direct numerical simulation of a hypersonic fluid flow. The method comprises the direct coupling of a solver for the fluid mechanical model and a library providing the physio-chemical model. The numerical method for the fluid mechanical model integrates the compressible Navier–Stokes equations using an explicit time advancement scheme and high-order finite differences. This Navier–Stokes code can be applied to the investigation of laminar-turbulent transition and boundary-layer instability. The numerical method for the physio-chemical model provides thermodynamic and transport properties for different gases as wellmore » as chemical production rates, while here we exclusively consider a five species air mixture. The new method is verified for a number of test cases at Mach 10, including the one-dimensional high-temperature flow downstream of a normal shock, a hypersonic chemical reacting boundary layer in local thermodynamic equilibrium and a hypersonic reacting boundary layer with finite-rate chemistry. We are able to confirm that the diffusion flux plays an important role for a high-temperature boundary layer in local thermodynamic equilibrium. Moreover, we demonstrate that the flow for a case previously considered as a benchmark for the investigation of non-equilibrium chemistry can be regarded as frozen. Finally, the new method is applied to investigate the effect of finite-rate chemistry on boundary layer instability by considering the downstream evolution of a small-amplitude wave and comparing results with those obtained for a frozen gas as well as a gas in local thermodynamic equilibrium.« less

Finite-Difference Solutions for Compressible Laminar Boundary-Layer Flows of a Dusty Gas over a Semi-Infinite Flat Plate.

DTIC Science & Technology

1986-08-01

AD-A174 952 FINITE - DIFFERENCE SOLUTIONS FOR CONPRESSIBLE LANINAR 1/2 BOUNDARY-LAYER FLOUS (U) TORONTO UNIV DOWNSVIEW (ONTARIO) INST FOR AEROSPACE...dilute dusty gas over a semi-infinite flat plate. Details are given of the impliit finite , difference schemes as well as the boundary conditions... FINITE - DIFFERENCE SOLUTIONS FOR COMPRESSIBLE LAMINAR BOUNDARY-LAYER FLOWS OF A DUSTY GAS OVER A SEMI-INFINITE FLAT PLATE by B. Y. Wang and I. I

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

Mixed models and reduction method for dynamic analysis of anisotropic shells

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1985-01-01

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

ICAN/PART: Particulate composite analyzer, user's manual and verification studies

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Murthy, Pappu L. N.; Mital, Subodh K.

1996-01-01

A methodology for predicting the equivalent properties and constituent microstresses for particulate matrix composites, based on the micromechanics approach, is developed. These equations are integrated into a computer code developed to predict the equivalent properties and microstresses of fiber reinforced polymer matrix composites to form a new computer code, ICAN/PART. Details of the flowchart, input and output for ICAN/PART are described, along with examples of the input and output. Only the differences between ICAN/PART and the original ICAN code are described in detail, and the user is assumed to be familiar with the structure and usage of the original ICAN code. Detailed verification studies, utilizing dim dimensional finite element and boundary element analyses, are conducted in order to verify that the micromechanics methodology accurately models the mechanics of particulate matrix composites. ne equivalent properties computed by ICAN/PART fall within bounds established by the finite element and boundary element results. Furthermore, constituent microstresses computed by ICAN/PART agree in average sense with results computed using the finite element method. The verification studies indicate that the micromechanics programmed into ICAN/PART do indeed accurately model the mechanics of particulate matrix composites.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vay, Jean-Luc, E-mail: jlvay@lbl.gov; Haber, Irving; Godfrey, Brendan B.

Pseudo-spectral electromagnetic solvers (i.e. representing the fields in Fourier space) have extraordinary precision. In particular, Haber et al. presented in 1973 a pseudo-spectral solver that integrates analytically the solution over a finite time step, under the usual assumption that the source is constant over that time step. Yet, pseudo-spectral solvers have not been widely used, due in part to the difficulty for efficient parallelization owing to global communications associated with global FFTs on the entire computational domains. A method for the parallelization of electromagnetic pseudo-spectral solvers is proposed and tested on single electromagnetic pulses, and on Particle-In-Cell simulations of themore » wakefield formation in a laser plasma accelerator. The method takes advantage of the properties of the Discrete Fourier Transform, the linearity of Maxwell’s equations and the finite speed of light for limiting the communications of data within guard regions between neighboring computational domains. Although this requires a small approximation, test results show that no significant error is made on the test cases that have been presented. The proposed method opens the way to solvers combining the favorable parallel scaling of standard finite-difference methods with the accuracy advantages of pseudo-spectral methods.« less

A finite element model of a MEMS-based surface acoustic wave hydrogen sensor.

PubMed

El Gowini, Mohamed M; Moussa, Walied A

2010-01-01

Hydrogen plays a significant role in various industrial applications, but careful handling and continuous monitoring are crucial since it is explosive when mixed with air. Surface Acoustic Wave (SAW) sensors provide desirable characteristics for hydrogen detection due to their small size, low fabrication cost, ease of integration and high sensitivity. In this paper a finite element model of a Surface Acoustic Wave sensor is developed using ANSYS12© and tested for hydrogen detection. The sensor consists of a YZ-lithium niobate substrate with interdigital electrodes (IDT) patterned on the surface. A thin palladium (Pd) film is added on the surface of the sensor due to its high affinity for hydrogen. With increased hydrogen absorption the palladium hydride structure undergoes a phase change due to the formation of the β-phase, which deteriorates the crystal structure. Therefore with increasing hydrogen concentration the stiffness and the density are significantly reduced. The values of the modulus of elasticity and the density at different hydrogen concentrations in palladium are utilized in the finite element model to determine the corresponding SAW sensor response. Results indicate that with increasing the hydrogen concentration the wave velocity decreases and the attenuation of the wave is reduced.

Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.

The Magnetic Field of a Finite Solenoid

NASA Technical Reports Server (NTRS)

Callaghan, Edmund E.; Maslen, Stephen H.

1960-01-01

The axial and radial fields at any point inside or outside a finite solenoid with infinitely thin walls are derived. Solution of the equations has been obtained in terms of tabulated complete elliptic integrals. For the axial field an accurate approximation is given in terms of elementary functions. Fields internal and external to the solenoid are presented in graphical form for a wide variety of solenoid lengths.

