NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Volakis, John L.
1989-01-01
A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principle advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.
Finite temperature holographic duals of 2-dimensional BCFTs
NASA Astrophysics Data System (ADS)
Estes, J.
2015-07-01
We consider holographic duals of 2-dimensional conformal field theories in the presence of a boundary, interface, defect and/or junction, referred to collectively as BCFTs. In general, the presence of a boundary reduces the SO(2, 2) conformal symmetry to SO(2, 1) and the dual geometry is realized as a warped product of the form , where is not compact. In particular, it will contain points where the warp factor of the AdS 2 space diverges, leading to asymptotically AdS 3 regions. We show that the AdS 2 space-time may always be replaced with an AdS 2-"black-hole" space-time. We argue the resulting geometry describes the BCFT at finite temperature. To motivate this claim, we compute the entanglement entropy holographically for a segment centered around the defect or ending on the boundary and find agreement with a known universal formula.
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
2006-03-08
MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operationmore » of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.« less
2005-05-07
CONEX is a code for joining sequentially in time multiple exodusll database files which all represent the same base mesh topology and geometry. It is used to create a single results or restart file from multiple results or restart files which typically arise as the result of multiple restarted analyses. CONEX is used to postprocess the results from a series of finite element analyses. It can join sequentially the data from multiple results databases intomore » a single database which makes it easier to postprocess the results data.« less
2005-06-26
Exotxt is an analysis code that reads finite element results data stored in an exodusII file and generates a file in a structured text format. The text file can be edited or modified via a number of text formatting tools. Exotxt is used by analysis to translate data from the binary exodusII format into a structured text format which can then be edited or modified and then either translated back to exodusII format or tomore » another format.« less
Probabilistic fracture finite elements
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Lua, Y. J.
1991-01-01
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Toward automatic finite element analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Perucchio, Renato; Voelcker, Herbert
1987-01-01
Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.
Second order tensor finite element
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Probabilistic Finite Element: Variational Theory
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.
1985-01-01
The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.
The NESSUS finite element code
NASA Technical Reports Server (NTRS)
Dias, J. B.; Nagiegaal, J. C.; Nakazawa, S.
1987-01-01
The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.
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.
Finite Element Modeling of Crustal Deformation in the North American Caribbean Plate Boundary Zone
NASA Technical Reports Server (NTRS)
Lundgren, P.; Russo, R.
1995-01-01
We have developed 2-dimensional spherical shell finite element models of elastic displacement in the North American-Caribbean (NA-Ca) plate boundary zone (PBZ) in order to quantify crust and fault motions in the PBZ.
Nonlinear, finite deformation, finite element analysis
NASA Astrophysics Data System (ADS)
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
ANSYS duplicate finite-element checker routine
NASA Technical Reports Server (NTRS)
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
Infinite Possibilities for the Finite Element.
ERIC Educational Resources Information Center
Finlayson, Bruce A.
1981-01-01
Describes the uses of finite element methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of finite element methods. (Author/WB)
Peridynamic Multiscale Finite Element Methods
Costa, Timothy; Bond, Stephen D.; Littlewood, David John; Moore, Stan Gerald
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
Finite element methods in numerical relativity.
NASA Astrophysics Data System (ADS)
Mann, P. J.
The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.
Finite element and finite difference methods in electromagnetic scattering
NASA Astrophysics Data System (ADS)
Morgan, Michael A.
Finite-difference and finite-element methods for the computational analysis of EM scattering phenomena are examined in chapters contributed by leading experts. Topics addressed include an FEM for composite scatterers, coupled finite- and boundary-element methods for EM scattering, absorbing boundary conditions for the direct solution PDEs arising in EM scattering problems, application of the control-region approximation to two-dimensional EM scattering, coupled potentials for EM fields in inhomogeneous media, the method of conforming boundary elements for transient electromagnetics, and the finite-difference time-domain method for numerical modeling of EM wave interactions with arbitrary structures. Extensive diagrams and graphs of typical results are provided.
Probabilistic finite element analysis of a craniofacial finite element model.
Berthaume, Michael A; Dechow, Paul C; Iriarte-Diaz, Jose; Ross, Callum F; Strait, David S; Wang, Qian; Grosse, Ian R
2012-05-01
We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed. We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth. When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
FEBio: finite elements for biomechanics.
Maas, Steve A; Ellis, Benjamin J; Ateshian, Gerard A; Weiss, Jeffrey A
2012-01-01
In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics. PMID:22482660
Finite element coiled cochlea model
NASA Astrophysics Data System (ADS)
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
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.
Graphics for Finite-Element Analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1982-01-01
ELPLOT program is a passive computer graphics system that could be utilized for display of models and responses of general finite-element analyses. Program includes: Wide range of view-orientation selections, number of alternative data-input formats, extensive family of finite-element types, and capabilities for both static and dynamic-response displays.
Finite element analysis of helicopter structures
NASA Technical Reports Server (NTRS)
Rich, M. J.
1978-01-01
Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.
Finite-Element Composite-Analysis Program
NASA Technical Reports Server (NTRS)
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
3-D Finite Element Code Postprocessor
1996-07-15
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
Modeling of coal stockpiles using a finite elements method
Ozdeniz, A.H.; Sensogut, C.
2008-07-01
In the case of coal stockpiles finding suitable environmental conditions, spontaneous combustion phenomenon will be unavoidable. In this study, an industrial-sized stockpile having a shape of triangle prism was constituted in a coal stockyard of Western Lignite Corporation (WLC), Turkey. The parameters of time, humidity and temperature of air, atmospheric pressure, velocity and direction of wind values that are effective on coal stockpile were measured in a continuous manner. These experimental works were transferred into a computer media in order to obtain similar outcomes by carrying out 2-dimensional analysis of the stockpile with Finite Elements Method (FEM). The performed experimental studies and obtained results were then compared.
Will Finite Elements Replace Structural Mechanics?
NASA Astrophysics Data System (ADS)
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
The finite element method in thermomechanics
Hsu, T.
1986-01-01
Thermal stress analysis is critical in the design and operation of energy-efficient power plant components and engines as well as in nuclear and aerospace systems. The Finite Element Method in Thermomechanics attempts to embrace a wide range of topics in the nonlinear thermomechanical analysis. The book covers the basic principles of the finite element method: the formulations for the base thermomechanical analysis, including thermoelastic-plastic-creep stress analysis; the use of Fourier series for nonaxisymmetric loadings, and stress waves in solids in thermal environments; and the base finite element code called TEPSAC.
Assignment Of Finite Elements To Parallel Processors
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.
1990-01-01
Elements assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform finite-element computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of elements to subdomains minimizes cost of computation.
Visualization of higher order finite elements.
Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay
2004-04-01
Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Finite element modeling of the human pelvis
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Finite-Element Modeling For Structural Analysis
NASA Technical Reports Server (NTRS)
Min, J. B.; Androlake, S. G.
1995-01-01
Report presents study of finite-element mathematical modeling as used in analyzing stresses and strains at joints between thin, shell-like components (e.g., ducts) and thicker components (e.g., flanges or engine blocks). First approach uses global/local model to evaluate system. Provides correct total response and correct representation of stresses away from any discontinuities. Second approach involves development of special transition finite elements to model transitions between shells and thicker structural components.
Finite element analysis of flexible, rotating blades
NASA Technical Reports Server (NTRS)
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
A robust, finite element model for hydrostatic surface water flows
Walters, R.A.; Casulli, V.
1998-01-01
A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Finite-element models of continental extension
NASA Technical Reports Server (NTRS)
Lynch, H. David; Morgan, Paul
1990-01-01
Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.
NASA Astrophysics Data System (ADS)
Zhu, Lu; Liu, Yuanyuan; Chen, Suhua; Hu, Fei; Chen, Zhizhang (David)
2015-04-01
Synthetic aperture imaging radiometer (SAIR) has the potential to meet the spatial resolution requirement of passive millimeter remote sensing from space. A new two-dimensional (2-D) imaging radiometer at millimeter wave (MMW) band is described in this paper; it uses a one-dimensional (1-D) synthetic aperture digital radiometer (SADR) to obtain an image on one dimension and a rotary platform to provide a scan on the second dimension. Due to the ill-posed inverse problem of SADR, we proposed a new reconstruction algorithm based on Finite Difference (FD) regularization to improve brightness temperature images. Experimental results show that the proposed 2-D MMW radiometer can give the brightness temperature images of natural scenes and the FD regularization reconstruction algorithm is able to improve the quality of brightness temperature images.
Verification of Orthogrid Finite Element Modeling Techniques
NASA Technical Reports Server (NTRS)
Steeve, B. E.
1996-01-01
The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.
Visualizing higher order finite elements. Final report
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
Finite element radiation transport in one dimension
Painter, J.F.
1997-05-09
A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature `in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte`s two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.
Studies of finite element analysis of composite material structures
NASA Technical Reports Server (NTRS)
Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.
1975-01-01
Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.
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.
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 modeling of nonisothermal polymer flows
NASA Technical Reports Server (NTRS)
Roylance, D.
1981-01-01
A finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer are important is described, and the numerical model is illustrated by means of computer experiments using extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments.
Evolution of assumed stress hybrid finite element
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1984-01-01
Early versions of the assumed stress hybrid finite elements were based on the a priori satisifaction of stress equilibrium conditions. In the new version such conditions are relaxed but are introduced through additional internal displacement functions as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are now of complete polynomials up to the same degree as that of the assumed stresses. Several example problems indicate that optimal element properties are resulted by this method.
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.
Quadrilateral/hexahedral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E
2012-10-16
A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.
Finite Element Simulation of Smart Structures
NASA Technical Reports Server (NTRS)
Cui, Y. Lawrence; Panahandeh, M.
1996-01-01
Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.
Finite element displacement analysis of a lung.
NASA Technical Reports Server (NTRS)
Matthews, F. L.; West, J. B.
1972-01-01
A method is given based on the technique of finite elements which determines theoretically the mechanical behavior of a lung-shaped body loaded by its own weight. The results of this theoretical analysis have been compared with actual measurements of alveolar size and pleural pressures in animal lungs.
Animation of finite element models and results
NASA Technical Reports Server (NTRS)
Lipman, Robert R.
1992-01-01
This is not intended as a complete review of computer hardware and software that can be used for animation of finite element models and results, but is instead a demonstration of the benefits of visualization using selected hardware and software. The role of raw computational power, graphics speed, and the use of videotape are discussed.
On Hybrid and mixed finite element methods
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Finite element computation with parallel VLSI
NASA Technical Reports Server (NTRS)
Mcgregor, J.; Salama, M.
1983-01-01
This paper describes a parallel processing computer consisting of a 16-bit microcomputer as a master processor which controls and coordinates the activities of 8086/8087 VLSI chip set slave processors working in parallel. The hardware is inexpensive and can be flexibly configured and programmed to perform various functions. This makes it a useful research tool for the development of, and experimentation with parallel mathematical algorithms. Application of the hardware to computational tasks involved in the finite element analysis method is demonstrated by the generation and assembly of beam finite element stiffness matrices. A number of possible schemes for the implementation of N-elements on N- or n-processors (N is greater than n) are described, and the speedup factors of their time consumption are determined as a function of the number of available parallel processors.
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Finite Element Interface to Linear Solvers
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on themore » problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.« less
Finite Element Heat & Mass Transfer Code
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; andmore » double porosity and double porosity/double permeability capabilities.« less
Diagonal multisoliton matrix elements in finite volume
NASA Astrophysics Data System (ADS)
Pálmai, T.; Takács, G.
2013-02-01
We consider diagonal matrix elements of local operators between multisoliton states in finite volume in the sine-Gordon model and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture, we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Plasticity - Theory and finite element applications.
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H. S.
1972-01-01
A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
2-d Finite Element Code Postprocessor
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
Finite Element Analysis of Honeycomb Impact Attenuator
NASA Astrophysics Data System (ADS)
Yang, Seung-Yong; Choi, Seung-Kyu; Kim, Nohyu
To participate in Student Formula Society of Automotive Engineers (SAE) competitions, it is necessary to build an impact attenuator that would give an average deceleration not to exceed 20g when it runs into a rigid wall. Students can use numerical simulations or experimental test data to show that their car satisfies this safety requirement. A student group to study formula cars at the Korea University of Technology and Education has designed a vehicle to take part in a SAE competition, and a honeycomb structure was adopted as the impact attenuator. In this paper, finite element calculations were carried out to investigate the dynamic behavior of the honeycomb attenuator. Deceleration and deformation behaviors were studied. Effect of the yield strength was checked by comparing the numerical results. ABAQUS/Explicit finite element code was used.
Finite Element Analysis of Reverberation Chambers
NASA Technical Reports Server (NTRS)
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
Finite element analysis of wrinkling membranes
NASA Technical Reports Server (NTRS)
Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.
1984-01-01
The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.
ExodusII Finite Element Data Model
2005-05-14
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface. (exodus II is based on netcdf)
Finite element based electric motor design optimization
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1993-01-01
The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.
Finite Element Results Visualization for Unstructured Grids
Speck, Douglas E.; Dovey, Donald J.
1996-07-15
GRIZ is a general-purpose post-processing application supporting interactive visualization of finite element analysis results on unstructured grids. In addition to basic pseudocolor renderings of state variables over the mesh surface, GRIZ provides modern visualization techniques such as isocontours and isosurfaces, cutting planes, vector field display, and particle traces. GRIZ accepts both command-line and mouse-driven input, and is portable to virtually any UNIX platform which provides Motif and OpenGl libraries.
Finite element model of needle electrode sensitivity
NASA Astrophysics Data System (ADS)
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
FESDIF -- Finite Element Scalar Diffraction theory code
Kraus, H.G.
1992-09-01
This document describes the theory and use of a powerful scalar diffraction theory based computer code for calculation of intensity fields due to diffraction of optical waves by two-dimensional planar apertures and lenses. This code is called FESDIF (Finite Element Scalar Diffraction). It is based upon both Fraunhofer and Kirchhoff scalar diffraction theories. Simplified routines for circular apertures are included. However, the real power of the code comes from its basis in finite element methods. These methods allow the diffracting aperture to be virtually any geometric shape, including the various secondary aperture obstructions present in telescope systems. Aperture functions, with virtually any phase and amplitude variations, are allowed in the aperture openings. Step change aperture functions are accommodated. The incident waves are considered to be monochromatic. Plane waves, spherical waves, or Gaussian laser beams may be incident upon the apertures. Both area and line integral transformations were developed for the finite element based diffraction transformations. There is some loss of aperture function generality in the line integral transformations which are typically many times more computationally efficient than the area integral transformations when applicable to a particular problem.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1987-01-01
Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Enhancements to modal testing using finite elements
NASA Astrophysics Data System (ADS)
Jarvis, Brian
In calculating the natural frequencies and mode shapes from a finite element analysis, there are generally many more degrees of freedom than can be handled for the eigensolution. A reduction process is employed to reduce the number to a master set and chosen so that the modes of interest are well defined. By choosing those freedoms where the inertia terms are high or the stiffness terms are low then an automatic procedure for selecting the best freedoms can be defined. For modal testing, these master freedoms also indicate the best transducer locations for optimum low order mode identification. Having carried out the modal test, the mode shapes obtained can be forced onto the finite element model giving greatly enhanced results. By examining terms in all mode shapes from the finite element model in the frequency range of interest, the best reference or excitation position can be found. An example of the use of this technique to study the modal properties of an aero-engine compressor blade is given.
Variational approach to probabilistic finite elements
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.
1991-01-01
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Mixed Finite Element Method for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Modelling bucket excavation by finite element
NASA Astrophysics Data System (ADS)
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
Finite element methods in probabilistic mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Mani, A.; Belytschko, Ted
1987-01-01
Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.
Shape optimization including finite element grid adaptation
NASA Technical Reports Server (NTRS)
Kikuchi, N.; Taylor, J. E.
1984-01-01
The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.
Chemorheology of reactive systems: Finite element analysis
NASA Technical Reports Server (NTRS)
Douglas, C.; Roylance, D.
1982-01-01
The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.
Finite element solutions of free surface flows
NASA Technical Reports Server (NTRS)
Zarda, P. R.; Marcus, M. S.
1977-01-01
A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.
System software for the finite element machine
NASA Technical Reports Server (NTRS)
Crockett, T. W.; Knott, J. D.
1985-01-01
The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested.
NASA Technical Reports Server (NTRS)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
Adaptive Finite Element Methods in Geodynamics
NASA Astrophysics Data System (ADS)
Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2006-12-01
Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever
2-D Finite Element Heat Conduction
1989-10-30
AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less
Iterative methods for mixed finite element equations
NASA Technical Reports Server (NTRS)
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
Dynamic analysis of mechanisms by finite elements
Botsali, F.M.; Uenuevar, A.
1996-11-01
The need to increase productivity in order to decrease manufacturing costs lead to an increase in the working speeds of machines and mechanical systems used in manufacturing. A method is presented for investigating the dynamics of mechanisms with elastic links. Finite element method is used in the formulation of the dynamic problem. Modal transformation is used in order to reduce the number of equations of motion. Using the presented technique, elastic and rigid body motions of mechanism links are solved simultaneously. The presented method may be applied to spatial and open loop mechanisms including robot manipulators as well.
Finite element modeling of piezoelectric elements with complex electrode configuration
NASA Astrophysics Data System (ADS)
Paradies, R.; Schläpfer, B.
2009-02-01
It is well known that the material properties of piezoelectric materials strongly depend on the state of polarization of the individual element. While an unpolarized material exhibits mechanically isotropic material properties in the absence of global piezoelectric capabilities, the piezoelectric material properties become transversally isotropic with respect to the polarization direction after polarization. Therefore, for evaluating piezoelectric elements the material properties, including the coupling between the mechanical and the electromechanical behavior, should be addressed correctly. This is of special importance for the micromechanical description of piezoelectric elements with interdigitated electrodes (IDEs). The best known representatives of this group are active fiber composites (AFCs), macro fiber composites (MFCs) and the radial field diaphragm (RFD), respectively. While the material properties are available for a piezoelectric wafer with a homogeneous polarization perpendicular to its plane as postulated in the so-called uniform field model (UFM), the same information is missing for piezoelectric elements with more complex electrode configurations like the above-mentioned ones with IDEs. This is due to the inhomogeneous field distribution which does not automatically allow for the correct assignment of the material, i.e. orientation and property. A variation of the material orientation as well as the material properties can be accomplished by including the polarization process of the piezoelectric transducer in the finite element (FE) simulation prior to the actual load case to be investigated. A corresponding procedure is presented which automatically assigns the piezoelectric material properties, e.g. elasticity matrix, permittivity, and charge vector, for finite element models (FEMs) describing piezoelectric transducers according to the electric field distribution (field orientation and strength) in the structure. A corresponding code has been
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A.; Mrozek, Randy A.; Lenhart, Joseph Ludlow; Rao, Rekha Ranjana; Collins, Robert; Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
Quantum algorithms and the finite element method
NASA Astrophysics Data System (ADS)
Montanaro, Ashley; Pallister, Sam
2016-03-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretizes the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution to a boundary value problem and compare the quantum algorithm's theoretical performance with that of a standard classical algorithm—the conjugate gradient method. Prior work claimed that the quantum algorithm could be exponentially faster but did not determine the overall classical and quantum run times required to achieve a predetermined solution accuracy. Taking this into account, we find that the quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation. In addition, we give evidence that no improvement of the quantum algorithm can lead to a superpolynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.