Accurate Solution of Multi-Region Continuum Biomolecule Electrostatic Problems Using the Linearized Poisson-Boltzmann Equation with Curved Boundary Elements

PubMed Central

Altman, Michael D.; Bardhan, Jaydeep P.; White, Jacob K.; Tidor, Bruce

2009-01-01

We present a boundary-element method (BEM) implementation for accurately solving problems in biomolecular electrostatics using the linearized Poisson–Boltzmann equation. Motivating this implementation is the desire to create a solver capable of precisely describing the geometries and topologies prevalent in continuum models of biological molecules. This implementation is enabled by the synthesis of four technologies developed or implemented specifically for this work. First, molecular and accessible surfaces used to describe dielectric and ion-exclusion boundaries were discretized with curved boundary elements that faithfully reproduce molecular geometries. Second, we avoided explicitly forming the dense BEM matrices and instead solved the linear systems with a preconditioned iterative method (GMRES), using a matrix compression algorithm (FFTSVD) to accelerate matrix-vector multiplication. Third, robust numerical integration methods were employed to accurately evaluate singular and near-singular integrals over the curved boundary elements. Finally, we present a general boundary-integral approach capable of modeling an arbitrary number of embedded homogeneous dielectric regions with differing dielectric constants, possible salt treatment, and point charges. A comparison of the presented BEM implementation and standard finite-difference techniques demonstrates that for certain classes of electrostatic calculations, such as determining absolute electrostatic solvation and rigid-binding free energies, the improved convergence properties of the BEM approach can have a significant impact on computed energetics. We also demonstrate that the improved accuracy offered by the curved-element BEM is important when more sophisticated techniques, such as non-rigid-binding models, are used to compute the relative electrostatic effects of molecular modifications. In addition, we show that electrostatic calculations requiring multiple solves using the same molecular geometry, such as charge optimization or component analysis, can be computed to high accuracy using the presented BEM approach, in compute times comparable to traditional finite-difference methods. PMID:18567005

Finite Mathematics and Discrete Mathematics: Is There a Difference?

ERIC Educational Resources Information Center

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds

NASA Technical Reports Server (NTRS)

Evvard, John C

1950-01-01

A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions.

LS-DYNA Analysis of a Full-Scale Helicopter Crash Test

NASA Technical Reports Server (NTRS)

Annett, Martin S.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26 ft/sec and 40 ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated LS-DYNA finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test and continuing through post test validation.

Improved methods of vibration analysis of pretwisted, airfoil blades

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1984-01-01

Vibration analysis of pretwisted blades of asymmetric airfoil cross section is performed by using two mixed variational approaches. Numerical results obtained from these two methods are compared to those obtained from an improved finite difference method and also to those given by the ordinary finite difference method. The relative merits, convergence properties and accuracies of all four methods are studied and discussed. The effects of asymmetry and pretwist on natural frequencies and mode shapes are investigated. The improved finite difference method is shown to be far superior to the conventional finite difference method in several respects. Close lower bound solutions are provided by the improved finite difference method for untwisted blades with a relatively coarse mesh while the mixed methods have not indicated any specific bound.

Further studies of propellant sloshing under low-gravity conditions

NASA Technical Reports Server (NTRS)

Dodge, F. T.

1971-01-01

A variational integral is formulated from Hamilton's Principle and is proved to be equivalent to the usual differential equations of low-gravity sloshing in ellipsoidal tanks. It is shown that for a zero-degree contact angle the contact line boundary condition corresponds to the stuck condition, a result that is due to the linearization of the equations and the ambiguity in the definition of the wave height at the wall. The variational integral is solved by a Rayleigh-Ritz technique. Results for slosh frequency when the free surface is not bent-over compare well with previous numerical solutions. When the free surface is bent over, however, the results for slosh frequency are considerably larger than those predicted by previous finite-difference, numerical approaches: the difference may be caused by the use of a zero degree contact angle in the present theory in contrast to the nonzero contact angle used in the numerical approaches.

Multiplexed Simultaneous High Sensitivity Sensors with High-Order Mode Based on the Integration of Photonic Crystal 1 × 3 Beam Splitter and Three Different Single-Slot PCNCs.

PubMed

Zhou, Jian; Huang, Lijun; Fu, Zhongyuan; Sun, Fujun; Tian, Huiping

2016-07-07

We simulated an efficient method for the sensor array of high-sensitivity single-slot photonic crystal nanobeam cavities (PCNCs) on a silicon platform. With the combination of a well-designed photonic crystal waveguide (PhCW) filter and an elaborate single-slot PCNC, a specific high-order resonant mode was filtered for sensing. A 1 × 3 beam splitter carefully established was implemented to split channels and integrate three sensors to realize microarrays. By applying the three-dimensional finite-difference-time-domain (3D-FDTD) method, the sensitivities calculated were S₁ = 492 nm/RIU, S₂ = 244 nm/RIU, and S₃ = 552 nm/RIU, respectively. To the best of our knowledge, this is the first multiplexing design in which each sensor cite features such a high sensitivity simultaneously.

Multiplexed Simultaneous High Sensitivity Sensors with High-Order Mode Based on the Integration of Photonic Crystal 1 × 3 Beam Splitter and Three Different Single-Slot PCNCs

PubMed Central

Zhou, Jian; Huang, Lijun; Fu, Zhongyuan; Sun, Fujun; Tian, Huiping

2016-01-01

We simulated an efficient method for the sensor array of high-sensitivity single-slot photonic crystal nanobeam cavities (PCNCs) on a silicon platform. With the combination of a well-designed photonic crystal waveguide (PhCW) filter and an elaborate single-slot PCNC, a specific high-order resonant mode was filtered for sensing. A 1 × 3 beam splitter carefully established was implemented to split channels and integrate three sensors to realize microarrays. By applying the three-dimensional finite-difference-time-domain (3D-FDTD) method, the sensitivities calculated were S1 = 492 nm/RIU, S2 = 244 nm/RIU, and S3 = 552 nm/RIU, respectively. To the best of our knowledge, this is the first multiplexing design in which each sensor cite features such a high sensitivity simultaneously. PMID:27399712

The PLUTO code for astrophysical gasdynamics .

NASA Astrophysics Data System (ADS)

Mignone, A.

Present numerical codes appeal to a consolidated theory based on finite difference and Godunov-type schemes. In this context we have developed a versatile numerical code, PLUTO, suitable for the solution of high-mach number flow in 1, 2 and 3 spatial dimensions and different systems of coordinates. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. The code is freely distributed under the GNU public license and it is available for download to the astrophysical community at the URL http://plutocode.to.astro.it.

COMPUTERIZED TRAINING OF CRYOSURGERY – A SYSTEM APPROACH

PubMed Central

Keelan, Robert; Yamakawa, Soji; Shimada, Kenji; Rabin, Yoed

2014-01-01

The objective of the current study is to provide the foundation for a computerized training platform for cryosurgery. Consistent with clinical practice, the training process targets the correlation of the frozen region contour with the target region shape, using medical imaging and accepted criteria for clinical success. The current study focuses on system design considerations, including a bioheat transfer model, simulation techniques, optimal cryoprobe layout strategy, and a simulation core framework. Two fundamentally different approaches were considered for the development of a cryosurgery simulator, based on a finite-elements (FE) commercial code (ANSYS) and a proprietary finite-difference (FD) code. Results of this study demonstrate that the FE simulator is superior in terms of geometric modeling, while the FD simulator is superior in terms of runtime. Benchmarking results further indicate that the FD simulator is superior in terms of usage of memory resources, pre-processing, parallel processing, and post-processing. It is envisioned that future integration of a human-interface module and clinical data into the proposed computer framework will make computerized training of cryosurgery a practical reality. PMID:23995400

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Computation of turbulent boundary layers employing the defect wall-function method. M.S. Thesis

NASA Technical Reports Server (NTRS)

Brown, Douglas L.