Impeller deflection and modal finite element analysis.
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
A finite element model for ultrasonic cutting.
Lucas, Margaret; MacBeath, Alan; McCulloch, Euan; Cardoni, Andrea
2006-12-22
Using a single-blade ultrasonic cutting device, a study of ultrasonic cutting of three very different materials is conducted using specimens of cheese, polyurethane foam and epoxy resin. Initial finite element models are created, based on the assumption that the ultrasonic blade causes a crack to propagate in a controlled mode 1 opening, and these are validated against experimental data from three point bend fracture tests and ultrasonic cutting experiments on the materials. Subsequently, the finite element model is developed to represent ultrasonic cutting of a multi-layered material. Materials are chosen whose properties allow a model to be developed that could represent a multi-layer food product or biological structure, to enable ultrasonic cutting systems to be designed for applications both in the field of food processing and surgical procedures. The model incorporates an estimation of the friction condition between the cutting blade and the material to be cut and allows adjustment of the frequency, cutting amplitude and cutting speed. PMID:16814351
Overcoming element erosion limitations within Lagrangian finite element codes
NASA Astrophysics Data System (ADS)
Vignjevic, Rade; Hughes, Kevin; Walker, Andrew; Taylor, Emma A.
2001-10-01
Lagrangian finite element methods have been used extensively in the past to study the non-linear transient behaviour of materials, ranging from crash test of cars to simulating bird strikes on planes.... However, as this type of space discretization does not allow for motion of the material through the mesh when modelling extremely large deformations, the mesh becomes highly distorted. This paper describes some limitations and applicability of this type of analysis for high velocity impacts. A method for dealing with this problem is by the erosion of elements is proposed where the main issue is the deformation of element failure strains. Results were compared with empirical perforation results and were found to be in good agreement. The results were then used to simulate high velocity impacts upon a multi-layered aluminium target, in order to predict a ballistic limit curve. LS-DYNA3D was used as the FE solver for all simulations. Meshes were generated with Truegrid.
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Finite element analysis enhancement of cryogenic testing
NASA Astrophysics Data System (ADS)
Thiem, Clare D.; Norton, Douglas A.
1991-12-01
Finite element analysis (FEA) of large space optics enhances cryogenic testing by providing an analytical method by which to ensure that a test article survives proposed testing. The analyses presented in this paper were concerned with determining the reliability of a half meter mirror in an environment where the exact environmental profile was unknown. FEA allows the interaction between the test object and the environment to be simulated to detect potential problems prior to actual testing. These analyses examined worse case scenerios related to cooling the mirror, its structural integrity for the proposed test environment, and deformation of the reflective surface. The FEA was conducted in-house on the System's Reliability Division's VAX 11-750 and Decstation 3100 using Engineering Mechanics Research Corporation's numerically integrated elements for systems analysis finite element software. The results of the analyses showed that it would take at least 48 hours to cool the mirror to its desired testing temperature. It was also determined that the proposed mirror mount would not cause critical concentrated thermal stresses that would fracture the mirror. FEA and actual measurements of the front reflective face were compared and good agreement between computer simulation and physical tests were seen. Space deployment of large optics requires lightweight mirrors which can perform under the harsh conditions of space. The physical characteristics of these mirrors must be well understood in order that their deployment and operation are successful. Evaluating design approaches by analytical simulation, like FEA, verifies the reliability and structural integrity of a space optic during design prior to prototyping and testing. Eliminating an optic's poor design early in its life saves money, materials, and human resources while ensuring performance.
Elbow stress indices using finite element analysis
NASA Astrophysics Data System (ADS)
Yu, Lixin
Section III of the ASME Boiler and Pressure Vessel Code (the Code) specifies rules for the design of nuclear power plant components. NB-3600 of the Code presents a simplified design method using stress indices---Scalar Coefficients used the modify straight pipe stress equations so that they can be applied to elbows, tees and other piping components. The stress indices of piping components are allowed to be determined both analytically and experimentally. This study concentrates on the determination of B2 stress indices for elbow components using finite element analysis (FEA). First, the previous theoretical, numerical and experimental investigations on elbow behavior were comprehensively reviewed, as was the philosophy behind the use of stress indices. The areas of further research was defined. Then, a comprehensive investigation was carried out to determine how the finite element method should be used to correctly simulate an elbow's structural behavior. This investigation included choice of element type, convergence of mesh density, use of boundary restraint and a reconciliation study between FEA and laboratory experiments or other theoretical formulations in both elastic and elasto-plastic domain. Results from different computer programs were also compared. Reasonably good reconciliation was obtained. Appendix II of the Code describes the experimental method to determine B2 stress indices based on load-deflection curves. This procedure was used to compute the B2 stress indices for various loading modes on one particular elbow configuration. The B2 stress indices thus determined were found to be about half of the value calculated from the Code equation. Then the effect on B2 stress indices of those factors such as internal pressure and flange attachments were studied. Finally, the investigation was extended to other configurations of elbow components. A parametric study was conducted on different elbow sizes and schedules. Regression analysis was then used to
Mixed Finite Element Methods for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
NASA Astrophysics Data System (ADS)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
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 analyses is presented. New thermal finite elements which yield exact nodal and element temperature 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.
A Viscoelastic Hybrid Shell Finite Element
NASA Technical Reports Server (NTRS)
Johnson, Arthur
1999-01-01
An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
Asymmetric quadrilateral shell elements for finite strains
NASA Astrophysics Data System (ADS)
Areias, P.; Dias-da-Costa, D.; Pires, E. B.; Van Goethem, N.
2013-07-01
Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov-Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.
Fuzzy finite element analysis of smart structures
NASA Astrophysics Data System (ADS)
Akpan, Unyime O.; Koko, Tamunoiyala S.; Orisamolu, Irewole R.; Gallant, B. Keith
2000-06-01
A fuzzy finite element based approach is developed for modelling smart structures with vague or imprecise uncertainties. Fuzzy sets are used to represent the uncertainties present in the piezoelectric, mechanical, thermal, and physical properties of the smart structure. In order to facilitate efficient computation, a sensitivity analysis procedure is used to streamline the number of input fuzzy variables, and the vertex fuzzy analysis technique is then used to compute the possibility distributions of the responses of the smart structural system. The methodology has been developed within the framework of the SMARTCOM computational tool for the design/analysis of smart composite structures. The methodology developed is found to be accurate and computationally efficient for solution of practical problems.
Continuation finite element analysis of viscoelastic fluids
NASA Astrophysics Data System (ADS)
Chow, Tai-Whang
A finite element procedure using a mixed formulation and a predictor-corrector type continuation algorithm for the analysis of two dimensional steady state flows of viscoelastic fluids is described. As a simple but nontrivial test example, radial flow immenating from a line by the numerical discretization and believed to be the cause for previous numerical failures, are shown and branch solution paths are followed by step length adjustment and by convergent tolerance relaxation. A technique for jumping over bifurcation points is presented and used to increase the Weissenberg number with no apparent limit for the radial flow problem. A second example related to extrusion of viscoelastic material is also analyzed. Steady state velocity fields, deviatoric stress distributions and pressure distributions for several different Weissenberg numbers are presented with bifurcation points and turning points noted.
Quality management of finite element analysis
NASA Astrophysics Data System (ADS)
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
Finite-element modeling of nanoindentation
Knapp, J.A.; Follstaedt, D.M.; Myers, S.M.; Barbour, J.C.; Friedmann, T.A.
1999-02-01
Procedures have been developed based on finite-element modeling of nanoindentation data to obtain the mechanical properties of thin films and ion-beam-modified layers independently of the properties of the underlying substrates. These procedures accurately deduce the yield strength, Young{close_quote}s elastic modulus, and layer hardness from indentations as deep as 50{percent} of the layer thickness or more. We have used these procedures to evaluate materials ranging from ion implanted metals to deposited, diamond-like carbon layers. The technique increases the applicability of indentation testing to very thin layers, composite layers, and modulated compositions. This article presents an overview of the procedures involved and illustrates them with selected examples. {copyright} {ital 1999 American Institute of Physics.}
3-D Finite Element Heat Transfer
1992-02-01
TOPAZ3D is a three-dimensional implicit finite element computer code for heat transfer analysis. TOPAZ3D can be used to solve for the steady-state or transient temperature field on three-dimensional geometries. Material properties may be temperature-dependent and either isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions can be specified including temperature, flux, convection, and radiation. By implementing the user subroutine feature, users can model chemical reaction kinetics and allow for any type of functionalmore » representation of boundary conditions and internal heat generation. TOPAZ3D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in the material surrounding the enclosure. Additional features include thermal contact resistance across an interface, bulk fluids, phase change, and energy balances.« less
Finite element analysis: A boon to dentistry
Trivedi, Shilpa
2014-01-01
The finite element analysis (FEA) is an upcoming and significant research tool for biomechanical analyses in biological research. It is an ultimate method for modeling complex structures and analyzing their mechanical properties. In Implantology, FEA has been used to study the stress patterns in various implant components and also in the peri-implant bone. It is also useful for studying the biomechanical properties of implants as well as for predicting the success of implants in clinical condition. FEA of simulated traumatic loads can be used to understand the biomechanics of fracture. FEA has various advantages compared with studies on real models. The experiments are repeatable, there are no ethical considerations and the study designs may be modified and changed as per the requirement. There are certain limitations of FEA too. It is a computerized in vitro study in which clinical condition may not be completely replicated. So, further FEA research should be supplemented with clinical evaluation. PMID:25737944
Finite element simulation of pipe dynamic response
Slagis, G.C.; Litton, R.W.
1996-12-01
Nonlinear finite element dynamic analyses of the response of a pipe span to controlled-displacement, sinusoidal vibration have been performed. The objective of this preliminary study is to compare strain and acceleration response data to those generated by Beaney in the Berkeley Nuclear Laboratories experiments. Results for an unpressurized, 5 Hz, carbon steel pipe are in good agreement with the experiments. Hence, it appears that analytical simulation will be useful to assess seismic margins. Recommendations for additional studies are provided. The analyses confirm the test results--dynamic response is greatly attenuated by material plasticity. Analytical strains and accelerations are about 30% higher than test data. There are several possible explanations for the differences. To assess the effect of frequency on response, the length of the pipe span was increased. Analysis of the longer, 2 Hz, pipe span shows significantly greater cyclic strains than the 5 Hz span at the same input excitation levels.
Finite-element solutions for geothermal systems
NASA Technical Reports Server (NTRS)
Chen, J. C.; Conel, J. E.
1977-01-01
Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.
Optimizing electroslag cladding with finite element modeling
Li, M.V.; Atteridge, D.G.; Meekisho, L.
1996-12-31
Electroslag cladding of nickel alloys onto carbon steel propeller shafts was optimized in terms of interpass temperatures. A two dimensional finite element model was used in this study to analyze the heat transfer induced by multipass electroslag cladding. Changes of interpass temperatures during a cladding experiment with uniform initial temperature distribution on a section of shaft were first simulated. It was concluded that uniform initial temperature distribution would lead to interpass temperatures out of the optimal range if continuous cladding is expected. The difference in the cooling conditions among experimental and full size shafts and its impact on interpass temperatures during the cladding were discussed. Electroslag cladding onto a much longer shaft, virtually an semi infinite long shaft, was analyzed with specific reference to the practical applications of electroslag cladding. Optimal initial preheating temperature distribution was obtained for continuous cladding on full size shafts which would keep the interpass temperatures within the required range.
Finite element or Galerkin type semidiscrete schemes
NASA Technical Reports Server (NTRS)
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
Boundary element and finite element coupling for aeroacoustics simulations
NASA Astrophysics Data System (ADS)
Balin, Nolwenn; Casenave, Fabien; Dubois, François; Duceau, Eric; Duprey, Stefan; Terrasse, Isabelle
2015-08-01
We consider the scattering of acoustic perturbations in the presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary. Validations against analytic, another numerical method and measurements on different test cases are presented.
Finite element analyses of CCAT preliminary design
NASA Astrophysics Data System (ADS)
Sarawit, Andrew T.; Kan, Frank W.
2014-07-01
This paper describes the development of the CCAT telescope finite element model (FEM) and the analyses performed to support the preliminary design work. CCAT will be a 25 m diameter telescope operating in the 0.2 to 2 mm wavelength range. It will be located at an elevation of 5600 m on Cerro Chajnantor in Northern Chile, near ALMA. The telescope will be equipped with wide-field cameras and spectrometers mounted at the two Nasmyth foci. The telescope will be inside an enclosure to protect it from wind buffeting, direct solar heating, and bad weather. The main structures of the telescope include a steel Mount and a carbon-fiber-reinforced-plastic (CFRP) primary truss. The finite element model developed in this study was used to perform modal, frequency response, seismic response spectrum, stress, and deflection analyses of telescope. Modal analyses of telescope were performed to compute the structure natural frequencies and mode shapes and to obtain reduced order modal output at selected locations in the telescope structure to support the design of the Mount control system. Modal frequency response analyses were also performed to compute transfer functions at these selected locations. Seismic response spectrum analyses of the telescope subject to the Maximum Likely Earthquake were performed to compute peak accelerations and seismic demand stresses. Stress analyses were performed for gravity load to obtain gravity demand stresses. Deflection analyses for gravity load, thermal load, and differential elevation drive torque were performed so that the CCAT Observatory can verify that the structures meet the stringent telescope surface and pointing error requirements.
NASA Technical Reports Server (NTRS)
1976-01-01
The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
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.
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.
Finite element analysis in a minicomputer/mainframe environment
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Murphy, R. C.
1978-01-01
Design considerations were evaluated for general purpose finite element systems to maximize performance when installed on distributed computer hardware/software systems. It is shown how the features of current minicomputers complement those of a modular implementation of the finite element method for increasing the control, speed, and visibility (interactive graphics) in solving structural problems at reduced cost. The approach used is to implement a finite element system in a distributed computer environment to solve structural problems and to explore alternatives in distributing finite element computations.
A multi-microprocessor system for finite element structural analysis
NASA Technical Reports Server (NTRS)
Jordan, H. F.; Sawyer, P. L.
1978-01-01
During the last few years, advances in microprocessor technology have spurred a renewed interest in special-purpose computers. The microprocessor has become small, inexpensive, and powerful enough to be considered as a building block for special-purpose hardware. A description is presented of the architecture of a prototype 'finite element machine' currently being built. Attention is given to details regarding the finite element analysis problem, the arrangement of the processors as finite element nodes in the structural model, the influence of the architecture on the solution algorithm, interprocessor communication primitives, and the performance of the finite element machine.
Ablative Thermal Response Analysis Using the Finite Element Method
NASA Technical Reports Server (NTRS)
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Isoparametric 3-D Finite Element Mesh Generation Using Interactive Computer Graphics
NASA Technical Reports Server (NTRS)
Kayrak, C.; Ozsoy, T.
1985-01-01
An isoparametric 3-D finite element mesh generator was developed with direct interface to an interactive geometric modeler program called POLYGON. POLYGON defines the model geometry in terms of boundaries and mesh regions for the mesh generator. The mesh generator controls the mesh flow through the 2-dimensional spans of regions by using the topological data and defines the connectivity between regions. The program is menu driven and the user has a control of element density and biasing through the spans and can also apply boundary conditions, loads interactively.
Integrated finite element model of composite materials
NASA Astrophysics Data System (ADS)
Teply, Jan L.; Herbein, William C.
1989-05-01
Two problems traditionally addressed in the area of micromechanics of composite materials can be briefly summarized as follows: (1) for a macroscopically uniform volume of composite material, which is subjected to macroscopically uniform boundary tractions, displacements or heat influx, find overall thermomechanical properties in terms of the thermomechanical properties of the individual constituents; and (2) for the same material volume and boundary conditions as above, find the local stress, strain, and temperature fields in the constituents and on the interfaces. Two different types of micromechanical models are usually applied to the solutions of these two types of problems. For linear elastic materials, the micromechanical models to solve problem (1) offer simple solutions of overall thermomechanical properties either in terms of bound which are derived from periodic or random microstructures, or in terms of single estimates, which are derived from a solution of an isolated inclusion. The finite element variational approaches are applied to integrate the solutions of problems (1) and (2) into one model. The application of displacement and equilibrium variational approaches to the calculation of overall elastic-plastic properties, are extended to the solution of the second problem. The integrated model is then applied to calculate the overall properties and local stress and strain fields of boron-aluminum composites subjected to transverse tension, in-plane shear and bending.
Laterally displaced pipelines: Finite element analysis
Altaee, A.; Boivin, R.
1995-12-31
The rate effect of lateral soil movement against buried pipes in clay soils is investigated in finite element analyzes using two different computer programs, AGAC and CRISP. Rapid and slow ground movements are considered in ideal undrained and ideal drained analysis, respectively, which represent the two extreme boundaries with respect to rate of loading (rate of ground movement). The analyses address a typical full-scale buried pipe as described by Rizkalla et al. (1992). The pipe considered for the analysis has a diameter of 0.914 m and is placed in a backfilled 2.0 m wide and 1.8 m deep excavation. Results from both AGAC and CRISP analyzes are similar in terms of total lateral force versus lateral pipe movement. For example, both programs indicate the same clear difference in the resulting pipe movement for cases of rapid and slow ground movement, especially at large movement. When the ground movement is rapid, the pipe moves both laterally and upward. One the other hand, when the ground movement is slow, the pipe experiences only lateral movement and no noticeable vertical movement. The total force acting on the pipe (and stresses and strains within the pipe) is larger for the slow rate of loading. The results of analyzes presented herein agree with results of tests on a 5.5 m beam centrifuge performed by the Center for Cold Oceans Resources Engineering.
Finite element modeling of retinal prosthesis mechanics
NASA Astrophysics Data System (ADS)
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
Finite Element Modeling of Human Placental Tissue
Yu, Mao; Manoogian, Sarah; Duma, Stefan M.; Stitzel, Joel D.
2009-01-01
Motor vehicle crashes account for a large portion of placental abruption and fetal losses. To better understand the material properties of the human placenta, a Finite Element (FE) model of human placenta tissue was created and verified using data from uniaxial tension tests. Sixty-four tensile tests at three different strain rates of 7% strain/s, 70% strain/s, and 700% strain/s from six whole human placentas were used for model development. Nominal stresses were calculated by dividing forces at the grips by the original cross-sectional area. Nominal strains were calculated by dividing cross-head displacement by the original gauge length. A detailed methodology for interpreting experimental data for application to material model development is presented. A model of the tension coupon was created in LS-DYNA and stretched in the same manner as the uniaxial tension tests. The behavior of the material was optimized to the uniaxial tension test using a multi-island genetic algorithm. The results demonstrate good correlation between experiments and the model, with an average difference of 2% between the optimized FE and experimental first principal stress at the termination state. The material parameters found in this study can be utilized in FE models of placental tissues for behavior under dynamic loading. PMID:20184849
TACO: a finite element heat transfer code
Mason, W.E. Jr.
1980-02-01
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code.
Finite Element Analysis (FEA) in Design and Production.
ERIC Educational Resources Information Center
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
FINITE-ELEMENT ANALYSIS OF MULTIPHASE IMMISCIBLE FLOW THROUGH SOILS
A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equation...
A computer graphics program for general finite element analyses
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1978-01-01
Documentation for a computer graphics program for displays from general finite element analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid finite element analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.
Solution-adaptive finite element method in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
Finite element meshing of ANSYS (trademark) solid models
NASA Technical Reports Server (NTRS)
Kelley, F. S.
1987-01-01
A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.
Modular Finite Element Methods Library Version: 1.0
2010-06-22
MFEM is a general, modular library for finite element methods. It provides a variety of finite element spaces and bilinear/linear forms in 2D and 3D. MFEM also includes classes for dealing with various types of meshes and their refinement.
Finite Element analyses of soil bioengineered slopes
NASA Astrophysics Data System (ADS)
Tamagnini, Roberto; Switala, Barbara Maria; Sudan Acharya, Madhu; Wu, Wei; Graf, Frank; Auer, Michael; te Kamp, Lothar
2014-05-01
Soil Bioengineering methods are not only effective from an economical point of view, but they are also interesting as fully ecological solutions. The presented project is aimed to define a numerical model which includes the impact of vegetation on slope stability, considering both mechanical and hydrological effects. In this project, a constitutive model has been developed that accounts for the multi-phase nature of the soil, namely the partly saturated condition and it also includes the effects of a biological component. The constitutive equation is implemented in the Finite Element (FE) software Comes-Geo with an implicit integration scheme that accounts for the collapse of the soils structure due to wetting. The mathematical formulation of the constitutive equations is introduced by means of thermodynamics and it simulates the growth of the biological system during the time. The numerical code is then applied in the analysis of an ideal rainfall induced landslide. The slope is analyzed for vegetated and non-vegetated conditions. The final results allow to quantitatively assessing the impact of vegetation on slope stability. This allows drawing conclusions and choosing whenever it is worthful to use soil bioengineering methods in slope stabilization instead of traditional approaches. The application of the FE methods show some advantages with respect to the commonly used limit equilibrium analyses, because it can account for the real coupled strain-diffusion nature of the problem. The mechanical strength of roots is in fact influenced by the stress evolution into the slope. Moreover, FE method does not need a pre-definition of any failure surface. FE method can also be used in monitoring the progressive failure of the soil bio-engineered system as it calculates the amount of displacements and strains of the model slope. The preliminary study results show that the formulated equations can be useful for analysis and evaluation of different soil bio
Nondestructive Evaluation Correlated with Finite Element Analysis
NASA Technical Reports Server (NTRS)
Abdul-Azid, Ali; Baaklini, George Y.
1999-01-01
Advanced materials are being developed for use in high-temperature gas turbine applications. For these new materials to be fully utilized, their deformation properties, their nondestructive evaluation (NDE) quality and material durability, and their creep and fatigue fracture characteristics need to be determined by suitable experiments. The experimental findings must be analyzed, characterized, modeled and translated into constitutive equations for stress analysis and life prediction. Only when these ingredients - together with the appropriate computational tools - are available, can durability analysis be performed in the design stage, long before the component is built. One of the many structural components being evaluated by the NDE group at the NASA Lewis Research Center is the flywheel system. It is being considered as an energy storage device for advanced space vehicles. Such devices offer advantages over electrochemical batteries in situations demanding high power delivery and high energy storage per unit weight. In addition, flywheels have potentially higher efficiency and longer lifetimes with proper motor-generator and rotor design. Flywheels made of fiber-reinforced polymer composite material show great promise for energy applications because of the high energy and power densities that they can achieve along with a burst failure mode that is relatively benign in comparison to those of flywheels made of metallic materials Therefore, to help improve durability and reduce structural uncertainties, we are developing a comprehensive analytical approach to predict the reliability and life of these components under these harsh loading conditions. The combination of NDE and two- and three-dimensional finite element analyses (e.g., stress analyses and fracture mechanics) is expected to set a standardized procedure to accurately assess the applicability of using various composite materials to design a suitable rotor/flywheel assembly.
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-08-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed.
Interpolation functions in the immersed boundary and finite element methods
NASA Astrophysics Data System (ADS)
Wang, Xingshi; Zhang, Lucy T.
2010-03-01
In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the existing interpolation functions such as the discretized Dirac delta function and the reproducing kernel interpolation function. The finite element shape function is easy to implement and it naturally satisfies the reproducing condition. They are interpolated through only one element layer instead of smearing to several elements. A pressure jump is clearly captured at the fluid-solid interface. Two example problems are studied and results are compared with other numerical methods. A convergence test is thoroughly conducted for the independent fluid and solid meshes in a fluid-structure interaction system. The required mesh size ratio between the fluid and solid domains is obtained.
A modified finite element procedure for underwater shock analysis
Chan, S.K.
1990-12-31
Using the regular finite element method for analyzing wave propagation problems presents difficulties: (a) The finite element mesh gives spurious reflection of the traveling wave and (b) Since a finite element model has to have a finite boundary, the wave is reflected by the outside boundary. However, for underwater shock problems, only the response of the structure is of major interest, not the behavior of the wave itself, and the shock wave can be assumed to be spherical. By taking advantage of the limited scope of the underwater shock problem, a finite element procedure can be developed that eliminates the above difficulties. This procedure not only can give very accurate solutions but it may also include structural nonlinearities and effect of cavitation.
Application of the Finite Element Method to Rotary Wing Aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Friedmann, P. P.
1982-01-01
A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.
Nonlinear finite element modeling of THUNDER piezoelectric actuators
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-06-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (Thin Layer Unimorph Ferroelectric Driver) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Quality assessment and control of finite element solutions
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Babuska, Ivo
1987-01-01
Status and some recent developments in the techniques for assessing the reliability of finite element solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the finite element solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the finite element solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.
P-Finite-Element Program For Analysis Of Plates
NASA Technical Reports Server (NTRS)
Smith, James P.
1995-01-01
BUCKY is p-finite-element computer program for highly accurate analysis of structures. Used to analyze buckling, bending, and in-plane stress-and-strain behaviors of plates. Provides elastic-plastic solutions for isotropic plates in states of plane stress, and axisymmetric solution sequence used to treat three-dimensional problems. Computes response of plate to variety of loading and boundary conditions by use of higher-order displacement function in p-finite-element method. Enables user to obtain results more accurate than obtained by use of traditional h-finite elements. Written in FORTRAN 77.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
NASA Technical Reports Server (NTRS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms
NASA Technical Reports Server (NTRS)
Kurdila, Andrew J.; Sharpley, Robert C.
1999-01-01
This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.
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.
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
Updating finite element dynamic models using an element-by-element sensitivity methodology
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Hemez, Francois M.
1993-09-01
A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.
North Atlantic Finite Element Ocean Modeling
NASA Astrophysics Data System (ADS)
Veluthedathekuzhiyil, Praveen
This thesis presents a modified version of the Finite Element Ocean Model (FEOM) developed at Alfred Wegener Institute for Polar and Marine Research (AWI) for the North Atlantic Ocean. A reasonable North Atlantic Ocean simulation is obtained against the observational data sets in a Control simulation (CS) where the surface boundary conditions are relaxed to a climatology. The vertical mixing in the model was tuned to represent convection in the model, also the horizontal mixing and diffusion coefficients to represent the changes in the resolution of the model’s unstructured grid. In addition, the open boundaries in the model are treated with a sponge layer where tracers are relaxed to climatology. The model is then further modified to accept the atmospheric flux forcing at the surface boundary with an added net heat flux correction and freshwater forcing from major rivers that are flowing into the North Atlantic Ocean. The impact of this boundary condition on the simulation results is then analyzed and shows many improvements albeit the drift in tracer properties around the Gulf Stream region remains as that of the CS case. However a comparison of the vertical sections at Cape Desolation and Cape Farewell with the available observational data sets shows many improvements in this simulation compared to that of the CS case. But the freshwater content in the Labrador Sea interior shows a continued drift as that of the CS case with an improvement towards the 10th model year. A detailed analysis of the boundary currents around the Labrador Sea shows the weak offshore transport of freshwater from the West Greenland Current (WGC) as one of the causes. To further improve the model and reasonably represent the boundary currents and associated sub-grid scale eddies in the model, a modified sub-grid scale parameterization based on Gent and McWilliams, (1990) is adopted. The sensitivity of using various approaches in the thickness diffusion parameter ( Kgm) for this
Application of Mass Lumped Higher Order Finite Elements
Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.
2005-11-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.
An enhanced finite element technique for diffuse phase transition
NASA Astrophysics Data System (ADS)
Münch, I.; Krauß, M.
2015-10-01
We propose a finite element technique to enhance phase-field simulations. As adaptive p-method it and can be generally applied to finite element formulations. However, diffuse interfaces have non-linear gradients within regions typically smaller compared to the size of the overall model. Thus, enhanced field interpolation with higher polynomial functions on demand allows for coarser meshing or lower regularization length for the phase transition. Our method preserves continuity of finite elements and is particularly advantageous in the context of parallelized computing. An analytical solution for the evolution of a phase-field variable governed by the Allen-Cahn equation is used to define an error measure and to investigate the proposed method. Several examples demonstrate the capability of this finite element technique.
Validation of high displacement piezoelectric actuator finite element models
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.
2000-08-01
The paper presents the results obtained by using NASTRAN and ANSYS finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness and important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN and ANSYS used different methods for modeling piezoelectric effects. In NASTRAN, a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Error analysis of finite element solutions for postbuckled cylinders
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1989-01-01
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
Generalized multiscale finite element method. Symmetric interior penalty coupling
NASA Astrophysics Data System (ADS)
Efendiev, Y.; Galvis, J.; Lazarov, R.; Moon, M.; Sarkis, M.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the “mass” matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples.
The finite element machine: An experiment in parallel processing
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Peebles, S. W.; Crockett, T. W.; Knott, J. D.; Adams, L.
1982-01-01
The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described.
Validation of High Displacement Piezoelectric Actuator Finite Element Models
NASA Technical Reports Server (NTRS)
Taleghani, B. K.
2000-01-01
The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
NASA Technical Reports Server (NTRS)
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
Mixed finite elements for the Richards' equation: linearization procedure
NASA Astrophysics Data System (ADS)
Pop, I. S.; Radu, F.; Knabner, P.
2004-07-01
We consider mixed finite element discretization for a class of degenerate parabolic problems including the Richards' equation. After regularization, time discretization is achieved by an Euler implicit scheme, while mixed finite elements are employed for the discretization in space. Based on the results obtained in (Radu et al. RANA Preprint 02-06, Eindhoven University of Technology, 2002), this paper considers a simple iterative scheme to solve the emerging nonlinear elliptic problems.
Finite element analysis of a composite wheelchair wheel design
NASA Technical Reports Server (NTRS)
Ortega, Rene
1994-01-01
The finite element analysis of a composite wheelchair wheel design is presented. The design is the result of a technology utilization request. The designer's intent is to soften the riding feeling by incorporating a mechanism attaching the wheel rim to the spokes that would allow considerable deflection upon compressive loads. A finite element analysis was conducted to verify proper structural function. Displacement and stress results are presented and conclusions are provided.
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.
Finite element analysis of vibration and damping of laminated composites
NASA Astrophysics Data System (ADS)
Rikards, Rolands
Simple finite elements are used to form a special laminated beam and plate superelements excluding all degrees of freedom in the nodes of the middle layer, and the finite element analysis of this structure is performed. To estimate damping of structures, modal loss factors are calculated, using two methods: the 'exact' method of complex eigenvalues and the approximate energy method. It was found that both methods give satisfactory results. However, the energy method needs less computer time than the exact method.
Mathematical aspects of finite element methods for incompressible viscous flows
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Evaluation of a hybrid, anisotropic, multilayered, quadrilateral finite element
NASA Technical Reports Server (NTRS)
Robinson, J. C.; Blackburn, C. L.
1978-01-01
A multilayered finite element with bending-extensional coupling is evaluated for: (1) buckling of general laminated plates; (2) thermal stresses of laminated plates cured at elevated temperatures; (3) displacements of a bimetallic beam; and (4) displacement and stresses of a single-cell box beam with warped cover panels. Also, displacements and stresses for flat and spherical orthotropic and anisotropic segments are compared with results from higher order plate and shell finite-element analyses.
Integration of geometric modeling and advanced finite element preprocessing
NASA Technical Reports Server (NTRS)
Shephard, Mark S.; Finnigan, Peter M.
1987-01-01
The structure to a geometry based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary based data structure for the major data sets within the system. The approach presented can support the finite element modeling procedures used today as well as the fully automated procedures under development.
Simulation of two-dimensional waterflooding using mixed finite elements
Chavent, G.; Jaffre, J.; Cohen, G.; Dupuy, M.; Dieste, I.
1982-01-01
A new method for the simulation of incompressible diphasic flows in two dimensions is presented, the distinctive features of which are: (1) reformation of the basic equation and specific choices of the finite element approximation of the same; (11) use of a mixed finite elements method, approximating both scalar and vector functions. Several test examples are shown, including gravity and capillary effects. The use of discontinuous basis functions proved successful for an accurate representation of sharp fronts. 16 refs.
Azimuthally-dependent Finite Element Solution to the Cylindrical Resonator
NASA Technical Reports Server (NTRS)
Osegueda, R.; Pierluissi, J.; Gil, L.; Revilla, A.; Villalva, G.; Dick, G.; Wang, D. SantiagoR.
1994-01-01
The cylindrical cavity resonator loaded with an anisotropic dielectric is analyzed as a two-dimensional problem using a finite element approach that assumes sinusoidal dependence in azimuth. This methodology allows the first finite element treatment of the technically important case of a resonator containing a sapphire element with a cylindrically aligned c axis. Second order trial functions together with quadrilateral elements are adopted in the calculations. The method was validated through comparisons with the analytical solutions for the hollow metal cavity and a coaxial cavity, as well as through measurements on a shielded sapphire resonator.
Dynamical observer for a flexible beam via finite element approximations
NASA Technical Reports Server (NTRS)
Manitius, Andre; Xia, Hong-Xing
1994-01-01
The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.
Finite element thermal analysis of convectively-cooled aircraft structures
NASA Technical Reports Server (NTRS)
Wieting, A. R.; Thornton, E. A.
1981-01-01
The design complexity and size of convectively-cooled engine and airframe structures for hypersonic transports necessitate the use of large general purpose computer programs for both thermal and structural analyses. Generally thermal analyses are based on the lumped-parameter finite difference technique, and structural analyses are based on the finite element technique. Differences in these techniques make it difficult to achieve an efficient interface. It appears, therefore, desirable to conduct an integrated analysis based on a common technique. A summary is provided of efforts by NASA concerned with the development of an integrated thermal structural analysis capability using the finite element method. Particular attention is given to the development of conduction/forced-convection finite element methodology and applications which illustrate the capabilities of the developed concepts.
Recent developments in finite element analysis for transonic airfoils
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.
1979-01-01
The prediction of aerodynamic forces in the transonic regime generally requires a flow field calculation to solve the governing non-linear mixed elliptic-hyperbolic partial differential equations. Finite difference techniques were developed to the point that design and analysis application are routine, and continual improvements are being made by various research groups. The principal limitation in extending finite difference methods to complex three-dimensional geometries is the construction of a suitable mesh system. Finite element techniques are attractive since their application to other problems have permitted irregular mesh elements to be employed. The purpose of this paper is to review the recent developments in the application of finite element methods to transonic flow problems and to report some recent results.
Finite elements based on consistently assumed stresses and displacements
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1985-01-01
Finite element stiffness matrices are derived using an extended Hellinger-Reissner principle in which internal displacements are added to serve as Lagrange multipliers to introduce the equilibrium constraint in each element. In a consistent formulation the assumed stresses are initially unconstrained and complete polynomials and the total displacements are also complete such that the corresponding strains are complete in the same order as the stresses. Several examples indicate that resulting properties for elements constructed by this consistent formulation are ideal and are less sensitive to distortions of element geometries. The method has been used to find the optimal stress terms for plane elements, 3-D solids, axisymmetric solids, and plate bending elements.
Probabilistic finite elements for fatigue and fracture analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Liu, Wing Kam
1992-01-01
Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.
Finite element analysis of two disk rotor system
NASA Astrophysics Data System (ADS)
Dixit, Harsh Kumar
2016-05-01
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
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.
Preconditioned CG-solvers and finite element grids
Bauer, R.; Selberherr, S.
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Adaptive grid finite element model of the tokamak scrapeoff layer
Kuprat, A.P.; Glasser, A.H.
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
Radiosity algorithms using higher order finite element methods
Troutman, R.; Max, N.
1993-08-01
Many of the current radiosity algorithms create a piecewise constant approximation to the actual radiosity. Through interpolation and extrapolation, a continuous solution is obtained. An accurate solution is found by increasing the number of patches which describe the scene. This has the effect of increasing the computation time as well as the memory requirements. By using techniques found in the finite element method, we can incorporate an interpolation function directly into our form factor computation. We can then use less elements to achieve a more accurate solution. Two algorithms, derived from the finite element method, are described and analyzed.
Design and finite element analysis of oval man way
Hari, Y.; Gryder, B.
1996-12-01
This paper presents the design of an oval man way in the side wall of a cylindrical pressure vessel. ASME Code Section 8 is used to obtain the design parameters of the oval man way, man way cover and bolts. The code calculations require some assumptions which may not be valid. A typical design example is taken. STAAD III finite element code with plate elements is used to model the oval man way, man way cover and bolts. The stresses calculated using ASME Code Section 8 and other analytical formulas for plate and shells are compared with the stresses obtained by Finite Element Modeling. This paper gives the designer of oval man way the ability to perform a finite element analysis and compare it with the analytical calculations and assumptions made. This gives added confidence to the designer as to the validity of his calculations and assumptions.
User's Guide for ENSAERO_FE Parallel Finite Element Solver
NASA Technical Reports Server (NTRS)
Eldred, Lloyd B.; Guruswamy, Guru P.
1999-01-01
A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple finite element and modal modules. Full aircraft structures may be more accurately modeled using the new finite element capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural finite element equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of elements can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.
Guo, Hongqiang; Shah, Mitul; Spilker, Robert L.