1994-01-01

In order to decrease overall computational time requirements of spatially-marching parabolized Navier-Stokes finite-difference computer code when applied to turbulent fluid flow, a wall-function methodology, originally proposed by R. Barnwell, was implemented. This numerical effort increases computational speed and calculates reasonably accurate wall shear stress spatial distributions and boundary-layer profiles. Since the wall shear stress is analytically determined from the wall-function model, the computational grid near the wall is not required to spatially resolve the laminar-viscous sublayer. Consequently, a substantially increased computational integration step size is achieved resulting in a considerable decrease in net computational time. This wall-function technique is demonstrated for adiabatic flat plate test cases from Mach 2 to Mach 8. These test cases are analytically verified employing: (1) Eckert reference method solutions, (2) experimental turbulent boundary-layer data of Mabey, and (3) finite-difference computational code solutions with fully resolved laminar-viscous sublayers. Additionally, results have been obtained for two pressure-gradient cases: (1) an adiabatic expansion corner and (2) an adiabatic compression corner.

Finite-difference model to simulate the areal flow of saltwater and fresh water separated by an interface

USGS Publications Warehouse

Mercer, James W.; Larson, S.P.; Faust, Charles R.

1980-01-01

Model documentation is presented for a two-dimensional (areal) model capable of simulating ground-water flow of salt water and fresh water separated by an interface. The partial differential equations are integrated over the thicknesses of fresh water and salt water resulting in two equations describing the flow characteristics in the areal domain. These equations are approximated using finite-difference techniques and the resulting algebraic equations are solved for the dependent variables, fresh water head and salt water head. An iterative solution method was found to be most appropriate. The program is designed to simulate time-dependent problems such as those associated with the development of coastal aquifers, and can treat water-table conditions or confined conditions with steady-state leakage of fresh water. The program will generally be most applicable to the analysis of regional aquifer problems in which the zone between salt water and fresh water can be considered a surface (sharp interface). Example problems and a listing of the computer code are included. (USGS).

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Accurate green water loads calculation using naval hydro pack

NASA Astrophysics Data System (ADS)

Jasak, H.; Gatin, I.; Vukčević, V.

2017-12-01

An extensive verification and validation of Finite Volume based CFD software Naval Hydro based on foam-extend is presented in this paper for green water loads. Two-phase numerical model with advanced methods for treating the free surface is employed. Pressure loads on horizontal deck of Floating Production Storage and Offloading vessel (FPSO) model are compared to experimental results from [1] for three incident regular waves. Pressure peaks and integrals of pressure in time are measured on ten different locations on deck for each case. Pressure peaks and integrals are evaluated as average values among the measured incident wave periods, where periodic uncertainty is assessed for both numerical and experimental results. Spatial and temporal discretization refinement study is performed providing numerical discretization uncertainties.

The numerical calculation of laminar boundary-layer separation

NASA Technical Reports Server (NTRS)

Klineberg, J. M.; Steger, J. L.

1974-01-01

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

New design of a triplexer using ring resonator integrated with directional coupler based on photonic crystals

NASA Astrophysics Data System (ADS)

Wu, Yaw-Dong; Shih, Tien-Tsorng; Lee, Jian-Jang

2009-11-01

In this paper, we proposed the design of directional coupler integrated with ring resonator based on two-dimensional photonic crystals (2D PCs) to develop a triplexer filter. It can be widely used as the fiber access network element for multiplexer-demultiplexer wavelength selective in fiber-to-the-home (FTTH) communication systems. The directional coupler is chosen to separate the wavelengths of 1490nm and 1310nm. The ring resonator separates the wavelength of 1550nm. The transmission efficiency is larger than 90%. Besides, the total size of propose triplexer is only 19μm×12μm. We present simulation results using the finite-difference time-domain (FDTD) method for the proposed structure.

Numerical simulation of the generation, propagation, and diffraction of nonlinear waves in a rectangular basin: A three-dimensional numerical wave tank

NASA Astrophysics Data System (ADS)

Darwiche, Mahmoud Khalil M.

The research presented herein is a contribution to the understanding of the numerical modeling of fully nonlinear, transient water waves. The first part of the work involves the development of a time-domain model for the numerical generation of fully nonlinear, transient waves by a piston type wavemaker in a three-dimensional, finite, rectangular tank. A time-domain boundary-integral model is developed for simulating the evolving fluid field. A robust nonsingular, adaptive integration technique for the assembly of the boundary-integral coefficient matrix is developed and tested. A parametric finite-difference technique for calculating the fluid- particle kinematics is also developed and tested. A novel compatibility and continuity condition is implemented to minimize the effect of the singularities that are inherent at the intersections of the various Dirichlet and/or Neumann subsurfaces. Results are presented which demonstrate the accuracy and convergence of the numerical model. The second portion of the work is a study of the interaction of the numerically-generated, fully nonlinear, transient waves with a bottom-mounted, surface-piercing, vertical, circular cylinder. The numerical model developed in the first part of this dissertation is extended to include the presence of the cylinder at the centerline of the basin. The diffraction of the numerically generated waves by the cylinder is simulated, and the particle kinematics of the diffracted flow field are calculated and reported. Again, numerical results showing the accuracy and convergence of the extended model are presented.

Plasma Theory and Simulation

DTIC Science & Technology

1988-06-30

equation using finite difference methods. The distribution function is represented by a large number of particles. The particle’s velocities change as a...Small angle Coulomb collisions The FP equation for describing small angle Coulomb collisions can be solved numerically using finite difference techniques...A finite Fourrier transform (FT) is made in z, then we can solve for each k using the following finite difference scheme [5]: 2{r 1 +l1 2 (,,+ 1 - fj

Rheological Models in the Time-Domain Modeling of Seismic Motion

NASA Astrophysics Data System (ADS)

Moczo, P.; Kristek, J.

2004-12-01

The time-domain stress-strain relation in a viscoelastic medium has a form of the convolutory integral which is numerically intractable. This was the reason for the oversimplified models of attenuation in the time-domain seismic wave propagation and earthquake motion modeling. In their pioneering work, Day and Minster (1984) showed the way how to convert the integral into numerically tractable differential form in the case of a general viscoelastic modulus. In response to the work by Day and Minster, Emmerich and Korn (1987) suggested using the rheology of their generalized Maxwell body (GMB) while Carcione et al. (1988) suggested using the generalized Zener body (GZB). The viscoelastic moduli of both rheological models have a form of the rational function and thus the differential form of the stress-strain relation is rather easy to obtain. After the papers by Emmerich and Korn and Carcione et al. numerical modelers decided either for the GMB or GZB rheology and developed 'non-communicating' algorithms. In the many following papers the authors using the GMB never commented the GZB rheology and the corresponding algorithms, and the authors using the GZB never related their methods to the GMB rheology and algorithms. We analyze and compare both rheologies and the corresponding incorporations of the realistic attenuation into the time-domain computations. We then focus on the most recent staggered-grid finite-difference modeling, mainly on accounting for the material heterogeneity in the viscoelastic media, and the computational efficiency of the finite-difference algorithms.

DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K., E-mail: lzhao@fit.edu

2016-04-10

A double power law or a power law with exponential rollover at a few to tens of MeV nucleon{sup −1} of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochasticmore » approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon{sup −1} is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.« less

Bending analysis of embedded nanoplates based on the integral formulation of Eringen's nonlocal theory using the finite element method

NASA Astrophysics Data System (ADS)

Ansari, R.; Torabi, J.; Norouzzadeh, A.

2018-04-01

Due to the capability of Eringen's nonlocal elasticity theory to capture the small length scale effect, it is widely used to study the mechanical behaviors of nanostructures. Previous studies have indicated that in some cases, the differential form of this theory cannot correctly predict the behavior of structure, and the integral form should be employed to avoid obtaining inconsistent results. The present study deals with the bending analysis of nanoplates resting on elastic foundation based on the integral formulation of Eringen's nonlocal theory. Since the formulation is presented in a general form, arbitrary kernel functions can be used. The first order shear deformation plate theory is considered to model the nanoplates, and the governing equations for both integral and differential forms are presented. Finally, the finite element method is applied to solve the problem. Selected results are given to investigate the effects of elastic foundation and to compare the predictions of integral nonlocal model with those of its differential nonlocal and local counterparts. It is found that by the use of proposed integral formulation of Eringen's nonlocal model, the paradox observed for the cantilever nanoplate is resolved.

Application of 'steady' state finite element and transient finite difference theory to sound propagation in a variable duct - A comparison with experiment

NASA Technical Reports Server (NTRS)

Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.

1981-01-01

Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.

Modeling Early-Stage Processes of U-10 Wt.%Mo Alloy Using Integrated Computational Materials Engineering Concepts

NASA Astrophysics Data System (ADS)

Wang, Xiaowo; Xu, Zhijie; Soulami, Ayoub; Hu, Xiaohua; Lavender, Curt; Joshi, Vineet

2017-12-01

Low-enriched uranium alloyed with 10 wt.% molybdenum (U-10Mo) has been identified as a promising alternative to high-enriched uranium. Manufacturing U-10Mo alloy involves multiple complex thermomechanical processes that pose challenges for computational modeling. This paper describes the application of integrated computational materials engineering (ICME) concepts to integrate three individual modeling components, viz. homogenization, microstructure-based finite element method for hot rolling, and carbide particle distribution, to simulate the early-stage processes of U-10Mo alloy manufacture. The resulting integrated model enables information to be passed between different model components and leads to improved understanding of the evolution of the microstructure. This ICME approach is then used to predict the variation in the thickness of the Zircaloy-2 barrier as a function of the degree of homogenization and to analyze the carbide distribution, which can affect the recrystallization, hardness, and fracture properties of U-10Mo in subsequent processes.

Global tectonic reconstructions with continuously deforming and evolving rigid plates

NASA Astrophysics Data System (ADS)

Gurnis, Michael; Yang, Ting; Cannon, John; Turner, Mark; Williams, Simon; Flament, Nicolas; Müller, R. Dietmar

2018-07-01

Traditional plate reconstruction methodologies do not allow for plate deformation to be considered. Here we present software to construct and visualize global tectonic reconstructions with deforming plates within the context of rigid plates. Both deforming and rigid plates are defined by continuously evolving polygons. The deforming regions are tessellated with triangular meshes such that either strain rate or cumulative strain can be followed. The finite strain history, crustal thickness and stretching factor of points within the deformation zones are tracked as Lagrangian points. Integrating these tools within the interactive platform GPlates enables specialized users to build and refine deforming plate models and integrate them with other models in time and space. We demonstrate the integrated platform with regional reconstructions of Cenozoic western North America, the Mesozoic South American Atlantic margin, and Cenozoic southeast Asia, embedded within global reconstructions, using different data and reconstruction strategies.

Numerical Modeling of Pressurization of Cryogenic Propellant Tank for Integrated Vehicle Fluid System

NASA Technical Reports Server (NTRS)

Majumdar, Alok K.; LeClair, Andre C.; Hedayat, Ali

2016-01-01

This paper presents a numerical model of pressurization of a cryogenic propellant tank for the Integrated Vehicle Fluid (IVF) system using the Generalized Fluid System Simulation Program (GFSSP). The IVF propulsion system, being developed by United Launch Alliance, uses boiloff propellants to drive thrusters for the reaction control system as well as to run internal combustion engines to develop power and drive compressors to pressurize propellant tanks. NASA Marshall Space Flight Center (MSFC) has been running tests to verify the functioning of the IVF system using a flight tank. GFSSP, a finite volume based flow network analysis software developed at MSFC, has been used to develop an integrated model of the tank and the pressurization system. This paper presents an iterative algorithm for converging the interface boundary conditions between different component models of a large system model. The model results have been compared with test data.

Thermal-Acoustic Analysis of a Metallic Integrated Thermal Protection System Structure

NASA Technical Reports Server (NTRS)

Behnke, Marlana N.; Sharma, Anurag; Przekop, Adam; Rizzi, Stephen A.

2010-01-01

A study is undertaken to investigate the response of a representative integrated thermal protection system structure under combined thermal, aerodynamic pressure, and acoustic loadings. A two-step procedure is offered and consists of a heat transfer analysis followed by a nonlinear dynamic analysis under a combined loading environment. Both analyses are carried out in physical degrees-of-freedom using implicit and explicit solution techniques available in the Abaqus commercial finite-element code. The initial study is conducted on a reduced-size structure to keep the computational effort contained while validating the procedure and exploring the effects of individual loadings. An analysis of a full size integrated thermal protection system structure, which is of ultimate interest, is subsequently presented. The procedure is demonstrated to be a viable approach for analysis of spacecraft and hypersonic vehicle structures under a typical mission cycle with combined loadings characterized by largely different time-scales.

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

NASA Astrophysics Data System (ADS)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Comparative study of BCS-BEC crossover theories above T{sub c}: The nature of the pseudogap in ultracold atomic Fermi gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chien, C.-C.; Guo Hao; He Yan

2010-02-15

This article presents a comparison of two finite-temperature BCS-Bose-Einstein condensation (BEC) crossover theories above the transition temperature: Nozieres-Schmitt-Rink (NSR) theory and finite-T extended BCS-Leggett theory. The comparison is cast in the form of numerical studies of the behavior of the fermionic spectral function both theoretically and as constrained by (primarily) radio frequency (rf) experiments. Both theories include pair fluctuations and exhibit pseudogap effects, although the nature of this pseudogap is very different. The pseudogap in finite-T extended BCS-Leggett theory is found to follow a BCS-like dispersion which, in turn, is associated with a broadened BCS-like self-energy, rather more similar tomore » what is observed in high-temperature superconductors (albeit, for a d-wave case). The fermionic quasiparticle dispersion is different in NSR theory and the damping is considerably larger. We argue that the two theories are appropriate in different temperature regimes with the BCS-Leggett approach being more suitable nearer to condensation. There should, in effect, be little difference at higher T as the pseudogap becomes weaker and where the simplifying approximations used in the BCS-Leggett approach break down. On the basis of momentum-integrated rf studies of unpolarized gases, it would be difficult to distinguish which theory is the better one. A full comparison for polarized gases is not possible since it is claimed that there are inconsistencies in the NSR approach (not found in the BCS-Leggett scheme). Future experiments along the lines of momentum-resolved experiments look to be very promising in distinguishing the two theories.« less

Integrating First-Year Technology and Finite Mathematics Courses

ERIC Educational Resources Information Center

Shafii-Mousavi, Morteza; Kochanowski, Paul

2006-01-01

This paper describes an interdisciplinary project-based mathematics course linked to a computer technology course. The linkage encourages an appreciation of mathematics and technology as students see an immediate use for these skills in completing actual real-world projects. Linking mathematics and technology integrates subjects taught in…

Noncommutative de Rham Cohomology of Finite Groups

NASA Astrophysics Data System (ADS)

Castellani, L.; Catenacci, R.; Debernardi, M.; Pagani, C.