2014-01-01
The study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. However, to date, few biphasic finite element contact analysis for 3D physiological geometries under finite deformation has been developed. The objective of this paper is to develop a hyperelastic biphasic contact implementation for finite deformation and sliding problem. An augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The finite element implementation was based on a general purpose software, COMSOL Multiphysics. The accuracy of the implementation is verified using example problems, for which solutions are available by alternative analyses. The implementation was proven to be robust and able to handle finite deformation and sliding. PMID:24496915
Coupled finite-difference/finite-element approach for wing-body aeroelasticity
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
1992-01-01
Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
Variational formulation of high performance finite elements: Parametrized variational principles
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Militello, Carmello
1991-01-01
High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational basis of high-performance elements, with emphasis on those constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parametrized variational principles that provide a foundation for the FF and ANS methods, as well as for a combination of both are presented.
New triangular and quadrilateral plate-bending finite elements
NASA Technical Reports Server (NTRS)
Narayanaswami, R.
1974-01-01
A nonconforming plate-bending finite element of triangular shape and associated quadrilateral elements are developed. The transverse displacement is approximated within the element by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.
Spectral finite-element methods for parametric constrained optimization problems.
Anitescu, M.; Mathematics and Computer Science
2009-01-01
We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.
Finite Element Method for Capturing Ultra-relativistic Shocks
NASA Technical Reports Server (NTRS)
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Hybrid finite element-finite difference method for thermal analysis of blood vessels.
Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B
2000-01-01
A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems. PMID:10949130
Finite element method for eigenvalue problems in electromagnetics
NASA Technical Reports Server (NTRS)
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
Flow Applications of the Least Squares Finite Element Method
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
An Object Oriented, Finite Element Framework for Linear Wave Equations
Koning, J M
2004-08-12
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Electrical and Joule heating relationship investigation using Finite Element Method
NASA Astrophysics Data System (ADS)
Thangaraju, S. K.; Munisamy, K. M.
2015-09-01
The finite element method is vastly used in material strength analysis. The nature of the finite element solver, which solves the Fourier equation of stress and strain analysis, made it possible to apply for conduction heat transfer Fourier Equation. Similarly the Current and voltage equation is also liner Fourier equation. The nature of the governing equation makes it possible to numerical investigate the electrical joule heating phenomena in electronic component. This paper highlights the Finite Element Method (FEM) application onto semiconductor interconnects to determine the specific contact resistance (SCR). Metal and semiconductor interconnects is used as model. The result confirms the possibility and validity of FEM utilization to investigate the Joule heating due electrical resistance.
Optimal mapping of irregular finite element domains to parallel processors
NASA Technical Reports Server (NTRS)
Flower, J.; Otto, S.; Salama, M.
1987-01-01
Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.
Finite Element Modelling and Analysis of Conventional Pultrusion Processes
NASA Astrophysics Data System (ADS)
Akishin, P.; Barkanov, E.; Bondarchuk, A.
2015-11-01
Pultrusion is one of many composite manufacturing techniques and one of the most efficient methods for producing fiber reinforced polymer composite parts with a constant cross-section. Numerical simulation is helpful for understanding the manufacturing process and developing scientific means for the pultrusion tooling design. Numerical technique based on the finite element method has been developed for the simulation of pultrusion processes. It uses the general purpose finite element software ANSYS Mechanical. It is shown that the developed technique predicts the temperature and cure profiles, which are in good agreement with those published in the open literature.
Development of non-linear finite element computer code
NASA Technical Reports Server (NTRS)
Becker, E. B.; Miller, T.
1985-01-01
Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows finite element analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional finite element code, TEXLESP-S, which is documented herein.
Substructure System Identification for Finite Element Model Updating
NASA Technical Reports Server (NTRS)
Craig, Roy R., Jr.; Blades, Eric L.
1997-01-01
This report summarizes research conducted under a NASA grant on the topic 'Substructure System Identification for Finite Element Model Updating.' The research concerns ongoing development of the Substructure System Identification Algorithm (SSID Algorithm), a system identification algorithm that can be used to obtain mathematical models of substructures, like Space Shuttle payloads. In the present study, particular attention was given to the following topics: making the algorithm robust to noisy test data, extending the algorithm to accept experimental FRF data that covers a broad frequency bandwidth, and developing a test analytical model (TAM) for use in relating test data to reduced-order finite element models.
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
NASA Astrophysics Data System (ADS)
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016-09-01
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
Finite element microscopic stress analysis of cracked composite systems
NASA Technical Reports Server (NTRS)
Ko, W. L.
1978-01-01
This paper considers the stress concentration problems of two types of cracked composite systems: (1) a composite system with a broken fiber (a penny-shaped crack problem), and (2) a composite system with a cracked matrix (an annular crack problem). The cracked composite systems are modeled with triangular and trapezoidal ring finite elements. Using NASTRAN (NASA Structural Analysis) finite element computer program, the stress and deformation fields in the cracked composite systems are calculated. The effect of fiber-matrix material combination on the stress concentrations and on the crack opening displacements is studied.
Global-local finite element analysis of composite structures
Deibler, J.E.
1992-06-01
The development of layered finite elements has facilitated analysis of laminated composite structures. However, the analysis of a structure containing both isotropic and composite materials remains a difficult problem. A methodology has been developed to conduct a ``global-local`` finite element analysis. A ``global`` analysis of the entire structure is conducted at the appropriate loads with the composite portions replaced with an orthotropic material of equivalent materials properties. A ``local`` layered composite analysis is then conducted on the region of interest. The displacement results from the ``global`` analysis are used as loads to the ``local`` analysis. the laminate stresses and strains can then be examined and failure criteria evaluated.
Global-local finite element analysis of composite structures
Deibler, J.E.
1992-06-01
The development of layered finite elements has facilitated analysis of laminated composite structures. However, the analysis of a structure containing both isotropic and composite materials remains a difficult problem. A methodology has been developed to conduct a global-local'' finite element analysis. A global'' analysis of the entire structure is conducted at the appropriate loads with the composite portions replaced with an orthotropic material of equivalent materials properties. A local'' layered composite analysis is then conducted on the region of interest. The displacement results from the global'' analysis are used as loads to the local'' analysis. the laminate stresses and strains can then be examined and failure criteria evaluated.
Error analysis of finite element solutions for postbuckled plates
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1988-01-01
An error analysis of results from finite-element solutions of problems in shell structures is further developed, incorporating the results of an additional numerical analysis by which oscillatory behavior is eliminated. The theory is extended to plates with initial geometric imperfections, and this novel analysis is programmed as a postprocessor for a general-purpose finite-element code. Numerical results are given for the case of a stiffened panel in compression and a plate loaded in shear by a 'picture-frame' test fixture.
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna.; Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Diffusive mesh relaxation in ALE finite element numerical simulations
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
Smith, N. A. S. E-mail: maciej.rokosz@npl.co.uk Correia, T. M. E-mail: maciej.rokosz@npl.co.uk; Rokosz, M. K. E-mail: maciej.rokosz@npl.co.uk
2014-07-28
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Adaptive finite-element method for diffraction gratings
NASA Astrophysics Data System (ADS)
Bao, Gang; Chen, Zhiming; Wu, Haijun
2005-06-01
A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
Two-dimensional finite-element temperature variance analysis
NASA Technical Reports Server (NTRS)
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
NASA Astrophysics Data System (ADS)
Smith, N. A. S.; Rokosz, M. K.; Correia, T. M.
2014-07-01
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
A weak Galerkin generalized multiscale finite element method
Mu, Lin; Wang, Junping; Ye, Xiu
2016-03-31
In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin finite element method. Convergence analysis and numerical experiments are obtained for the special case.
Fourier analysis of finite element preconditioned collocation schemes
NASA Technical Reports Server (NTRS)
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Finite element methods for nonlinear elastostatic problems in rubber elasticity
NASA Technical Reports Server (NTRS)
Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.
1983-01-01
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
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.
Finite element models of the space shuttle main engine
NASA Technical Reports Server (NTRS)
Muller, G. R.
1980-01-01
Finite element models were developed as input to dynamic simulations of the high pressure fuel turbopump (HPFTP), the high pressure oxidizer turbopump (HPOTP), and the space shuttle main engine (SSME). Descriptions are provided for the five basic finite element models: HPFTP rotor, HPFTP case, HPOTP rotor, HPOTP case, and SSME (excluding turbopumps). Modal results are presented for the HPFTP rotor, HPFTP case, HPOTP rotor, coupled HPFTP rotor and case, HPOTP case, coupled HPOTP rotor and case, SSME (excluding turbopumps), and SSME (including turbopumps). Results for the SSME (including turbopumps) model are compared to data from a SSME HPOTP modal survey.
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.
Considerations of crack growth and plasticity in finite element analysis
NASA Technical Reports Server (NTRS)
Lee, J. D.; Liebowitz, H.
1978-01-01
A finite-element analysis was made of crack growth in a center-cracked specimen subjected to monotonically increasing load until the point of fast fracture. Since part of the specimen experienced unloading, the boundary value problem which was formulated was based upon incremental theory of plasticity. Experimental load and crack size records were utilized. Linear relations between plastic energy and crack growth were observed. Fracture toughness parameters, which were evaluated at the onset of unstable crack propagation from finite-element analysis, were in good agreement with those determined experimentally.
Finite Element Aircraft Simulation of Turbulence
NASA Technical Reports Server (NTRS)
McFarland, R. E.
1997-01-01
A turbulence model has been developed for realtime aircraft simulation that accommodates stochastic turbulence and distributed discrete gusts as a function of the terrain. This model is applicable to conventional aircraft, V/STOL aircraft, and disc rotor model helicopter simulations. Vehicle angular activity in response to turbulence is computed from geometrical and temporal relationships rather than by using the conventional continuum approximations that assume uniform gust immersion and low frequency responses. By using techniques similar to those recently developed for blade-element rotor models, the angular-rate filters of conventional turbulence models are not required. The model produces rotational rates as well as air mass translational velocities in response to both stochastic and deterministic disturbances, where the discrete gusts and turbulence magnitudes may be correlated with significant terrain features or ship models. Assuming isotropy, a two-dimensional vertical turbulence field is created. A novel Gaussian interpolation technique is used to distribute vertical turbulence on the wing span or lateral rotor disc, and this distribution is used to compute roll responses. Air mass velocities are applied at significant centers of pressure in the computation of the aircraft's pitch and roll responses.
NASA Technical Reports Server (NTRS)
1976-01-01
A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity.
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-11-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-01-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Finite-element-based design tool for smart composite structures
NASA Astrophysics Data System (ADS)
Koko, Tamunoiyala S.; Orisamolu, Irewole R.; Smith, Malcolm J.; Akpan, Unyime O.
1997-06-01
This paper presents an integrated finite element-control methodology for the design/analysis of smart composite structures. The method forms part of an effort to develop an integrated computational tool that includes finite element modeling; control algorithms; and deterministic, fuzzy and probabilistic optimization and integrity assessment of the structures and control systems. The finite element analysis is based on a 20 node thermopiezoelectric composite element for modeling the composite structure with surface bonded piezoelectric sensors and actuators; and control is based on the linear quadratic regulator and the independent modal space control methods. The method has been implemented in a computer code called SMARTCOM. Several example problems have been used to verify various aspects of the formulations and the analysis results from the present study compare well against other numerical or experimental results. Being based on the finite element method, the present formation can be conveniently used for the analysis and design of smart composite structures with complex geometrical configurations and loadings.
Probabilistic nonlinear finite element analysis of composite structures
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells is developed. A total Lagrangian finite element formulation, employing a degenerated three-dimensional laminated composite shell element with the full Green-Lagrange strains and first-order shear deformable kinematics, is used. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed, and results are presented in the form of mean and variance of the structural response. Reliability calculations are made by using the first-order reliability method combined with sensitivity derivatives from the finite element analysis. Both ply-level and micromechanics-level random variables are incorporated, the latter by means of the Aboudi micromechanics model. Two sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. In general, the procedure is quite effective in determining the response statistics and reliability for linear and geometric nonlinear behavior of laminated composite shells.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2016-02-01
The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less
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.
Numerical techniques in linear duct acoustics. [finite difference and finite element analyses
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1980-01-01
Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.
Non-conforming finite element methods for transmission eigenvalue problem
NASA Astrophysics Data System (ADS)
Yang, Yidu; Han, Jiayu; Bi, Hai
2016-08-01
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we first discuss the non-conforming finite element approximation, and prove the error estimates of the discrete eigenvalues obtained by the Adini element, Morley-Zienkiewicz element, modified-Zienkiewicz element et. al. And we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem.
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.
Fluid structure interaction in electrohydraulic servovalve: a finite element approach
NASA Astrophysics Data System (ADS)
Hiremath, Somashekhar S.; Singaperumal, M.
2010-01-01
Electrohydraulic servovalves (EHSV) promise unique application opportunities and high performance, unmatched by other drive technologies. Typical applications include aerospace, robotic manipulators, motion simulators, injection molding, CNC machines and material testing machines. EHSV available are either a flapper/nozzle type or a jet pipe type. In the present paper an attempt has been made to study the dynamics of jet pipe EHSV with built-in mechanical feedback using Finite Element Method (FEM). In jet pipe EHSV, the dynamics of spool greatly depends on pressure recovery and hence the fluid flow at spool ends. The effect of pressure recovery on spool dynamics is studied using FEM by creating the fluid-structure-interaction. The mechanical parts were created using general purpose finite elements like shell, beam, and solid elements while fluid cavities were created using hydrostatic fluid elements. The analysis was carried out using the commercially available FE code ABAQUS. The jet pipe and spool dynamics are presented in the paper.
Fluid structure interaction in electrohydraulic servovalve: a finite element approach
NASA Astrophysics Data System (ADS)
Hiremath, Somashekhar S.; Singaperumal, M.
2009-12-01
Electrohydraulic servovalves (EHSV) promise unique application opportunities and high performance, unmatched by other drive technologies. Typical applications include aerospace, robotic manipulators, motion simulators, injection molding, CNC machines and material testing machines. EHSV available are either a flapper/nozzle type or a jet pipe type. In the present paper an attempt has been made to study the dynamics of jet pipe EHSV with built-in mechanical feedback using Finite Element Method (FEM). In jet pipe EHSV, the dynamics of spool greatly depends on pressure recovery and hence the fluid flow at spool ends. The effect of pressure recovery on spool dynamics is studied using FEM by creating the fluid-structure-interaction. The mechanical parts were created using general purpose finite elements like shell, beam, and solid elements while fluid cavities were created using hydrostatic fluid elements. The analysis was carried out using the commercially available FE code ABAQUS. The jet pipe and spool dynamics are presented in the paper.
ATESHIAN, GERARD A.; ALBRO, MICHAEL B.; MAAS, STEVE; WEISS, JEFFREY A.
2012-01-01
Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechano-chemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechano-chemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software). PMID:21950898
Ateshian, Gerard A; Albro, Michael B; Maas, Steve; Weiss, Jeffrey A
2011-08-01
Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http:∕∕mrl.sci.utah.edu∕software). PMID:21950898
A finite element code for electric motor design
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1994-01-01
FEMOT is a finite element program for solving the nonlinear magnetostatic problem. This version uses nonlinear, Newton first order elements. The code can be used for electric motor design and analysis. FEMOT can be embedded within an optimization code that will vary nodal coordinates to optimize the motor design. The output from FEMOT can be used to determine motor back EMF, torque, cogging, and magnet saturation. It will run on a PC and will be available to anyone who wants to use it.
Finite element error estimation and adaptivity based on projected stresses
Jung, J.
1990-08-01
This report investigates the behavior of a family of finite element error estimators based on projected stresses, i.e., continuous stresses that are a least squared error fit to the conventional Gauss point stresses. An error estimate based on element force equilibrium appears to be quite effective. Examples of adaptive mesh refinement for a one-dimensional problem are presented. Plans for two-dimensional adaptivity are discussed. 12 refs., 82 figs.
A General-Purpose Mesh Generator for Finite Element Codes.
1984-02-28
Version 00 INGEN is a general-purpose mesh generator for use in conjunction with two and three dimensional finite element programs. The basic components of INGEN are surface and three-dimensional region generators that use linear-blending interpolation formulae. These generators are based on an i, j, k index scheme, which is used to number nodal points, construct elements, and develop displacement and traction boundary conditions.
Finite Element Modeling of the Buckling Response of Sandwich Panels
NASA Technical Reports Server (NTRS)
Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.
2002-01-01
A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.
NASA Technical Reports Server (NTRS)
Fulton, R. E.
1986-01-01
The requirements of complex aerospace vehicles combined with the age of structural analysis systems enhance the need to advance technology toward a new generation of structural analysis capability. Recent and impeding advances in parallel and supercomputers provide the opportunity to significantly improve these structural analysis capabilities for large order finite element problems. Long-term research in parallel computing, associated with the NASA Finite Element Machine project, is discussed. The results show the potential of parallel computers to provide substantial increases in computation speed over sequential computers. Results are given for sample problems in the areas of eigenvalue analysis and transient response.
Dedicated finite elements for electrode thin films on quartz resonators.
Srivastava, Sonal A; Yong, Yook-Kong; Tanaka, Masako; Imai, Tsutomu
2008-08-01
The accuracy of the finite element analysis for thickness shear quartz resonators is a function of the mesh resolution; the finer the mesh resolution, the more accurate the finite element solution. A certain minimum number of elements are required in each direction for the solution to converge. This places a high demand on memory for computation, and often the available memory is insufficient. Typically the thickness of the electrode films is very small compared with the thickness of the resonator itself; as a result, electrode elements have very poor aspect ratios, and this is detrimental to the accuracy of the result. In this paper, we propose special methods to model the electrodes at the crystal interface of an AT cut crystal. This reduces the overall problem size and eliminates electrode elements having poor aspect ratios. First, experimental data are presented to demonstrate the effects of electrode film boundary conditions on the frequency-temperature curves of an AT cut plate. Finite element analysis is performed on a mesh representing the resonator, and the results are compared for testing the accuracy of the analysis itself and thus validating the results of analysis. Approximations such as lumping and Guyan reduction are then used to model the electrode thin films at the electrode interface and their results are studied. In addition, a new approximation called merging is proposed to model electrodes at the electrode interface. PMID:18986913
A finite element approach for prediction of aerothermal loads
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Vemaganti, G.
1986-01-01
A Taylor-Galerkin finite element approach is presented for analysis of high speed viscous flows with an emphasis on predicting heating rates. Five computational issues relevant to the computation of steady flows are examined. Numerical results for supersonic and hypersonic problems address the computational issues and demonstrate the validity for the approach for analysis of high speed flows.
Finite-Element Analysis of Multiphase Immiscible Flow Through Soils
NASA Astrophysics Data System (ADS)
Kuppusamy, T.; Sheng, J.; Parker, J. C.; Lenhard, R. J.
1987-04-01
A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equations governing flow in a three-fluid phase porous medium system with constant air phase pressure. Constitutive relationships for fluid conductivities and saturations as functions of fluid pressures, which are derived in a companion paper by J. C. Parker et al. (this issue) and which may be calibrated from two-phase laboratory measurements, are employed in the finite-element program. The solution procedure uses backward time integration with iteration by a modified Picard method to handle the nonlinear properties. Laboratory experiments involving water displacement from soil columns by p cymene (a benzene-derivative hydrocarbon) under constant pressure were simulated by the finite-element program to validate the numerical model and formulation for constitutive properties. Transient water outflow predicted using independently measured saturation-capillary head data agreed with observed outflow data within the limits of precision of the predictions as estimated by a first-order Taylor series approximation considering parameter uncertainty due to experimental reproducability and constitutive model accuracy. Two-dimensional simulations are presented for a hypothetical field case involving introduction of NAPL near the soil surface due to leakage from an underground storage tank. Subsequent transport of NAPL in the variably saturated vadose and groundwater zones is analyzed.
SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications
NASA Technical Reports Server (NTRS)
Kirk, Benjamin S.
2007-01-01
This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.
Implicit extrapolation methods for multilevel finite element computations
Jung, M.; Ruede, U.
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
Towards parallel I/O in finite element simulations
NASA Technical Reports Server (NTRS)
Farhat, Charbel; Pramono, Eddy; Felippa, Carlos
1989-01-01
I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.
the finite element machine: An experiment in parallel processing
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Peebles, S. W.; Crockett, T. W.; Knott, J. D.; Adams, L.
1982-01-01
The Finite Element Machine at the NASA Langley Research Center is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described. Directions for future work are presented.
Experiences in interfacing NASTRAN with another finite element program
NASA Technical Reports Server (NTRS)
Schwerzler, D. D.; Leverenz, R. K.
1972-01-01
The coupling of NASTRAN to another finite element program developed for the static analysis of automotive structures is discussed. The two programs were coupled together to use the substructuring capability of the in-house program and the normal mode analysis capability of NASTRAN. Modifications were made to the NASTRAN program in order to make the coupling feasible.
Spanwise variation of potential form drag. [finite element method
NASA Technical Reports Server (NTRS)
Clever, W. C.
1977-01-01
The finite element method is used to calculate the spanwise variation of potential form drag of a wing at subsonic and supersonic speeds using linearly varying panels. The wing may be of arbitrary planform and nonplanar provided the wing panels are parallel to the aircraft axis.
Boundary control of parabolic systems - Finite-element approximation
NASA Technical Reports Server (NTRS)
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
Design, development and use of the finite element machine
NASA Technical Reports Server (NTRS)
Adams, L. M.; Voigt, R. C.
1983-01-01
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.
Incorporation of Hysteresis Effects into Magnetc Finite Element Modeling
NASA Astrophysics Data System (ADS)
Lee, J. Y.; Lee, S. J.; Melikhov, Y.; Jiles, D. C.; Garton, M.; Lopez, R.; Brasche, L.
2004-02-01
Hysteresis effects have usually been ignored in magnetic modeling due to the multi-valued property causing difficulty in its incorporation into numerical calculations such as those based on finite elements. A linear approximation of magnetic permeability or a nonlinear B-H curve formed by connecting the tips of the hysteresis loops has been widely used in magnetic modeling for these types of calculations. We have employed the Jiles-Atherton (J-A) hysteresis model for development of a finite element method algorithm incorporating hysteresis effects. J-A model is suited for numerical analysis such as finite element modeling because of the small number of degrees of freedom and its simple form of equation. A finite element method algorithm for hysteretic materials has been developed for estimation of the volume and the distribution of retained magnetic particles around a defect site. The volume of retained magnetic particles was found to depend not only on the existing current source strength but also on the remaining magnetization of a hysteretic material. Detailed algorithm and simulation results are presented.
Finite element forced vibration analysis of rotating cyclic structures
NASA Technical Reports Server (NTRS)
Elchuri, V.; Smith, G. C. C.
1981-01-01
A capability was added to the general purpose finite element program NASTRAN Level 17.7 to conduct forced vibration analysis of tuned cyclic structures rotating about their axes of symmetry. The effects of Coriolis and centripetal accelerations together with those due to linear acceleration of the axis of rotation were included. The theoretical development of this capability is presented.
A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains
NASA Technical Reports Server (NTRS)
Kandil, Osama A.
1998-01-01
Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.
The finite element method: Is weighted volume integration essential?
NASA Astrophysics Data System (ADS)
Narasimhan, T. N.
In developing finite element equations for steady state and transient diffusion-type processes, weighted volume integration is generally assumed to be an intrinsic requirement. It is shown that such finite element equations can be developed directly and with ease on the basis of the elementary notion of a surface integral. Although weighted volume integration is mathematically correct, the algebraic equations stemming from it are no more informative than those derived directly on the basis of a surface integral. An interesting upshot is that the derivation based on surface integration does not require knowledge of a partial differential equation but yet is logically rigorous. It is commonly stated that weighted volume integration of the differential equation helps one carry out analyses of errors, convergence and existence, and therefore, weighted volume integration is preferable. It is suggested that because the direct derivation is logically consistent, numerical solutions emanating from it must be testable for accuracy and internal consistency in ways that the style of which may differ from the classical procedures of error- and convergence-analysis. In addition to simplifying the teaching of the finite element method, the thoughts presented in this paper may lead to establishing the finite element method independently in its own right, rather than it being a surrogate of the differential equation. The purpose of this paper is not to espouse any one particular way of formulating the finite element equations. Rather, it is one of introspection. The desire is to critically examine our traditional way of doing things and inquire whether alternate approaches may reveal to us new and interesting insights.
Advance finite element modeling of rotor blade aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Sangha, K. B.; Panda, B.
1994-01-01
An advanced beam finite element has been developed for modeling rotor blade dynamics and aeroelasticity. This element is part of the Element Library of the Second Generation Comprehensive Helicopter Analysis System (2GCHAS). The element allows modeling of arbitrary rotor systems, including bearingless rotors. It accounts for moderately large elastic deflections, anisotropic properties, large frame motion for maneuver simulation, and allows for variable order shape functions. The effects of gravity, mechanically applied and aerodynamic loads are included. All kinematic quantities required to compute airloads are provided. In this paper, the fundamental assumptions and derivation of the element matrices are presented. Numerical results are shown to verify the formulation and illustrate several features of the element.
Discontinuous dual-primal mixed finite elements for elliptic problems
NASA Technical Reports Server (NTRS)
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
2000-01-01
We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.
Finite Element Modeling of the NASA Langley Aluminum Testbed Cylinder
NASA Technical Reports Server (NTRS)
Grosveld, Ferdinand W.; Pritchard, Joselyn I.; Buehrle, Ralph D.; Pappa, Richard S.
2002-01-01
The NASA Langley Aluminum Testbed Cylinder (ATC) was designed to serve as a universal structure for evaluating structural acoustic codes, modeling techniques and optimization methods used in the prediction of aircraft interior noise. Finite element models were developed for the components of the ATC based on the geometric, structural and material properties of the physical test structure. Numerically predicted modal frequencies for the longitudinal stringer, ring frame and dome component models, and six assembled ATC configurations were compared with experimental modal survey data. The finite element models were updated and refined, using physical parameters, to increase correlation with the measured modal data. Excellent agreement, within an average 1.5% to 2.9%, was obtained between the predicted and measured modal frequencies of the stringer, frame and dome components. The predictions for the modal frequencies of the assembled component Configurations I through V were within an average 2.9% and 9.1%. Finite element modal analyses were performed for comparison with 3 psi and 6 psi internal pressurization conditions in Configuration VI. The modal frequencies were predicted by applying differential stiffness to the elements with pressure loading and creating reduced matrices for beam elements with offsets inside external superelements. The average disagreement between the measured and predicted differences for the 0 psi and 6 psi internal pressure conditions was less than 0.5%. Comparably good agreement was obtained for the differences between the 0 psi and 3 psi measured and predicted internal pressure conditions.
Finite-element calculations on alliant FX/80
Watson, B.C.; Kamat, M.P.
1994-10-01
The finite-element method has proven to be an invaluable tool for analysis and design of complex, high-performance systems, such as those typically encountered in the aerospace or automotive industries. However, as the size of the finite-element models of such systems increases, analysis computation time using conventional computers can become prohibitively high. Parallel processing computers provide the means to overcome these computation-time limits, provided the algorithms used in the analysis can take advantage of multiple processors. The writers have examined several algorithms for linear and nonlinear static analysis, as well as dynamic finite-element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been investigated. For single load-case linear static analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear static analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms. For eigenvalue/eigenvector analysis, the subspace iteration algorithm with a parallel decomposition is shown to achieve a relatively high parallel efficiency. 12 refs.
Visualization of transient finite element analyses on large unstructured grids
Dovey, D.
1995-03-22
Three-dimensional transient finite element analysis is performed on unstructured grids. A trend toward running larger analysis problems, combined with a desire for interactive animation of analysis results, demands efficient visualization techniques. This paper discusses a set of data structures and algorithms for visualizing transient analysis results on unstructured grids and introduces some modifications in order to better support large grids. In particular, an element grouping approach is used to reduce the amount of memory needed for external surface determination and to speed up ``point in element`` tests. The techniques described lend themselves to visualization of analyses carried out in parallel on a massively parallel computer (MPC).
Computerized symbolic manipulation in nonlinear finite element analysis
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1981-01-01
The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness coefficients of nonlinear finite elements, (2) generation of FORTRAN source code for numerical evaluation of stiffness coefficients, and (3) checking the correctness of the FORTRAN statements for the arrays of coefficients. The symbolic and algebraic manipulation system MACSYMA is used in the present study. Two sample MACSYMA programs are presented for the development of the nonlinear stiffness coefficients of two-dimensional, shear-flexible, doubly-curved deep shell elements. The first program is for displacement models and the second program is for mixed models with discontinuous stress-resultant fields at interelement boundaries.
The finite element method for calculating the marine structural design
NASA Astrophysics Data System (ADS)
Ion, A.; Ticu, I.
2015-11-01
The aim of this paper is to optimally design and dimension marine structures in order for them to fulfil both functional and safety requirements. A master level of structural mechanics is vital in order to check tests and analysis and to develop new structures. This study can improve the calculation and estimation of the effects of hydrodynamics and of other loads; movements, strains and internal forces in fixed and floating platforms and ships. The finite element method (FEM) ensures basic understanding of the finite element model as applied on static cases including beam and plate elements, experience with static analysis of marine structures like platforms and ships, along with the basic understanding of dynamic response of systems with one degree of freedom and simple continuous beams, and also how analysis models can be established for real structures by the use of generalized coordinates and superposition.
Finite element dynamic analysis on CDC STAR-100 computer
NASA Technical Reports Server (NTRS)
Noor, A. K.; Lambiotte, J. J., Jr.
1978-01-01
Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.
PWSCC Assessment by Using Extended Finite Element Method
NASA Astrophysics Data System (ADS)
Lee, Sung-Jun; Lee, Sang-Hwan; Chang, Yoon-Suk
2015-12-01
The head penetration nozzle of control rod driving mechanism (CRDM) is known to be susceptible to primary water stress corrosion cracking (PWSCC) due to the welding-induced residual stress. Especially, the J-groove dissimilar metal weld regions have received many attentions in the previous studies. However, even though several advanced techniques such as weight function and finite element alternating methods have been introduced to predict the occurrence of PWSCC, there are still difficulties in respect of applicability and efficiency. In this study, the extended finite element method (XFEM), which allows convenient crack element modeling by enriching degree of freedom (DOF) with special displacement function, was employed to evaluate structural integrity of the CRDM head penetration nozzle. The resulting stress intensity factors of surface cracks were verified for the reliability of proposed method through the comparison with those suggested in the American Society of Mechanical Engineering (ASME) code. The detailed results from the FE analyses are fully discussed in the manuscript.
EXODUS: A finite element file format for pre- and postprocessing
Mills-Curran, W.C.; Gilkey, A.P.; Flanagan, D.P.
1988-09-01
The EXODUS format defines a binary file which is used for finite element analysis pre- and postprocessing. It includes data to define the finite element mesh and label both boundary condition and load application points. EXODUS accommodates multiple element types and is sufficiently general format for analysis results. A benefit of combining the mesh definition data and the results data in the same file is that the user is assured that the results data are consistent with the model. EXODUS is currently in use by the entire range of Department 1520 codes (including preprocessors, translators, linear and nonlinear analyses, and postprocessors) and is finding applications in codes outside Department 1520. 2 refs., 2 figs., 1 tab.
Finite Element Modelling of Fluid Coupling in the Coiled Cochlea
NASA Astrophysics Data System (ADS)
Ni, Guangjian; Elliott, S. J.; Lineton, B.; Saba, R.
2011-11-01
A finite element model is first used to calculate the modal pressure difference for a box model of the cochlea, which shows that the number of fluid elements across the width of the cochlea determines the accuracy with which the near field, or short wavenumber, component of the fluid coupling is reproduced. Then results are compared with the analytic results to validate the accuracy of the FE model. It is, however, the far field, or long wavelength, component of the fluid coupling that is most affected by the geometry. A finite element model of the coiled cochlea is then used to calculate fluid coupling in this case, which has similar characteristics to the uncoiled model.
Finite element modelling for materials with size effect
NASA Astrophysics Data System (ADS)
Swaddiwudhipong, S.; Hua, J.; Tho, K. K.; Liu, Z. S.
2006-10-01
This paper involves the formulation of the C0 finite elements incorporating the conventional mechanism-based strain gradient plasticity theory. Higher-order variables and consequently higher-order continuity conditions are not required allowing the direct applications of conventional plasticity algorithms in the existing finite element package. Implementation of the model whether analytically or computationally is efficient and straightforward as the strain gradient effect is confined in the material constitutive relation. The accuracy of the proposed elements in simulating the response of materials with strong size effect is verified through several numerical examples. The approach is applicable and valid to any materials with non-uniform plastic deformation larger than about 100 nm onwards. The proposed model becomes imperative when the deformation is less than 10 µm as classical plasticity is unable to describe the phenomenon comprehensively at this low level of deformation.
Wu, H.W.; Shii, Sheng Hwa . Dept. of Naval Architecture and Marine Engineering)
1994-06-01
A new method, involving the combined use of analysis and the finite-element method, is applicable to the heat conduction problem with isolated heat sources. Unlike the finite-element method the analysis/finite-element combined method is able to discretize the distributed sources with discontinuities into course elements, and the solution is still calculated accurately. The results are compared in tables with exact solutions and other numerical data, and the agreement is found to be good.
NASA Technical Reports Server (NTRS)
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
Modelling the core convection using finite element and finite difference methods
NASA Astrophysics Data System (ADS)
Chan, K. H.; Li, Ligang; Liao, Xinhao
2006-08-01
Applications of both parallel finite element and finite difference methods to thermal convection in a rotating spherical shell modelling the fluid dynamics of the Earth's outer core are presented. The numerical schemes are verified by reproducing the convection benchmark test by Christensen et al. [Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wilcht, J., Zhang, K., 2001. A numerical dynamo benchmark. Phys. Earth Planet. Interiors 128, 25-34.]. Both global average and local characteristics agree satisfactorily with the benchmark solution. With the element-by-element (EBE) parallelization technique, the finite element code demonstrates nearly optimal linear scalability in computational speed. The finite difference code is also efficient and scalable by utilizing a parallel library Aztec [Tuminaro, R.S., Heroux, M., Hutchinson, S.A., Shadid, J.N., 1999. Official AZTEC User's Guide: Version 2.1.].
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.
A tensor artificial viscosity using a finite element approach
NASA Astrophysics Data System (ADS)
Kolev, Tz. V.; Rieben, R. N.
2009-12-01
We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian-Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads to novel insights as well as improved numerical results. We begin with a generalized tensor version of the Von Neumann-Richtmyer artificial viscosity, then convert it to a variational formulation and apply a Galerkin discretization process using high order Gaussian quadrature to obtain a generalized nodal force term and corresponding zonal heating (or shock entropy) term. This technique is modular and is therefore suitable for coupling to a traditional staggered grid discretization of the momentum and energy conservation laws; however, we motivate the use of such finite element approaches for discretizing each term in the Euler equations. We review the key properties that any artificial viscosity must possess and use these to formulate specific constraints on the total artificial viscosity force term as well as the artificial viscosity coefficient. We also show, that under certain simplifying assumptions, the two-dimensional scheme from [1] can be viewed as an under-integrated version of our finite element method. This equivalence holds on general distorted quadrilateral grids. Finally, we present computational results on some standard shock hydro test problems, as well as some more challenging problems, indicating the advantages of the new approach with respect to symmetry preservation for shock wave propagation over general grids.
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. PMID:22587208
Finite-size scaling for quantum criticality using the finite-element method
NASA Astrophysics Data System (ADS)
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an “exact” formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
NASA Astrophysics Data System (ADS)
Cheng, Jiahao; Shahba, Ahmad; Ghosh, Somnath
2016-05-01
Image-based CPFE modeling involves computer generation of virtual polycrystalline microstructures from experimental data, followed by discretization into finite element meshes. Discretization is commonly accomplished using three-dimensional four-node tetrahedral or TET4 elements, which conform to the complex geometries. It has been commonly observed that TET4 elements suffer from severe volumetric locking when simulating deformation of incompressible or nearly incompressible materials. This paper develops and examines three locking-free stabilized finite element formulations in the context of crystal plasticity finite element analysis. They include a node-based uniform strain (NUS) element, a locally integrated B-bar (LIB) based element and a F-bar patch (FP) based element. All three formulations are based on the partitioning of TET4 element meshes and integrating over patches to obtain favorable incompressibility constraint ratios without adding large degrees of freedom. The results show that NUS formulation introduces unstable spurious energy modes, while the LIB and FP elements stabilize the solutions and are preferred for reliable CPFE analysis. The FP element is found to be computationally efficient over the LIB element.
Finite element evaluation of erosion/corrosion affected reducing elbow
Basavaraju, C.
1996-12-01
Erosion/corrosion is a primary source for wall thinning or degradation of carbon steel piping systems in service. A number of piping failures in the power industry have been attributed to erosion/corrosion. Piping elbow is one of such susceptible components for erosion/corrosion because of increased flow turbulence due to its geometry. In this paper, the acceptability of a 12 in. x 8 in. reducing elbow in RHR service water pump discharge piping, which experienced significant degradation due to wall thinning in localized areas, was evaluated using finite element analysis methodology. Since the simplified methods showed very small margin and recommended replacement of the elbow, a detailed 3-D finite element model was built using shell elements and analyzed for internal pressure and moment loadings. The finite element analysis incorporated the U.T. measured wall thickness data at various spots that experienced wall thinning. The results showed that the elbow is acceptable as-is until the next fuel cycle. FEA, though cumbersome, and time consuming is a valuable analytical tool in making critical decisions with regard to component replacement of border line situation cases, eliminating some conservatism while not compromising the safety.