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S3, the dihedral group D4 and the quaternion group Q. Poincaré duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential calculus on finite G is given for selfconsistency. Exterior derivative, exterior product, metric, Hodge dual, connections, torsion, curvature, and biinvariant integration can be defined algebraically. A projector decomposition of the braiding operator is found, and used in constructing the projector on the space of two-forms. By means of the braiding operator and the metric a knot invariant is defined for any finite group.

Drekar v.2.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

Automated Planning and Scheduling for Space Mission Operations

NASA Technical Reports Server (NTRS)

Chien, Steve; Jonsson, Ari; Knight, Russell

2005-01-01

Research Trends: a) Finite-capacity scheduling under more complex constraints and increased problem dimensionality (subcontracting, overtime, lot splitting, inventory, etc.) b) Integrated planning and scheduling. c) Mixed-initiative frameworks. d) Management of uncertainty (proactive and reactive). e) Autonomous agent architectures and distributed production management. e) Integration of machine learning capabilities. f) Wider scope of applications: 1) analysis of supplier/buyer protocols & tradeoffs; 2) integration of strategic & tactical decision-making; and 3) enterprise integration.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units.

PubMed

Qi, Ruxi; Botello-Smith, Wesley M; Luo, Ray

2017-07-11

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Jin, Jian-Ming; Volakis, John L.

1990-01-01

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

NASA Technical Reports Server (NTRS)

Noor, A. K.; Stephens, W. B.

1973-01-01

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Transient Finite Element Computations on a Variable Transputer System

NASA Technical Reports Server (NTRS)

Smolinski, Patrick J.; Lapczyk, Ireneusz

1993-01-01

A parallel program to analyze transient finite element problems was written and implemented on a system of transputer processors. The program uses the explicit time integration algorithm which eliminates the need for equation solving, making it more suitable for parallel computations. An interprocessor communication scheme was developed for arbitrary two dimensional grid processor configurations. Several 3-D problems were analyzed on a system with a small number of processors.

Slave finite elements: The temporal element approach to nonlinear analysis

NASA Technical Reports Server (NTRS)

Gellin, S.

1984-01-01

A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.

KAM Tori Construction Algorithms

NASA Astrophysics Data System (ADS)

Wiesel, W.

In this paper we evaluate and compare two algorithms for the calculation of KAM tori in Hamiltonian systems. The direct fitting of a torus Fourier series to a numerically integrated trajectory is the first method, while an accelerated finite Fourier transform is the second method. The finite Fourier transform, with Hanning window functions, is by far superior in both computational loading and numerical accuracy. Some thoughts on applications of KAM tori are offered.

Shape and Stress Sensing of Multilayered Composite and Sandwich Structures Using an Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Cerracchio, Priscilla; Gherlone, Marco; Di Sciuva, Marco; Tessler, Alexander

2013-01-01

The marked increase in the use of composite and sandwich material systems in aerospace, civil, and marine structures leads to the need for integrated Structural Health Management systems. A key capability to enable such systems is the real-time reconstruction of structural deformations, stresses, and failure criteria that are inferred from in-situ, discrete-location strain measurements. This technology is commonly referred to as shape- and stress-sensing. Presented herein is a computationally efficient shape- and stress-sensing methodology that is ideally suited for applications to laminated composite and sandwich structures. The new approach employs the inverse Finite Element Method (iFEM) as a general framework and the Refined Zigzag Theory (RZT) as the underlying plate theory. A three-node inverse plate finite element is formulated. The element formulation enables robust and efficient modeling of plate structures instrumented with strain sensors that have arbitrary positions. The methodology leads to a set of linear algebraic equations that are solved efficiently for the unknown nodal displacements. These displacements are then used at the finite element level to compute full-field strains, stresses, and failure criteria that are in turn used to assess structural integrity. Numerical results for multilayered, highly heterogeneous laminates demonstrate the unique capability of this new formulation for shape- and stress-sensing.

Neural network disturbance observer-based distributed finite-time formation tracking control for multiple unmanned helicopters.

PubMed

Wang, Dandan; Zong, Qun; Tian, Bailing; Shao, Shikai; Zhang, Xiuyun; Zhao, Xinyi

2018-02-01

The distributed finite-time formation tracking control problem for multiple unmanned helicopters is investigated in this paper. The control object is to maintain the positions of follower helicopters in formation with external interferences. The helicopter model is divided into a second order outer-loop subsystem and a second order inner-loop subsystem based on multiple-time scale features. Using radial basis function neural network (RBFNN) technique, we first propose a novel finite-time multivariable neural network disturbance observer (FMNNDO) to estimate the external disturbance and model uncertainty, where the neural network (NN) approximation errors can be dynamically compensated by adaptive law. Next, based on FMNNDO, a distributed finite-time formation tracking controller and a finite-time attitude tracking controller are designed using the nonsingular fast terminal sliding mode (NFTSM) method. In order to estimate the second derivative of the virtual desired attitude signal, a novel finite-time sliding mode integral filter is designed. Finally, Lyapunov analysis and multiple-time scale principle ensure the realization of control goal in finite-time. The effectiveness of the proposed FMNNDO and controllers are then verified by numerical simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Optical performance assessment under environmental and mechanical perturbations in large, deployable telescopes

NASA Astrophysics Data System (ADS)

Folley, Christopher; Bronowicki, Allen

2005-09-01

Prediction of optical performance for large, deployable telescopes under environmental conditions and mechanical disturbances is a crucial part of the design verification process of such instruments for all phases of design and operation: ground testing, commissioning, and on-orbit operation. A Structural-Thermal-Optical-Performance (STOP) analysis methodology is often created that integrates the output of one analysis with the input of another. The integration of thermal environment predictions with structural models is relatively well understood, while the integration of structural deformation results into optical analysis/design software is less straightforward. A Matlab toolbox has been created that effectively integrates the predictions of mechanical deformations on optical elements generated by, for example, finite element analysis, and computes optical path differences for the distorted prescription. The engine of the toolbox is the real ray-tracing algorithm that allows the optical surfaces to be defined in a single, global coordinate system thereby allowing automatic alignment of the mechanical coordinate system with the optical coordinate system. Therefore, the physical location of the optical surfaces is identical in the optical prescription and the finite element model. The application of rigid body displacements to optical surfaces, however, is more general than for use solely in STOP analysis, such as the analysis of misalignments during the commissioning process. Furthermore, all the functionality of Matlab is available for optimization and control. Since this is a new tool for use on flight programs, it has been verified against CODE V. The toolbox' functionality, to date, is described, verification results are presented, and, as an example of its utility, results of a thermal distortion analysis are presented using the James Webb Space Telescope (JWST) prescription.