FECAP - FINITE ELEMENT COMPOSITE ANALYSIS PROGRAM FOR A MICROCOMPUTER
NASA Technical Reports Server (NTRS)
Bowles, D. E.
1994-01-01
Advanced composite materials have gained use in the aerospace industry over the last 20 years because of their high specific strength and stiffness, and low coefficient of thermal expansion. Design of composite structures requires the analysis of composite material behavior. The Finite Element Composite Analysis Program, FECAP, is a special purpose finite element analysis program for analyzing composite material behavior with a microcomputer. Composite materials, in regard to this program, are defined as the combination of at least two distinct materials to form one nonhomogeneous anisotropic material. FECAP assumes a state of generalized plane strain exists in a material consisting of two or more orthotropic phases, subjected to mechanical and/or thermal loading. The finite element formulation used in FECAP is displacement based and requires the minimization of the total potential energy for each element with respect to the unknown variables. This procedure leads to a set of linear simultaneous equations relating the unknown nodal displacements to the applied loads. The equations for each element are assembled into a global system, the boundary conditions are applied, and the system is solved for the nodal displacements. The analysis may be performed using either 4-mode linear or 8-mode quadratic isoparametric elements. Output includes the nodal displacements, and the element stresses and strains. FECAP was written for a Hewlett Packard HP9000 Series 200 Microcomputer with the HP Basic operating system. It was written in HP BASIC 3.0 and requires approximately 0.5 Mbytes of RAM in addition to what is required for the operating system. A math coprocessor card is highly recommended. FECAP was developed in 1988.
Finite element structural redesign by large admissible perturbations
NASA Technical Reports Server (NTRS)
Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.
1991-01-01
In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.
Dynamic finite element modeling of poroviscoelastic soft tissue.
Yang, Zhaochun; Smolinski, Patrick
2006-02-01
Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-beta method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects. PMID:16880152
Nonlinear Finite Element Analysis of FRP Strengthened Reinforced Concrete Beams
NASA Astrophysics Data System (ADS)
Sasmal, S.; Kalidoss, S.; Srinivas, V.
2012-12-01
This paper focuses on nonlinear analysis of parent and fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beam using general purpose finite element software, ANSYS. Further, it is aimed to investigate the suitability of different elements available in ANSYS library to represent FRP, epoxy and interface. 3-D structural RC solid element has been used to model concrete and truss element is employed for modeling the reinforcements. FRP has been modelled using 3-D membrane element and layered element with number of layers, epoxy is modelled using eight node brick element, and eight node layered solid shell is used to mathematically represent the concrete-FRP interface behavior. Initially, the validation of the numerical model for the efficacy of different elements (SOLID65 for concrete and LINK8 for reinforcement) and material models is carried out on the experimental beam reported in literature. The validated model, elements and material properties is used to evaluate the load-displacement and load-strain response behavior and crack patterns of the FRP strengthened RC beams. The numerical results indicated that significant improvement in the displacement in the strengthened RC beams with the advancement of cracks. The study shows that FRP with shell elements is recommended when single layer of FRP is used. When multi layered FRP is used, solid layered element can be a reasonably good choice whereas the epoxy matrix with linear solid element does not need further complicated model. Interfacial element makes the analysis minimally improved at the cost of complicated modeling issues and considerable computation time. Hence, for nonlinear analysis of usual strengthened structures, unless it is specifically required for, interface element may not be required and a full contact can be assumed at interface.
Finite element solution of transient fluid-structure interaction problems
NASA Technical Reports Server (NTRS)
Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.
1991-01-01
A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.
Parallel, adaptive finite element methods for conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.
1994-01-01
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
A finite element model of ferroelectric/ferroelastic polycrystals
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Finite element neural networks for electromagnetic inverse problems
NASA Astrophysics Data System (ADS)
Ramuhalli, P.; Udpa, L.; Udpa, S.
2002-05-01
Iterative approaches using numerical forward models are commonly used for solving inverse problems in nondestructive evaluation. The drawbacks of these approaches include their high computational cost and the difficulty in computing gradients for updating defect profiles. This paper proposes a finite element neural network (FENN) that embeds finite element models into a neural network format. This approach enables fast and accurate solution of the forward problem. The FENN can then be used as the forward model in an iterative approach to solve the inverse problem. Gradient-based optimization methods are easily applied since the FENN provides an explicit functional mapping between the defect profile and the measured signal. Results of applying the FENN to several simple electromagnetic forward and inverse problems are presented.
Finite Element Simulation of Metal-Semiconductor-Metal Photodetector
Guarino, G.; Donaldson, W.R.; Mikulics, M.; Marso, M.; Kordos, P.; Sobolewski, R.
2009-08-19
The successful application of finite element analysis to ultrafast optoelectronic devices is demonstrated. Finite element models have been developed for both an alloyed- and surface-contact metal–semiconductor–metal photodetectors. The simulation results agree with previously reported experimental data. The alloyed device, despite having a somewhat larger capacitance, has a non-illuminated region of lower resistance with a more-uniform and deeper-penetrating electric field and carrier transport current. The latter explains, in terms of the equivalent lumped parameters, the experimentally observed faster response of the alloyed device. The model is further used to predict improved responsivity, based on electrode spacing and antireflective coating. We project that increasing the depth of the alloyed contact beyond approximately half of the optical penetration depth will not yield significantly improved responsivity.
Experimental validation of a finite-element model updating procedure
NASA Astrophysics Data System (ADS)
Kanev, S.; Weber, F.; Verhaegen, M.
2007-02-01
This paper validates an approach to damage detection and localization based on finite-element model updating (FEMU). The approach has the advantage over other existing methods to FEMU that it simultaneously updates all three finite-element model matrices at the same time preserving their structure (connectivity), symmetry and positive-definiteness. The approach is tested in this paper on an experimental setup consisting of a steel cable, where local mass changes and global change in the tension of the cable are introduced. The new algorithm is applied to identify the size and location of different changes in the structural parameters (mass, stiffness and damping). The obtained results clearly indicate that even small structural changes can be detected and localized with the new method. Additionally, a comparison with many other FEMU-based methods has been performed to show the superiority of the considered method.
Finite Element Modeling of Micromachined MEMS Photon Devices
Datskos, P.G.; Evans, B.M.; Schonberger, D.
1999-09-20
The technology of microelectronics that has evolved over the past half century is one of great power and sophistication and can now be extended to many applications (MEMS and MOEMS) other than electronics. An interesting application of MEMS quantum devices is the detection of electromagnetic radiation. The operation principle of MEMS quantum devices is based on the photoinduced stress in semiconductors, and the photon detection results from the measurement of the photoinduced bending. These devices can be described as micromechanical photon detectors. In this work, we have developed a technique for simulating electronic stresses using finite element analysis. We have used our technique to model the response of micromechanical photon devices to external stimuli and compared these results with experimental data. Material properties, geometry, and bimaterial design play an important role in the performance of micromechanical photon detectors. We have modeled these effects using finite element analysis and included the effects of bimaterial thickness coating, effective length of the device, width, and thickness.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1989-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Finite Element Analysis Applied to Dentoalveolar Trauma: Methodology Description
da Silva, B. R.; Moreira Neto, J. J. S.; da Silva, F. I.; de Aguiar, A. S. W.
2011-01-01
Dentoalveolar traumatic injuries are among the clinical conditions most frequently treated in dental practice. However, few studies so far have addressed the biomechanical aspects of these events, probably as a result of difficulties in carrying out satisfactory experimental and clinical studies as well as the unavailability of truly scientific methodologies. The aim of this paper was to describe the use of finite element analysis applied to the biomechanical evaluation of dentoalveolar trauma. For didactic purposes, the methodological process was divided into steps that go from the creation of a geometric model to the evaluation of final results, always with a focus on methodological characteristics, advantages, and disadvantages, so as to allow the reader to customize the methodology according to specific needs. Our description shows that the finite element method can faithfully reproduce dentoalveolar trauma, provided the methodology is closely followed and thoroughly evaluated. PMID:21991463
Compatibility conditions of structural mechanics for finite element analysis
NASA Technical Reports Server (NTRS)
Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.
1990-01-01
The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's; (2) the cluster or field CC's; and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown.
Finite Element Analysis of Extrusion of Multifilamentary Superconductor Precursor
Peng, X.; Sumption, M.D.; Collings, E.W.
2004-06-28
The extrusion of multifilamentary superconductor precursor billets has been modeled using finite element analysis. The billet configuration was 6 around 1, with the subelement consisting of Nb rods, and the outer can or sleeve was Cu. Two general cases were investigated, those in which the re-stack rods were initially; (i) round, and (ii) hexed. A thermo-mechanical, elasto-plastic, finite-element method was used to analyze the extrusion process. In this 3D FEM model, the initial state of the billet was assumed to be absent of bonding. A typical die angle (2{alpha}=45 deg.) and a series of extrusion ratios were selected to perform the simulation and the corresponding stress and strain distributions of the two billet variants processed were compared. Based on the stress and deformation created at the rod/rod and rod/sleeve interfaces, the bonding conditions generated through the extrusion were investigated.
Exemplifying Quantum Systems in a Finite Element Basis
Young, Toby D.
2009-08-13
This paper presents a description of the abstractions required for the expression and solution of the linear single-particle Schroedinger equation in a finite element basis. This paper consists of two disparate themes: First, to layout and establish the foundations of finite element analysis as an approximate numerical solution to extendable quantum mechanical systems; and second, to promote a high-performance open-source computational model for the approximate numerical solution to quantum mechanical systems. The structural foundation of the one-and two-dimensional time-independent Schroedinger equation describing an infinite potential well is explored and a brief overview of the hierarchal design of the computational library written in C++ is given.
Finite element simulation of temperature dependent free surface flows
NASA Technical Reports Server (NTRS)
Engelman, M. S.; Sani, R. L.
1985-01-01
The method of Engelman and Sani (1984) for a finite-element simulation of incompressible surface flows with a free and/or moving fluid interface, such as encountered in crystal growth and coating and polymer technology, is extended to temperature-dependent flows, including the effect of temperature-dependent surface tension. The basic algorithm of Saito and Scriven (1981) and Ruschak (1980) has been generalized and implemented in a robust and versatile finite-element code that can be employed with relative ease for the simulation of free-surface problems in complex geometries. As a result, the costly dependence on the Newton-Raphson algorithm has been eliminated by replacing it with a quasi-Newton iterative method, which nearly retains the superior convergence properties of the Newton-Raphson method.
Finite element solution theory for three-dimensional boundary flows
NASA Technical Reports Server (NTRS)
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
Surface subsidence prediction by nonlinear finite-element analysis
Najjar, Y. . Dept. of Civil Engineering); Zaman, M. . School of Civil Engineering and Environmental Science)
1993-11-01
An improved two-dimensional plane-strain numerical procedure based on the incremental-iterative nonlinear finite-element is developed to predict ground subsidence caused by underground mining. The procedure emphasizes the use of the following features: (1) an appropriate constitutive model that can accurately describe the nonlinear behavior of geological strata; and (2) an accurate algorithm for simulation of excavation sequences consistent with the actual underground mining process. The computer code is used to analyze a collapse that occurred in the Blue Goose Lease [number sign]1 Mine in northeastern Oklahoma. A parametric study is conducted to investigate the effects of some selected factors on the shape and extent of subsidence profiles. Analyses of the numerical results indicate that the nonlinear finite-element technique can be employed to meaningfully predict and characterize the potential for ground subsidence due to underground mining.
Cyclic creep analysis from elastic finite-element solutions
NASA Technical Reports Server (NTRS)
Kaufman, A.; Hwang, S. Y.
1986-01-01
A uniaxial approach was developed for calculating cyclic creep and stress relaxation at the critical location of a structure subjected to cyclic thermomechanical loading. This approach was incorporated into a simplified analytical procedure for predicting the stress-strain history at a crack initiation site for life prediction purposes. An elastic finite-element solution for the problem was used as input for the simplified procedure. The creep analysis includes a self-adaptive time incrementing scheme. Cumulative creep is the sum of the initial creep, the recovery from the stress relaxation and the incremental creep. The simplified analysis was exercised for four cases involving a benchmark notched plate problem. Comparisons were made with elastic-plastic-creep solutions for these cases using the MARC nonlinear finite-element computer code.
A finite element model for residual stress in repair welds
Feng, Z.; Wang, X.L.; Spooner, S.; Goodwin, G.M.; Maziasz, P.J.; Hubbard, C.R.; Zacharia, T.
1996-03-28
This paper describes a three-dimensional finite element model for calculation of the residual stress distribution caused by repair welding. Special user subroutines were developed to simulate the continuous deposition of filler metal during welding. The model was then tested by simulating the residual stress/strain field of a FeAl weld overlay clad on a 2{1/4}Cr-1 Mo steel plate, for which neutron diffraction measurement data of the residual strain field were available. It is shown that the calculated residual stress distribution was consistent with that determined with neutron diffraction. High tensile residual stresses in both the longitudinal and transverse directions were observed around the weld toe at the end of the weld. The strong spatial dependency of the residual stresses in the region around the weld demonstrates that the common two-dimensional cross-section finite element models should not be used for repair welding analysis.
Phased array antenna analysis using hybrid finite element methods
NASA Astrophysics Data System (ADS)
McGrath, Daniel T.
1993-06-01
This research in computational electromagnetics developed a new method for predicting the near-field mutual coupling effects in phased array antennas, using the finite element method (FEM) in combination with integral equations. Accurate feed modeling is accomplished by enforcing continuity between the FEM solution and an arbitrary number of wave guide models across a ground plane aperture. A periodic integral equation is imposed above the antenna's physical structure in order to enforce the radiation condition and to confine the analysis to an array unit cell. The electric field is expanded in terms of vector finite elements, and Galerkin's method is used to write the problem as a matrix equation. A general-purpose computer code was developed and validated by comparing its results to published data for several array types. Its versatility was demonstrated with predictions of the scanning properties of arrays of printed dipoles and printed flared notches.
An emulator for minimizing computer resources for finite element analysis
NASA Technical Reports Server (NTRS)
Melosh, R.; Utku, S.; Islam, M.; Salama, M.
1984-01-01
A computer code, SCOPE, has been developed for predicting the computer resources required for a given analysis code, computer hardware, and structural problem. The cost of running the code is a small fraction (about 3 percent) of the cost of performing the actual analysis. However, its accuracy in predicting the CPU and I/O resources depends intrinsically on the accuracy of calibration data that must be developed once for the computer hardware and the finite element analysis code of interest. Testing of the SCOPE code on the AMDAHL 470 V/8 computer and the ELAS finite element analysis program indicated small I/O errors (3.2 percent), larger CPU errors (17.8 percent), and negligible total errors (1.5 percent).
An emulator for minimizing finite element analysis implementation resources
NASA Technical Reports Server (NTRS)
Melosh, R. J.; Utku, S.; Salama, M.; Islam, M.
1982-01-01
A finite element analysis emulator providing a basis for efficiently establishing an optimum computer implementation strategy when many calculations are involved is described. The SCOPE emulator determines computer resources required as a function of the structural model, structural load-deflection equation characteristics, the storage allocation plan, and computer hardware capabilities. Thereby, it provides data for trading analysis implementation options to arrive at a best strategy. The models contained in SCOPE lead to micro-operation computer counts of each finite element operation as well as overall computer resource cost estimates. Application of SCOPE to the Memphis-Arkansas bridge analysis provides measures of the accuracy of resource assessments. Data indicate that predictions are within 17.3 percent for calculation times and within 3.2 percent for peripheral storage resources for the ELAS code.
Finite-element thermo-viscoplastic analysis of aerospace structures
NASA Technical Reports Server (NTRS)
Pandey, Ajay; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
Finite element thermo-viscoplastic analysis of aerospace structures
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Thornton, Earl A.
1990-01-01
The time-dependent thermo-viscoplastic response of aerospace structures subjected to intense aerothermal loads is predicted using the finite-element method. The finite-element analysis uses the Bodner-Partom unified viscoplastic constitutive relations to determine rate-dependent nonlinear material behavior. The methodology is verified by comparison with experimental data and other numerical results for a uniaxially-loaded bar. The method is then used (1) to predict the structural response of a rectangular plate subjected to line heating along a centerline, and (2) to predict the thermal-structural response of a convectively-cooled engine cowl leading edge subjected to aerodynamic shock-shock interference heating. Compared to linear elastic analysis, the viscoplastic analysis results in lower peak stresses and regions of plastic deformations.
A comparison of the capabilities of three finite element programs
NASA Technical Reports Server (NTRS)
Loendorf, D. D.
1972-01-01
Three finite element programs are compared to assess their capabilities as an analysis tool in a structural design process. Because of the need for repetitive analyses as an integral part of a design loop, a candidate program must be capable of handling large problems, operate efficiently, and be readily adaptable for use in computer-aided design. The three programs considered in the study, ELAS,SNAP, and NASTRAN, range from a relatively small finite element program limited to static structural analysis (ELAS) to a large complex general analysis system (NASTRAN). Results are given for comparative speeds and computer resources required for each program in the analysis of sample fuselage problems representative of practical aircraft design.
Finite element calculation of residual stress in dental restorative material
NASA Astrophysics Data System (ADS)
Grassia, Luigi; D'Amore, Alberto
2012-07-01
A finite element methodology for residual stresses calculation in dental restorative materials is proposed. The material under concern is a multifunctional methacrylate-based composite for dental restorations, activated by visible light. Reaction kinetics, curing shrinkage, and viscoelastic relaxation functions were required as input data on a structural finite element solver. Post cure effects were considered in order to quantify the residual stresses coming out from natural contraction with respect to those debited to the chemical shrinkage. The analysis showed for a given test case that residual stresses frozen in the dental restoration at uniform temperature of 37°C are of the same order of magnitude of the strength of the dental composite material per se.
A weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1990-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Weak Hamiltonian finite element method for optimal control problems
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Bless, Robert R.
1991-01-01
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.
Finite element dynamic analysis of finite beams on a bilinear foundation under a moving load
NASA Astrophysics Data System (ADS)
Castro Jorge, P.; Pinto da Costa, A.; Simões, F. M. F.
2015-06-01
The present paper is concerned with the behaviour of finite elastic beams, acted by a moving transverse concentrated load, interacting with elastic foundations of different stiffnesses in compression and in tension. Using finite element analyses, the displacement amplitudes and the critical velocities of the load on a UIC-60 rail are computed and their dependence with respect to the difference between the foundation's moduli in compression and in tension is evaluated. The limit case of a tensionless foundation is as well analyzed. The numerical algorithm relies on the internal force vectors and tangent stiffness matrices computed exactly with automatic symbolic manipulation.
A comparison of the finite difference and finite element methods for heat transfer calculations
NASA Technical Reports Server (NTRS)
Emery, A. F.; Mortazavi, H. R.
1982-01-01
The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.
Finite element method - A companion in experimental mechanics
NASA Technical Reports Server (NTRS)
Kobayashi, A. S.