Thermodynamics and structural transition of binary atomic Bose-Fermi mixtures in box or harmonic potentials: A path-integral study

NASA Astrophysics Data System (ADS)

Kim, Tom; Chien, Chih-Chun

2018-03-01

Experimental realizations of a variety of atomic binary Bose-Fermi mixtures have brought opportunities for studying composite quantum systems with different spin statistics. The binary atomic mixtures can exhibit a structural transition from a mixture into phase separation as the boson-fermion interaction increases. By using a path-integral formalism to evaluate the grand partition function and the thermodynamic grand potential, we obtain the effective potential of binary Bose-Fermi mixtures. Thermodynamic quantities in a broad range of temperatures and interactions are also derived. The structural transition can be identified as a loop of the effective potential curve, and the volume fraction of phase separation can be determined by the lever rule. For 6Li-7Li and 6Li-41K mixtures, we present the phase diagrams of the mixtures in a box potential at zero and finite temperatures. Due to the flexible densities of atomic gases, the construction of phase separation is more complicated when compared to conventional liquid or solid mixtures where the individual densities are fixed. For harmonically trapped mixtures, we use the local density approximation to map out the finite-temperature density profiles and present typical trap structures, including the mixture, partially separated phases, and fully separated phases.

76 FR 70896 - Polyethylene Glycol; Tolerance Exemption

Federal Register 2010, 2011, 2012, 2013, 2014

2011-11-16

... a finite tolerance is not necessary to ensure that there is a reasonable certainty that no harm will... integral part of its composition the atomic elements carbon, hydrogen, and oxygen. 3. The polymer does not contain as an integral part of its composition, except as impurities, any element other than those listed...

On Calculation Methods and Results for Straight Cylindrical Roller Bearing Deflection, Stiffness, and Stress

NASA Technical Reports Server (NTRS)

Krantz, Timothy L.

2011-01-01

The purpose of this study was to assess some calculation methods for quantifying the relationships of bearing geometry, material properties, load, deflection, stiffness, and stress. The scope of the work was limited to two-dimensional modeling of straight cylindrical roller bearings. Preparations for studies of dynamic response of bearings with damaged surfaces motivated this work. Studies were selected to exercise and build confidence in the numerical tools. Three calculation methods were used in this work. Two of the methods were numerical solutions of the Hertz contact approach. The third method used was a combined finite element surface integral method. Example calculations were done for a single roller loaded between an inner and outer raceway for code verification. Next, a bearing with 13 rollers and all-steel construction was used as an example to do additional code verification, including an assessment of the leading order of accuracy of the finite element and surface integral method. Results from that study show that the method is at least first-order accurate. Those results also show that the contact grid refinement has a more significant influence on precision as compared to the finite element grid refinement. To explore the influence of material properties, the 13-roller bearing was modeled as made from Nitinol 60, a material with very different properties from steel and showing some potential for bearing applications. The codes were exercised to compare contact areas and stress levels for steel and Nitinol 60 bearings operating at equivalent power density. As a step toward modeling the dynamic response of bearings having surface damage, static analyses were completed to simulate a bearing with a spall or similar damage.

Nonlinear mesomechanics of composites with periodic microstructure

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Jordan, Eric H.; Freed, Alan D.

1989-01-01

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

NASA Astrophysics Data System (ADS)

Abert, Claas; Exl, Lukas; Bruckner, Florian; Drews, André; Suess, Dieter

2013-11-01

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Anisotropic Resistivity Forward Modelling Using Automatic Generated Higher-order Finite Element Codes

NASA Astrophysics Data System (ADS)

Wang, W.; Liu, J.

2016-12-01

Forward modelling is the general way to obtain responses of geoelectrical structures. Field investigators might find it useful for planning surveys and choosing optimal electrode configurations with respect to their targets. During the past few decades much effort has been put into the development of numerical forward codes, such as integral equation method, finite difference method and finite element method. Nowadays, most researchers prefer the finite element method (FEM) for its flexible meshing scheme, which can handle models with complex geometry. Resistivity Modelling with commercial sofewares such as ANSYS and COMSOL is convenient, but like working with a black box. Modifying the existed codes or developing new codes is somehow a long period. We present a new way to obtain resistivity forward modelling codes quickly, which is based on the commercial sofeware FEPG (Finite element Program Generator). Just with several demanding scripts, FEPG could generate FORTRAN program framework which can easily be altered to adjust our targets. By supposing the electric potential is quadratic in each element of a two-layer model, we obtain quite accurate results with errors less than 1%, while more than 5% errors could appear by linear FE codes. The anisotropic half-space model is supposed to concern vertical distributed fractures. The measured apparent resistivities along the fractures are bigger than results from its orthogonal direction, which are opposite of the true resistivities. Interpretation could be misunderstood if this anisotropic paradox is ignored. The technique we used can obtain scientific codes in a short time. The generated powerful FORTRAN codes could reach accurate results by higher-order assumption and can handle anisotropy to make better interpretations. The method we used could be expand easily to other domain where FE codes are needed.

Efficient Use of Distributed Systems for Scientific Applications

NASA Technical Reports Server (NTRS)

Taylor, Valerie; Chen, Jian; Canfield, Thomas; Richard, Jacques

2000-01-01

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Finite difference and Runge-Kutta methods for solving vibration problems

NASA Astrophysics Data System (ADS)

Lintang Renganis Radityani, Scolastika; Mungkasi, Sudi

2017-11-01

The vibration of a storey building can be modelled into a system of second order ordinary differential equations. If the number of floors of a building is large, then the result is a large scale system of second order ordinary differential equations. The large scale system is difficult to solve, and if it can be solved, the solution may not be accurate. Therefore, in this paper, we seek for accurate methods for solving vibration problems. We compare the performance of numerical finite difference and Runge-Kutta methods for solving large scale systems of second order ordinary differential equations. The finite difference methods include the forward and central differences. The Runge-Kutta methods include the Euler and Heun methods. Our research results show that the central finite difference and the Heun methods produce more accurate solutions than the forward finite difference and the Euler methods do.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Atherosclerotic plaque delamination: Experiments and 2D finite element model to simulate plaque peeling in two strains of transgenic mice.