1984-01-01
The hybrid experimental-numerical procedure for structural analysis is described by its applications in fracture mechanics. The procedure was first verified by the excellent agreements between the dynamic stress intensity factors obtained directly by dynamic photoelasticity and those generated by the hybrid procedure where a dynamic finite element code was executed in its generation mode. The hybrid procedure was then used to determine the dynamic fracture toughness of reaction bonded silicon nitride.
Finite Element Model for Hydrocephalus and Idiopathic Intracranial Hypertension.
Kim, Dong-Joo; Kim, Hakseung; Park, Dae-Hyeon; Lee, Hack-Jin; Czosnyka, Zofia; Sutcliffe, Michael P F; Czosnyka, Marek
2016-01-01
Hydrocephalus and idiopathic intracranial hypertension (IIH) are neuropathies associated with disturbed cerebrospinal fluid dynamics. Several finite element (FE) brain models were suggested to simulate the pathological changes in hydrocephalus, but with overly simplified assumptions regarding the properties of the brain parenchyma. This study proposes a two-dimensional FE brain model, capable of simulating both hydrocephalus and IIH by incorporating poro-hyperelasticity of the brain and detailed structural information (i.e., sulci). PMID:27165898
Finite element analysis of the 2240 MW HTGR PCRV
Fugelso, L.E.
1986-04-01
Three-dimensional finite element calculations for the response of the prestressed concrete reactor vessel for the 2240 MW HTGR which evaluated the stress distributions and concentrations were accomplished. Constitutive equations utilized in this evaluation were linear elastic, Von Mises elastic-plastic and the empirical Kotsovos-Newman concrete fit with and without steel reinforcing. Ultimate values of the internal pressures without initial prestress were obtained. Also stresses in the annular concrete retaining cover over the stream generator were evaluated.
An interactive virtual environment for finite element analysis
Bradshaw, S.; Canfield, T.; Kokinis, J.; Disz, T.
1995-06-01
Virtual environments (VE) provide a powerful human-computer interface that opens the door to exciting new methods of interaction with high-performance computing applications in several areas of research. The authors are interested in the use of virtual environments as a user interface to real-time simulations used in rapid prototyping procedures. Consequently, the authors are developing methods for coupling finite element models of complex mechanical systems with a VE interface for real-time interaction.
Study of the available finite element software packages at KSC
NASA Technical Reports Server (NTRS)
Lu, Chu-Ho
1990-01-01
The interaction among the three finite element software packages, SDRCI/I-DEAS, MSC/NASTRAN, and I/FEM, used at NASA, Kennedy Space Center is addressed. The procedures for using more than one of these application software packages to model and analyze a structure design are discussed. Design and stress analysis of a solid rocket booster fixture is illustrated by using four different combinations of the three software packages. Their results are compared and show small yet acceptable differences.
An Efficient Vector Finite Element Method for Nonlinear Electromagnetic Modeling
Fisher, A C; White, D A; Rodrigue, G H
2006-06-27
We have developed a mixed Vector Finite Element Method (VFEM) for Maxwell's equations with a nonlinear polarization term. The method allows for discretization of complicated geometries with arbitrary order representations of the B and E fields. In this paper we will describe the method and a series of optimizations that significantly reduce the computational cost. Additionally, a series of test simulations will be presented to validate the method. Finally, a nonlinear waveguide mode mixing example is presented and discussed.
Least-squares finite element method for fluid dynamics
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
A verification procedure for MSC/NASTRAN Finite Element Models
NASA Technical Reports Server (NTRS)
Stockwell, Alan E.
1995-01-01
Finite Element Models (FEM's) are used in the design and analysis of aircraft to mathematically describe the airframe structure for such diverse tasks as flutter analysis and actively controlled landing gear design. FEM's are used to model the entire airplane as well as airframe components. The purpose of this document is to describe recommended methods for verifying the quality of the FEM's and to specify a step-by-step procedure for implementing the methods.
Finite element analysis of a deployable space structure
NASA Technical Reports Server (NTRS)
Hutton, D. V.
1982-01-01
To assess the dynamic characteristics of a deployable space truss, a finite element model of the Scientific Applications Space Platform (SASP) truss has been formulated. The model incorporates all additional degrees of freedom associated with the pin-jointed members. Comparison of results with SPAR models of the truss show that the joints of the deployable truss significantly affect the vibrational modes of the structure only if the truss is relatively short.
Parallel finite element simulation of large ram-air parachutes
NASA Astrophysics Data System (ADS)
Kalro, V.; Aliabadi, S.; Garrard, W.; Tezduyar, T.; Mittal, S.; Stein, K.
1997-06-01
In the near future, large ram-air parachutes are expected to provide the capability of delivering 21 ton payloads from altitudes as high as 25,000 ft. In development and test and evaluation of these parachutes the size of the parachute needed and the deployment stages involved make high-performance computing (HPC) simulations a desirable alternative to costly airdrop tests. Although computational simulations based on realistic, 3D, time-dependent models will continue to be a major computational challenge, advanced finite element simulation techniques recently developed for this purpose and the execution of these techniques on HPC platforms are significant steps in the direction to meet this challenge. In this paper, two approaches for analysis of the inflation and gliding of ram-air parachutes are presented. In one of the approaches the point mass flight mechanics equations are solved with the time-varying drag and lift areas obtained from empirical data. This approach is limited to parachutes with similar configurations to those for which data are available. The other approach is 3D finite element computations based on the Navier-Stokes equations governing the airflow around the parachute canopy and Newtons law of motion governing the 3D dynamics of the canopy, with the forces acting on the canopy calculated from the simulated flow field. At the earlier stages of canopy inflation the parachute is modelled as an expanding box, whereas at the later stages, as it expands, the box transforms to a parafoil and glides. These finite element computations are carried out on the massively parallel supercomputers CRAY T3D and Thinking Machines CM-5, typically with millions of coupled, non-linear finite element equations solved simultaneously at every time step or pseudo-time step of the simulation.
Discontinuous Galerkin Finite Element Method for Parabolic Problems
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
Three-dimensional finite element modeling of liquid crystal devices
NASA Astrophysics Data System (ADS)
Vanbrabant, Pieter J. M.; James, Richard; Beeckman, Jeroen; Neyts, Kristiaan; Willman, Eero; Fernandez, F. Anibal
2011-03-01
A finite element framework is presented to combine advanced three-dimensional liquid crystal director calculations with a full-vector beam propagation analysis. This approach becomes especially valuable to analyze and design structures in which disclinations or diffraction effects play an important role. The wide applicability of the approach is illustrated in our overview from several examples including small pixel LCOS microdisplays with homeotropic alignment.
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.
Quantify Resonance Inspection with Finite Element-Based Modal Analyses
Lai, Canhai; Sun, Xin; Dasch, Cameron; Harmon, George; Jones, Martin
2011-06-01
Resonance inspection uses the natural acoustic resonances of a part to identify anomalous parts. Modern instrumentation can measure the many resonant frequencies rapidly and accurately. Sophisticated sorting algorithms trained on sets of good and anomalous parts can rapidly and reliably inspect and sort parts. This paper aims at using finite-element-based modal analysis to put resonance inspection on a more quantitative basis. A production-level automotive steering knuckle is used as the example part for our study. First, the resonance frequency spectra for the knuckle are measured with two different experimental techniques. Next, scanning laser vibrometry is used to determine the mode shape corresponding to each resonance. The material properties including anisotropy are next measured to high accuracy using resonance spectroscopy on cuboids cut from the part. Then, finite element model (FEM) of the knuckle is generated by meshing the actual part geometry obtained with computed tomography (CT). The resonance frequencies and mode shapes are next predicted with a natural frequency extraction analysis after extensive mesh size sensitivity study. The good comparison between the predicted and the experimentally measured resonance spectra indicate that finite-element-based modal analyses have the potential to be a powerful tool in shortening the training process and improving the accuracy of the resonance inspection process for a complex, production level part. The finite element based analysis can also provide a means to computationally test the sensitivity of the frequencies to various possible defects such as porosity or oxide inclusions especially in the high stress regions that the part will experience in service.
Quantify Resonance Inspection with Finite Element-Based Modal Analyses
Sun, Xin; Lai, Canhai; Dasch, Cameron
2010-11-10
Resonance inspection uses the natural acoustic resonances of a part to identify anomalous parts. Modern instrumentation can measure the many resonant frequencies rapidly and accurately. Sophisticated sorting algorithms trained on sets of good and anomalous parts can rapidly and reliably inspect and sort parts. This paper aims at using finite-element-based modal analysis to put resonance inspection on a more quantitative basis. A production-level automotive steering knuckle is used as the example part for our study. First, the resonance frequency spectra for the knuckle are measured with two different experimental techniques. Next, scanning laser vibrometry is used to determine the mode shape corresponding to each resonance. The material properties including anisotropy are next measured to high accuracy using resonance spectroscopy on cuboids cut from the part. Then, finite element model (FEM) of the knuckle is generated by meshing the actual part geometry obtained with computed tomography (CT). The resonance frequencies and mode shapes are next predicted with a natural frequency extraction analysis after extensive mesh size sensitivity study. The good comparison between the predicted and the experimentally measured resonance spectra indicate that finite-element-based modal analyses have the potential to be a powerful tool in shortening the training process and improving the accuracy of the resonance inspection process for a complex, production level part. The finite element based analysis can also provide a means to computationally test the sensitivity of the frequencies to various possible defects such as porosity or oxide inclusions especially in the high stress regions that the part will experience in service.
Enhanced finite element scheme for vibrational and flow induced sound
NASA Astrophysics Data System (ADS)
Kaltenbacher, M.; Triebenbacher, S.; Wohlmuth, B.; Zörnre, S.
2010-06-01
The paper presents Finite Element (FE) methods for classical vibroacoustics as well as computational aeroacoustics. Therewith, we can handle different grid sizes in different regions and ensure a correct coupling at the interfaces by applying the Mortar FE method. Furthermore, we can fully take into account free radiation by a new Perfectly Matched Layer (PML) technique, which is stable even for long term computations. The applicability of our developed numerical methods will be demonstrated by simulation results of the human phonation.
Finite Element Composite Analysis Program (FECAP) for a microcomputer
NASA Technical Reports Server (NTRS)
Bowles, David E.
1988-01-01
A special purpose finite element composite analysis program for analyzing composite material behavior with a microcomputer is described. The formulation assumes a state of generalized plane strain in a material consisting of two or more orthotropic phases. Loading can be mechanical and/or thermal. The theoretical background, computer implementation, and program users guide are described in detail. A sample program is solved showing the required user input and computer generated output.
Finite element model calibration using frequency responses with damping equalization
NASA Astrophysics Data System (ADS)
Abrahamsson, T. J. S.; Kammer, D. C.
2015-10-01
Model calibration is a cornerstone of the finite element verification and validation procedure, in which the credibility of the model is substantiated by positive comparison with test data. The calibration problem, in which the minimum deviation between finite element model data and experimental data is searched for, is normally characterized as being a large scale optimization problem with many model parameters to solve for and with deviation metrics that are nonlinear in these parameters. The calibrated parameters need to be found by iterative procedures, starting from initial estimates. Sometimes these procedures get trapped in local deviation function minima and do not converge to the globally optimal calibration solution that is searched for. The reason for such traps is often the multi-modality of the problem which causes eigenmode crossover problems in the iterative variation of parameter settings. This work presents a calibration formulation which gives a smooth deviation metric with a large radius of convergence to the global minimum. A damping equalization method is suggested to avoid the mode correlation and mode pairing problems that need to be solved in many other model updating procedures. By this method, the modal damping of a test data model and the finite element model is set to be the same fraction of critical modal damping. Mode pairing for mapping of experimentally found damping to the finite element model is thus not needed. The method is combined with model reduction for efficiency and employs the Levenberg-Marquardt minimizer with randomized starts to achieve the calibration solution. The performance of the calibration procedure, including a study of parameter bias and variance under noisy data conditions, is demonstrated by two numerical examples.
[Whiplash injury analysis of cervical vertebra by finite element method].
Wang, Tao; Li, Zheng-Dong; Shao, Yu; Chen, Yi-Jiu
2015-02-01
Finite element method (FEM) is an effective mathematical method for stress analysis, and has been gradually applied in the study of biomechanics of human body structures. This paper reviews the construction, development, materials assignment and verification of FEM model of cervical vertebra, and it also states the research results of injury mechanism of whiplash injury and biomechanical response analysis of the cervical vertebra using FEM by researchers at home and abroad. PMID:26058135
X-ray casting finite-element-modeling data
NASA Astrophysics Data System (ADS)
Dong, Feng; Cai, Wenli; Shi, Jiaoying
1996-03-01
An efficient technique is described for rendering Finite Element Modeling (FEM) volume data. The data are not a regular 3D grid. This algorithm can deal with most kinds of FEM data, such as hexahedron 8 nodes, hexahedron 20 nodes etc. Two methods to visualize the FEM data have been presented in the rendering stage. The comparison of these two methods have also been discussed later in this paper.
Better Finite-Element Analysis of Composite Shell Structures
NASA Technical Reports Server (NTRS)
Clarke, Gregory
2007-01-01
A computer program implements a finite-element-based method of predicting the deformations of thin aerospace structures made of isotropic materials or anisotropic fiber-reinforced composite materials. The technique and corresponding software are applicable to thin shell structures in general and are particularly useful for analysis of thin beamlike members having open cross-sections (e.g. I-beams and C-channels) in which significant warping can occur.
Piezoelectric theory for finite element analysis of ultrasonic motors
Emery, J.D.; Mentesana, C.P.
1997-06-01
The authors present the fundamental equations of piezoelectricity and references. They show how a second form of the equations and a second set of coefficients can be found, through inversions involving the elasticity tensor. They show how to compute the clamped permittivity matrix from the unclamped matrix. The authors list the program pzansys.ftn and present examples of its use. This program does the conversions and calculations needed by the finite element program ANSYS.
Application of Finite Element Method to Analyze Inflatable Waveguide Structures
NASA Technical Reports Server (NTRS)
Deshpande, M. D.
1998-01-01
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Material nonlinear analysis via mixed-iterative finite element method
NASA Technical Reports Server (NTRS)
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Finite element model for brittle fracture and fragmentation
Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; Samulyak, Roman; Lu, Cao
2016-06-01
A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.
Finite element analysis of the contact forces between viscoelastic particles
NASA Astrophysics Data System (ADS)
Zheng, Q. J.; Zhu, H. P.; Yu, A. B.
2013-06-01
The normal and tangential force-displacement (NFD and TFD) relations as well as the rolling friction between viscoelastic particles are investigated by means of finite element method (FEM). A new set of semi-theoretical models are proposed for the NFD, TFD and rolling friction based on the contact mechanics and the FEM results. Compared with previous empirical models (e.g. Linear-Spring-Dashpot model), the new models have an advantage that all parameters can be directly determined from the material properties. Therefore they can eliminate the uncertainty in parameter selection and should be more effective in discrete element method (DEM) simulations of viscoelastic granular materials.
Interactive Finite Elements for General Engine Dynamics Analysis
NASA Technical Reports Server (NTRS)
Adams, M. L.; Padovan, J.; Fertis, D. G.
1984-01-01
General nonlinear finite element codes were adapted for the purpose of analyzing the dynamics of gas turbine engines. In particular, this adaptation required the development of a squeeze-film damper element software package and its implantation into a representative current generation code. The ADINA code was selected because of prior use of it and familiarity with its internal structure and logic. This objective was met and the results indicate that such use of general purpose codes is viable alternative to specialized codes for general dynamics analysis of engines.
Periodic Boundary Conditions in the ALEGRA Finite Element Code
AIDUN,JOHN B.; ROBINSON,ALLEN C.; WEATHERBY,JOE R.
1999-11-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given.
Recent advances in hybrid/mixed finite elements
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1985-01-01
In formulations of Hybrid/Mixed finite element methods respectively by the Hellinger-Reissner principle and the Hu-Washizu principle, the stress equilibrium equations are brought in as conditions of constraint through the introduction of additional internal displacement parameters. These two approaches are more flexible and have better computing efficiencies. A procedure for the choice of assumed stress terms for 3-D solids is suggested. Example solutions are given for plates and shells using the present formulations and the idea of semiloof elements.
Finite element vibration analysis of tibia fixed by Ilizarov apparatus
NASA Astrophysics Data System (ADS)
Maslov, Leonid B.; Severin, Alexey L.
2002-02-01
Dynamic simulation of the biomechanical system consisting of the human tibia bone and external holding structure as the Ilisarov apparatus is considered. The finite element method implemented as the program code MechanicsFE3D_VEO on the basis of 20-nodal isoparametric elements is utilized. The numerical vibration analysis has allowed defining both the lowest resonance frequencies and forms of oscillations and amplitude-frequency characteristics of the system in the various points on the surface of the bone and holder. The obtained results can be used as theoretical fundament to developing resonance methods for physiological state diagnostics of the regenerating osseous tissue in fracture zone.
FEATURE-BASED MULTIBLOCK FINITE ELEMENT MESH GENERATION
Shivanna, Kiran H.; Tadepalli, Srinivas C.; Grosland, Nicole M.
2010-01-01
Hexahedral finite element mesh development for anatomic structures and biomedical implants can be cumbersome. Moreover, using traditional meshing techniques, detailed features may be inadequately captured. In this paper, we describe methodologies to handle multi-feature datasets (i.e., feature edges and surfaces). Coupling multi-feature information with multiblock meshing techniques has enabled anatomic structures, as well as orthopaedic implants, to be readily meshed. Moreover, the projection process, node and element set creation are automated, thus reducing the user interaction during model development. To improve the mesh quality, Laplacian- and optimization-based mesh improvement algorithms have been adapted to the multi-feature datasets. PMID:21076650
Finite element analysis of SMA beam bending using COMSOL
NASA Astrophysics Data System (ADS)
Yang, Shibin; Seelecke, Stefan S.; Li, Qifu
2009-03-01
Shape memory alloys (SMAs) represent a class of smart materials that has been extensively used in many engineering applications due to their unique material properties. To facilitate these new developments, an efficient computational tool like the finite element method has to be used in order to simulate the highly nonlinear, load-history and temperature dependent responses of SMA materials. The particular focus of this paper is on the aspects of modeling and simulation of the inhomogeneous beam bending problem. Based on small deformation Euler-Bernoulli beam theory, the SMA beam is treated as consisting of several layers. Each governed by a 1-D free energy SMA model. The SMA beam is implemented in the finite element software COMSOL using its general PDE form. The ordinary differential equations describing the kinetics of the phase transformations are treated as degenerated PDEs without a flux term and coupled with the mechanical equilibrium equation and the heat transfer equation. In this paper, we study the quasiplastic and superelastic isothermal behavior of an SMA cantilever beam at constant low and high temperature, respectively. Keywords: finite element analysis, shape memory alloy, COMSOL
3-D Finite Element Analyses of the Egan Cavern Field
Klamerus, E.W.; Ehgartner, B.L.