PubMed

Merei, Bilal; Badel, Pierre; Davis, Lindsey; Sutton, Michael A; Avril, Stéphane; Lessner, Susan M

2017-03-01

Finite element analyses using cohesive zone models (CZM) can be used to predict the fracture of atherosclerotic plaques but this requires setting appropriate values of the model parameters. In this study, material parameters of a CZM were identified for the first time on two groups of mice (ApoE -/- and ApoE -/- Col8 -/- ) using the measured force-displacement curves acquired during delamination tests. To this end, a 2D finite-element model of each plaque was solved using an explicit integration scheme. Each constituent of the plaque was modeled with a neo-Hookean strain energy density function and a CZM was used for the interface. The model parameters were calibrated by minimizing the quadratic deviation between the experimental force displacement curves and the model predictions. The elastic parameter of the plaque and the CZM interfacial parameter were successfully identified for a cohort of 11 mice. The results revealed that only the elastic parameter was significantly different between the two groups, ApoE -/- Col8 -/- plaques being less stiff than ApoE -/- plaques. Finally, this study demonstrated that a simple 2D finite element model with cohesive elements can reproduce fairly well the plaque peeling global response. Future work will focus on understanding the main biological determinants of regional and inter-individual variations of the material parameters used in the model. Copyright © 2016 Elsevier Ltd. All rights reserved.

An analytic solution for numerical modeling validation in electromagnetics: the resistive sphere

NASA Astrophysics Data System (ADS)

Swidinsky, Andrei; Liu, Lifei

2017-11-01

We derive the electromagnetic response of a resistive sphere to an electric dipole source buried in a conductive whole space. The solution consists of an infinite series of spherical Bessel functions and associated Legendre polynomials, and follows the well-studied problem of a conductive sphere buried in a resistive whole space in the presence of a magnetic dipole. Our result is particularly useful for controlled-source electromagnetic problems using a grounded electric dipole transmitter and can be used to check numerical methods of calculating the response of resistive targets (such as finite difference, finite volume, finite element and integral equation). While we elect to focus on the resistive sphere in our examples, the expressions in this paper are completely general and allow for arbitrary source frequency, sphere radius, transmitter position, receiver position and sphere/host conductivity contrast so that conductive target responses can also be checked. Commonly used mesh validation techniques consist of comparisons against other numerical codes, but such solutions may not always be reliable or readily available. Alternatively, the response of simple 1-D models can be tested against well-known whole space, half-space and layered earth solutions, but such an approach is inadequate for validating models with curved surfaces. We demonstrate that our theoretical results can be used as a complementary validation tool by comparing analytic electric fields to those calculated through a finite-element analysis; the software implementation of this infinite series solution is made available for direct and immediate application.

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

PubMed

Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue

2015-10-16

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

A Numerical Round Robin for the Reliability Prediction of Structural Ceramics

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Janosik, Lesley A.

1993-01-01

A round robin has been conducted on integrated fast fracture design programs for brittle materials. An informal working group (WELFEP-WEakest Link failure probability prediction by Finite Element Postprocessors) was formed to discuss and evaluate the implementation of the programs examined in the study. Results from the study have provided insight on the differences between the various programs examined. Conclusions from the study have shown that when brittle materials are used in design, analysis must understand how to apply the concepts presented herein to failure probability analysis.

Documentation of the Goddard Laboratory for atmospheres fourth-order two-layer shallow water model

NASA Technical Reports Server (NTRS)

Takacs, L. L. (Compiler)

1986-01-01

The theory and numerical treatment used in the 2-level GLA fourth-order shallow water model are described. This model was designed to emulate the horizontal finite differences used by the GLA Fourth-Order General Circulation Model (Kalnay et al., 1983) in addition to its grid structure, form of high-latitude and global filtering, and time-integration schemes. A user's guide is also provided instructing the user on how to create initial conditions, execute the model, and post-process the data history.

Calculation of wind-driven surface currents in the North Atlantic Ocean

NASA Technical Reports Server (NTRS)

Rees, T. H.; Turner, R. E.

1976-01-01

Calculations to simulate the wind driven near surface currents of the North Atlantic Ocean are described. The primitive equations were integrated on a finite difference grid with a horizontal resolution of 2.5 deg in longitude and latitude. The model ocean was homogeneous with a uniform depth of 100 m and with five levels in the vertical direction. A form of the rigid-lid approximation was applied. Generally, the computed surface current patterns agreed with observed currents. The development of a subsurface equatorial countercurrent was observed.

Numerical simulation of two-dimensional Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Grigoriev, Vasiliy V.; Zakharov, Petr E.

2017-11-01

This paper considered Rayleigh-Benard convection (natural convection). This is a flow, which is formed in a viscous medium when heated from below and cooled from above. As a result, are formed vortices (convective cells). This process is described by a system of nonlinear differential equations in Oberbeck-Boussinesq approximation. As the governing parameters characterizing convection states Rayleigh number, Prandtl number are picked. The problem is solved by using finite element method with computational package FEniCS. Numerical results for different Rayleigh numbers are obtained. Studied integral characteristic (Nusselt number) depending on the Rayleigh number.

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

NASA Technical Reports Server (NTRS)

Fan, Mark S.; Christou, Aris; Pecht, Michael G.

1992-01-01

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Micro-Coplanar Striplines: New Transmission Media for Microwave Applications

NASA Technical Reports Server (NTRS)

Goverdhanam, Kavita; Simons, Rainee N.; Katehi, Linda P. B.

1998-01-01

In this paper a new transmission line for microwave applications, referred to here as the Micro-Coplanar Stripline (MCPS), is introduced. The propagation characteristics, such as, characteristic impedance (Z(sub 0) and effective dielectric constant (epsilon eff) for a range of MCPS geometries have been modeled using the Finite Difference Time Domain (FDTD) Technique and presented here. Also, preliminary experimental results on the performance of an MCP-Microstrip transition and an MCPS-fed patch antenna are presented. The results indicate several potential applications of the MCPS line in microwave integrated circuit technology.

Scattering of ultrasonic wave by cracks in a plate

NASA Technical Reports Server (NTRS)

Liu, S. W.; Datta, S. K.

1993-01-01

A hybrid numerical method combining finite elements and the boundary integral representation is used to investigate the transient scattering of ultrasonic waves by a crack in a plate. The incident wave models the guided waves generated by a steel ball impact on the plate. Two surface-breaking cracks and one subsurface crack are studied here. The results show that the location and depth of cracks have measurable effects on the surface responses in time and frequency domains. Also, the scattered fields have distinct differences in the three cases.

Robust flow of light in three-dimensional dielectric photonic crystals.

PubMed

Chen, Wen-Jie; Jiang, Shao-Ji; Dong, Jian-Wen

2013-09-01

Chiral defect waveguides and waveguide bend geometry were designed in diamond photonic crystal to mold the flow of light in three dimensions. Propagations of electromagnetic waves in chiral waveguides are robust against isotropic obstacles, which would suppress backscattering in waveguides or integrated devices. Finite-difference time-domain simulations demonstrate that high coupling efficiency through the bend corner is preserved in the polarization gap, as it provides an additional constraint on the polarization state of the backscattered wave. Transport robustness is also demonstrated by inserting two metallic slabs into the waveguide bend.

Flow of rarefied gases over two-dimensional bodies

NASA Technical Reports Server (NTRS)

Jeng, Duen-Ren; De Witt, Kenneth J.; Keith, Theo G., Jr.; Chung, Chan-Hong

1989-01-01

A kinetic-theory analysis is made of the flow of rarefied gases over two-dimensional bodies of arbitrary curvature. The Boltzmann equation simplified by a model collision integral is written in an arbitrary orthogonal curvilinear coordinate system, and solved by means of finite-difference approximation with the discrete ordinate method. A numerical code is developed which can be applied to any two-dimensional submerged body of arbitrary curvature for the flow regimes from free-molecular to slip at transonic Mach numbers. Predictions are made for the case of a right circular cylinder.

Integrable particle systems vs solutions to the KP and 2D Toda equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruijsenaars, S.N.

Starting from the relation between integrable relativistic N-particle systems with hyperbolic interactions and elementary N-soliton solutions to the KP and 2D Toda equations, we show how fusion properties of the soliton solutions are mirrored by fusion properties of the Poisson commuting particle dynamics. We also obtain previously known relations between elliptic solutions and integrable N-particle systems with elliptic interactions, without invoking finite-gap integration theory. {copyright} 1997 Academic Press, Inc.

Determination of the Fracture Parameters in a Stiffened Composite Panel

NASA Technical Reports Server (NTRS)

Lin, Chung-Yi

2000-01-01

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

NASA Astrophysics Data System (ADS)

Liu, Chiu-Chu Melissa; Sheshmani, Artan

2017-07-01

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

A multidimensional finite element method for CFD

NASA Technical Reports Server (NTRS)

Pepper, Darrell W.; Humphrey, Joseph W.

1991-01-01

A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.

Stability and Convergence of Underintegrated Finite Element Approximations

NASA Technical Reports Server (NTRS)

Oden, J. T.

1984-01-01

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

A study of the response of nonlinear springs

NASA Technical Reports Server (NTRS)

Hyer, M. W.; Knott, T. W.; Johnson, E. R.

1991-01-01

The various phases to developing a methodology for studying the response of a spring-reinforced arch subjected to a point load are discussed. The arch is simply supported at its ends with both the spring and the point load assumed to be at midspan. The spring is present to off-set the typical snap through behavior normally associated with arches, and to provide a structure that responds with constant resistance over a finite displacement. The various phases discussed consist of the following: (1) development of the closed-form solution for the shallow arch case; (2) development of a finite difference analysis to study (shallow) arches; and (3) development of a finite element analysis for studying more general shallow and nonshallow arches. The two numerical analyses rely on a continuation scheme to move the solution past limit points, and to move onto bifurcated paths, both characteristics being common to the arch problem. An eigenvalue method is used for a continuation scheme. The finite difference analysis is based on a mixed formulation (force and displacement variables) of the governing equations. The governing equations for the mixed formulation are in first order form, making the finite difference implementation convenient. However, the mixed formulation is not well-suited for the eigenvalue continuation scheme. This provided the motivation for the displacement based finite element analysis. Both the finite difference and the finite element analyses are compared with the closed form shallow arch solution. Agreement is excellent, except for the potential problems with the finite difference analysis and the continuation scheme. Agreement between the finite element analysis and another investigator's numerical analysis for deep arches is also good.

Finite-time consensus for controlled dynamical systems in network

NASA Astrophysics Data System (ADS)

Zoghlami, Naim; Mlayeh, Rhouma; Beji, Lotfi; Abichou, Azgal

2018-04-01

The key challenges in networked dynamical systems are the component heterogeneities, nonlinearities, and the high dimension of the formulated vector of state variables. In this paper, the emphasise is put on two classes of systems in network include most controlled driftless systems as well as systems with drift. For each model structure that defines homogeneous and heterogeneous multi-system behaviour, we derive protocols leading to finite-time consensus. For each model evolving in networks forming a homogeneous or heterogeneous multi-system, protocols integrating sufficient conditions are derived leading to finite-time consensus. Likewise, for the networking topology, we make use of fixed directed and undirected graphs. To prove our approaches, finite-time stability theory and Lyapunov methods are considered. As illustrative examples, the homogeneous multi-unicycle kinematics and the homogeneous/heterogeneous multi-second order dynamics in networks are studied.

Finite-time output feedback control of uncertain switched systems via sliding mode design

NASA Astrophysics Data System (ADS)

Zhao, Haijuan; Niu, Yugang; Song, Jun

2018-04-01

The problem of sliding mode control (SMC) is investigated for a class of uncertain switched systems subject to unmeasurable state and assigned finite (possible short) time constraint. A key issue is how to ensure the finite-time boundedness (FTB) of system state during reaching phase and sliding motion phase. To this end, a state observer is constructed to estimate the unmeasured states. And then, a state estimate-based SMC law is designed such that the state trajectories can be driven onto the specified integral sliding surface during the assigned finite time interval. By means of partitioning strategy, the corresponding FTB over reaching phase and sliding motion phase are guaranteed and the sufficient conditions are derived via average dwell time technique. Finally, an illustrative example is given to illustrate the proposed method.

Optimization of finite difference forward modeling for elastic waves based on optimum combined window functions

NASA Astrophysics Data System (ADS)

Jian, Wang; Xiaohong, Meng; Hong, Liu; Wanqiu, Zheng; Yaning, Liu; Sheng, Gui; Zhiyang, Wang

2017-03-01

Full waveform inversion and reverse time migration are active research areas for seismic exploration. Forward modeling in the time domain determines the precision of the results, and numerical solutions of finite difference have been widely adopted as an important mathematical tool for forward modeling. In this article, the optimum combined of window functions was designed based on the finite difference operator using a truncated approximation of the spatial convolution series in pseudo-spectrum space, to normalize the outcomes of existing window functions for different orders. The proposed combined window functions not only inherit the characteristics of the various window functions, to provide better truncation results, but also control the truncation error of the finite difference operator manually and visually by adjusting the combinations and analyzing the characteristics of the main and side lobes of the amplitude response. Error level and elastic forward modeling under the proposed combined system were compared with outcomes from conventional window functions and modified binomial windows. Numerical dispersion is significantly suppressed, which is compared with modified binomial window function finite-difference and conventional finite-difference. Numerical simulation verifies the reliability of the proposed method.

Ceramic component reliability with the restructured NASA/CARES computer program

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Starlinger, Alois; Gyekenyesi, John P.

1992-01-01

The Ceramics Analysis and Reliability Evaluation of Structures (CARES) integrated design program on statistical fast fracture reliability and monolithic ceramic components is enhanced to include the use of a neutral data base, two-dimensional modeling, and variable problem size. The data base allows for the efficient transfer of element stresses, temperatures, and volumes/areas from the finite element output to the reliability analysis program. Elements are divided to insure a direct correspondence between the subelements and the Gaussian integration points. Two-dimensional modeling is accomplished by assessing the volume flaw reliability with shell elements. To demonstrate the improvements in the algorithm, example problems are selected from a round-robin conducted by WELFEP (WEakest Link failure probability prediction by Finite Element Postprocessors).