1999-02-01
Three-dimensional finite element analyses were performed for the two gas-filled storage caverns at the Egan field, Jennings dome, Louisiana. The effects of cavern enlargement on surface subsidence, storage loss, and cavern stability were investigated. The finite element model simulated the leaching of caverns to 6 and 8 billion cubic feet (BCF) and examined their performance at various operating conditions. Operating pressures varied from 0.15 psi/ft to 0.9 psi/ft at the bottom of the lowest cemented casing. The analysis also examined the stability of the web or pillar of salt between the caverns under differential pressure loadings. The 50-year simulations were performed using JAC3D, a three dimensional finite element analysis code for nonlinear quasistatic solids. A damage criterion based on onset of dilatancy was used to evaluate cavern instability. Dilation results from the development of microfractures in salt and, hence, potential increases in permeability onset occurs well before large scale failure. The analyses predicted stable caverns throughout the 50-year period for the range of pressures investigated. Some localized salt damage was predicted near the bottom walls of the caverns if the caverns are operated at minimum pressure for long periods of time. Volumetric cavern closures over time due to creep were moderate to excessive depending on the salt creep properties and operating pressures. However, subsidence above the cavern field was small and should pose no problem, to surface facilities.
Nonlinear probabilistic finite element models of laminated composite shells
NASA Technical Reports Server (NTRS)
Engelstad, S. P.; Reddy, J. N.
1993-01-01
A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.
Crystal level simulations using Eulerian finite element methods
Becker, R; Barton, N R; Benson, D J
2004-02-06
Over the last several years, significant progress has been made in the use of crystal level material models in simulations of forming operations. However, in Lagrangian finite element approaches simulation capabilities are limited in many cases by mesh distortion associated with deformation heterogeneity. Contexts in which such large distortions arise include: bulk deformation to strains approaching or exceeding unity, especially in highly anisotropic or multiphase materials; shear band formation and intersection of shear bands; and indentation with sharp indenters. Investigators have in the past used Eulerian finite element methods with material response determined from crystal aggregates to study steady state forming processes. However, Eulerian and Arbitrary Lagrangian-Eulerian (ALE) finite element methods have not been widely utilized for simulation of transient deformation processes at the crystal level. The advection schemes used in Eulerian and ALE codes control mesh distortion and allow for simulation of much larger total deformations. We will discuss material state representation issues related to advection and will present results from ALE simulations.
A phenomenological finite element model of stereolithography processing
Chambers, R.S.; Guess, T.R.; Hinnerichs, T.D.
1996-03-01
In the stereolithography process, three dimensional parts are built layer by layer using a laser to selectively cure slices of a photocurable resin, one on top of another. As the laser spot passes over the surface of the resin, the ensuing chemical reaction causes the resin to shrink and stiffen during solidification. When laser paths cross or when new layers are cured on top of existing layers, residual stresses are generated as the cure shrinkage of the freshly gelled resin is constrained by the adjoining previously-cured material. These internal stresses can cause curling in the compliant material. A capability for performing finite element analyses of the stereolithography process has been developed. Although no attempt has been made to incorporate all the physics of the process, a numerical platform suitable for such development has been established. A methodology and code architecture have been structured to allow finite elements to be birthed (activated) according to a prescribed order mimicking the procedure by which a laser is used to cure and build-up surface layers of resin to construct a three dimensional geometry. In its present form, the finite element code incorporates a simple phenomenological viscoelastic material model of solidification that is based on the shrinkage and relaxation observed following isolated, uncoupled laser exposures. The phenomenological material model has been used to analyze the curl in a simple cantilever beam and to make qualitative distinctions between two contrived build styles.
Interpreting finite element results for brittle materials in endodontic restorations
2011-01-01
Background Finite element simulation has been used in last years for analysing the biomechanical performance of post-core restorations in endodontics, but results of these simulations have been interpreted in most of the works using von Mises stress criterion. However, the validity of this failure criterion for brittle materials, which are present in these restorations, is questionable. The objective of the paper is to analyse how finite element results for brittle materials of endodontic restorations should be interpreted to obtain correct conclusions about the possible failure in the restoration. Methods Different failure criteria (Von Mises, Rankine, Coulomb-Mohr, Modified Mohr and Christensen) and material strength data (diametral tensile strength and flexural strength) were considered in the study. Three finite element models (FEM) were developed to simulate an endodontic restoration and two typical material tests: diametral tensile test and flexural test. Results Results showed that the Christensen criterion predicts similar results as the Von Mises criterion for ductile components, while it predicts similar results to all other criteria for brittle components. The different criteria predict different failure points for the diametral tensile test, all of them under multi-axial stress states. All criteria except Von Mises predict failure for flexural test at the same point of the specimen, with this point under uniaxial tensile stress. Conclusions From the results it is concluded that the Christensen criterion is recommended for FEM result interpretation in endodontic restorations and that the flexural test is recommended to estimate tensile strength instead of the diametral tensile test. PMID:21635759
A finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.; Nayani, S.
1990-01-01
Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.
Automated Finite Element Modeling of Wing Structures for Shape Optimization
NASA Technical Reports Server (NTRS)
Harvey, Michael Stephen
1993-01-01
The displacement formulation of the finite element method is the most general and most widely used technique for structural analysis of airplane configurations. Modem structural synthesis techniques based on the finite element method have reached a certain maturity in recent years, and large airplane structures can now be optimized with respect to sizing type design variables for many load cases subject to a rich variety of constraints including stress, buckling, frequency, stiffness and aeroelastic constraints (Refs. 1-3). These structural synthesis capabilities use gradient based nonlinear programming techniques to search for improved designs. For these techniques to be practical a major improvement was required in computational cost of finite element analyses (needed repeatedly in the optimization process). Thus, associated with the progress in structural optimization, a new perspective of structural analysis has emerged, namely, structural analysis specialized for design optimization application, or.what is known as "design oriented structural analysis" (Ref. 4). This discipline includes approximation concepts and methods for obtaining behavior sensitivity information (Ref. 1), all needed to make the optimization of large structural systems (modeled by thousands of degrees of freedom and thousands of design variables) practical and cost effective.
Finite element solver for 3-D compressible viscous flows
NASA Technical Reports Server (NTRS)
Reddy, K. C.; Reddy, J. N.
1986-01-01
The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.
Finite Element Modeling, Simulation, Tools, and Capabilities at Superform
NASA Astrophysics Data System (ADS)
Raman, Hari; Barnes, A. J.
2010-06-01
Over the past thirty years Superform has been a pioneer in the SPF arena, having developed a keen understanding of the process and a range of unique forming techniques to meet varying market needs. Superform’s high-profile list of customers includes Boeing, Airbus, Aston Martin, Ford, and Rolls Royce. One of the more recent additions to Superform’s technical know-how is finite element modeling and simulation. Finite element modeling is a powerful numerical technique which when applied to SPF provides a host of benefits including accurate prediction of strain levels in a part, presence of wrinkles and predicting pressure cycles optimized for time and part thickness. This paper outlines a brief history of finite element modeling applied to SPF and then reviews some of the modeling tools and techniques that Superform have applied and continue to do so to successfully superplastically form complex-shaped parts. The advantages of employing modeling at the design stage are discussed and illustrated with real-world examples.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J.; Ramirez, M.R.; Gupta, S.
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Plaskacz, E.J. ); Ramirez, M.R.; Gupta, S. . Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Process control of large-scale finite element simulation software
Spence, P.A.; Weingarten, L.I.; Schroder, K.; Tung, D.M.; Sheaffer, D.A.
1996-02-01
We have developed a methodology for coupling large-scale numerical codes with process control algorithms. Closed-loop simulations were demonstrated using the Sandia-developed finite element thermal code TACO and the commercially available finite element thermal-mechanical code ABAQUS. This new capability enables us to use computational simulations for designing and prototyping advanced process-control systems. By testing control algorithms on simulators before building and testing hardware, enormous time and cost savings can be realized. The need for a closed-loop simulation capability was demonstrated in a detailed design study of a rapid-thermal-processing reactor under development by CVC Products Inc. Using a thermal model of the RTP system as a surrogate for the actual hardware, we were able to generate response data needed for controller design. We then evaluated the performance of both the controller design and the hardware design by using the controller to drive the finite element model. The controlled simulations provided data on wafer temperature uniformity as a function of ramp rate, temperature sensor locations, and controller gain. This information, which is critical to reactor design, cannot be obtained from typical open-loop simulations.
Finite element mesh refinement criteria for stress analysis
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.
1990-01-01
This paper discusses procedures for finite-element mesh selection and refinement. The objective is to improve accuracy. The procedures are based on (1) the minimization of the stiffness matrix race (optimizing node location); (2) the use of h-version refinement (rezoning, element size reduction, and increasing the number of elements); and (3) the use of p-version refinement (increasing the order of polynomial approximation of the elements). A step-by-step procedure of mesh selection, improvement, and refinement is presented. The criteria for 'goodness' of a mesh are based on strain energy, displacement, and stress values at selected critical points of a structure. An analysis of an aircraft lug problem is presented as an example.
Finite-element time evolution operator for the anharmonic oscillator
NASA Technical Reports Server (NTRS)
Milton, Kimball A.
1995-01-01
The finite-element approach to lattice field theory is both highly accurate (relative errors approximately 1/N(exp 2), where N is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly preserved at the lattice sites). In this talk I construct matrix elements for dynamical variables and for the time evolution operator for the anharmonic oscillator, for which the continuum Hamiltonian is H = p(exp 2)/2 + lambda q(exp 4)/4. Construction of such matrix elements does not require solving the implicit equations of motion. Low order approximations turn out to be extremely accurate. For example, the matrix element of the time evolution operator in the harmonic oscillator ground state gives a results for the anharmonic oscillator ground state energy accurate to better than 1 percent, while a two-state approximation reduces the error to less than 0.1 percent.
A hybrid-stress finite element for linear anisotropic elasticity
NASA Technical Reports Server (NTRS)
Fly, Gerald W.; Oden, J. Tinsley; Pearson, Mark L.
1988-01-01
Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.
Higher Order Lagrange Finite Elements In M3D
J. Chen; H.R. Strauss; S.C. Jardin; W. Park; L.E. Sugiyama; G. Fu; J. Breslau
2004-12-17
The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.
Effect of grid system on finite element calculation
NASA Technical Reports Server (NTRS)
Lee, K. D.; Yen, S. M.
1980-01-01
Detailed parametric studies of the effect of grid system on finite element calculation for potential flows were made. These studies led to the formulation of a design criteria for optimum mesh system and the development of two methods to generate the optimum mesh system. The guidelines for optimum mesh system are: (1) the mesh structure should be regular; (2) the element should be as regular and equilateral as possible; (3) the distribution of size of element should be consistent with that of flow variables to insure maximum uniformity in error distribution; (4) for non-Dirichlet boundary conditions, smaller boundary elements or higher order interpolation functions should be used; and (5) the mesh should accommodate the boundary geometry as accurately as possible. The results of the parametric studies are presented.
Finite element simulation of impact response of wire mesh screens
NASA Astrophysics Data System (ADS)
Wang, Caizheng; Shankar, Krishna; Fien, Alan
2015-09-01
In this paper, the response of wire mesh screens to low velocity impact with blunt objects is investigated using finite element (FE) simulation. The woven wire mesh is modelled with homogeneous shell elements with equivalent smeared mechanical properties. The mechanical behaviour of the woven wire mesh was determined experimentally with tensile tests on steel wire mesh coupons to generate the data for the smeared shell material used in the FE. The effects of impacts with a low mass (4 kg) and a large mass (40 kg) providing the same impact energy are studied. The joint between the wire mesh screen and the aluminium frame surrounding it is modelled using contact elements with friction between the corresponding elements. Damage to the screen of different types compromising its structural integrity, such as mesh separation and pulling out from the surrounding frame is modelled. The FE simulation is validated with results of impact tests conducted on woven steel wire screen meshes.
A multiscale modeling technique for bridging molecular dynamics with finite element method
Lee, Yongchang Basaran, Cemal
2013-11-15
In computational mechanics, molecular dynamics (MD) and finite element (FE) analysis are well developed and most popular on nanoscale and macroscale analysis, respectively. MD can very well simulate the atomistic behavior, but cannot simulate macroscale length and time due to computational limits. FE can very well simulate continuum mechanics (CM) problems, but has the limitation of the lack of atomistic level degrees of freedom. Multiscale modeling is an expedient methodology with a potential to connect different levels of modeling such as quantum mechanics, molecular dynamics, and continuum mechanics. This study proposes a new multiscale modeling technique to couple MD with FE. The proposed method relies on weighted average momentum principle. A wave propagation example has been used to illustrate the challenges in coupling MD with FE and to verify the proposed technique. Furthermore, 2-Dimensional problem has also been used to demonstrate how this method would translate into real world applications. -- Highlights: •A weighted averaging momentum method is introduced for bridging molecular dynamics (MD) with finite element (FE) method. •The proposed method shows excellent coupling results in 1-D and 2-D examples. •The proposed method successfully reduces the spurious wave reflection at the border of MD and FE regions. •Big advantages of the proposed method are simplicity and inexpensive computational cost of multiscale analysis.
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Pates, Carl S., III
1994-01-01
A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.
Beam and Truss Finite Element Verification for DYNA3D
Rathbun, H J
2007-07-16
The explicit finite element (FE) software program DYNA3D has been developed at Lawrence Livermore National Laboratory (LLNL) to simulate the dynamic behavior of structures, systems, and components. This report focuses on verification of beam and truss element formulations in DYNA3D. An efficient protocol has been developed to verify the accuracy of these structural elements by generating a set of representative problems for which closed-form quasi-static steady-state analytical reference solutions exist. To provide as complete coverage as practically achievable, problem sets are developed for each beam and truss element formulation (and their variants) in all modes of loading and physical orientation. Analyses with loading in the elastic and elastic-plastic regimes are performed. For elastic loading, the FE results are within 1% of the reference solutions for all cases. For beam element bending and torsion loading in the plastic regime, the response is heavily dependent on the numerical integration rule chosen, with higher refinement yielding greater accuracy (agreement to within 1%). Axial loading in the plastic regime produces accurate results (agreement to within 0.01%) for all integration rules and element formulations. Truss elements are also verified to provide accurate results (within 0.01%) for elastic and elastic-plastic loading. A sample problem to verify beam element response in ParaDyn, the parallel version DYNA3D, is also presented.
Finite volume and finite element methods applied to 3D laminar and turbulent channel flows
Louda, Petr; Příhoda, Jaromír; Sváček, Petr; Kozel, Karel
2014-12-10
The work deals with numerical simulations of incompressible flow in channels with rectangular cross section. The rectangular cross section itself leads to development of various secondary flow patterns, where accuracy of simulation is influenced by numerical viscosity of the scheme and by turbulence modeling. In this work some developments of stabilized finite element method are presented. Its results are compared with those of an implicit finite volume method also described, in laminar and turbulent flows. It is shown that numerical viscosity can cause errors of same magnitude as different turbulence models. The finite volume method is also applied to 3D turbulent flow around backward facing step and good agreement with 3D experimental results is obtained.
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.
NASA Astrophysics Data System (ADS)
Ying, Jinyong; Xie, Dexuan
2015-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.
Bochev, Pavel Blagoveston
2011-06-01
We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl; {Omega})-compatible finite element basis. The SG formula is applied to the edges of the elements to express the Nedelec element degree of freedom on this edge in terms of the nodal degrees of freedom associated with the endpoints of the edge. The resulting upwind flux incorporates the upwind effects from all edges and is defined at the interior of the element. This allows for accurate evaluation of integrals on the boundaries of the control volumes for arbitrary quadrilateral elements. The new formulation admits efficient implementation through a standard loop over the elements in the mesh followed by loops over the element nodes (associated with control volume fractions in the element) and element edges (associated with flux degrees of freedom). The quantities required for the SG formula can be precomputed and stored for each edge in the mesh for additional efficiency gains. For clarity the details are presented for two-dimensional quadrilateral grids. Extension to other element shapes and three dimensions is straightforward.
A finite element simulation of sound attenuation in a finite duct with a peripherally variable liner
NASA Technical Reports Server (NTRS)
Watson, W. R.
1977-01-01
Using multimodal analysis, a variational finite element method is presented for analyzing sound attenuation in a three-dimensional finite duct with a peripherally variable liner in the absence of flow. A rectangular element, with cubic shaped functions, is employed. Once a small portion of a peripheral liner is removed, the attenuation rate near the frequency where maximum attenuation occurs drops significantly. The positioning of the liner segments affects the attenuation characteristics of the liner. Effects of the duct termination are important in the low frequency ranges. The main effect of peripheral variation of the liner is a broadening of the attenuation characteristics in the midfrequency range. Because of matrix size limitations of the presently available computer program, the eigenvalue equations should be solved out of core in order to handle realistic sources.
Simulating Space Capsule Water Landing with Explicit Finite Element Method
NASA Technical Reports Server (NTRS)
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Finite Element Analysis of the LOLA Receiver Telescope Lens
NASA Technical Reports Server (NTRS)
Matzinger, Elizabeth
2007-01-01
This paper presents the finite element stress and distortion analysis completed on the Receiver Telescope lens of the Lunar Orbiter Laser Altimeter (LOLA). LOLA is one of six instruments on the Lunar Reconnaissance Orbiter (LRO), scheduled to launch in 2008. LOLA's main objective is to produce a high-resolution global lunar topographic model to aid in safe landings and enhance surface mobility in future exploration missions. The Receiver Telescope captures the laser pulses transmitted through a diffractive optical element (DOE) and reflected off the lunar surface. The largest lens of the Receiver Telescope, Lens 1, is a 150 mm diameter aspheric lens originally designed to be made of BK7 glass. The finite element model of the Receiver Telescope Lens 1 is comprised of solid elements and constrained in a manner consistent with the behavior of the mounting configuration of the Receiver Telescope tube. Twenty-one temperature load cases were mapped to the nodes based on thermal analysis completed by LOLA's lead thermal analyst, and loads were applied to simulate the preload applied from the ring flexure. The thermal environment of the baseline design (uncoated BK7 lens with no baffle) produces large radial and axial gradients in the lens. These large gradients create internal stresses that may lead to part failure, as well as significant bending that degrades optical performance. The high stresses and large distortions shown in the analysis precipitated a design change from BK7 glass to sapphire.
Fuzzy logic to improve efficiency of finite element and finite difference schemes
Garcia, M.D.; Heger, A.S.
1994-05-01
This paper explores possible applications of logic in the areas of finite element and finite difference methods applied to engineering design problems. The application of fuzzy logic to both front-end selection of computational options and within the numerical computation itself are proposed. Further, possible methods of overcoming these limitations through the application of methods are explored. Decision strategy is a fundamental limitation in performing finite element calculations, such as selecting the optimum coarseness of the grid, numerical integration algorithm, element type, implicit versus explicit schemes, and the like. This is particularly true of novice analysts who are confronted with a myriad of choices in performing a calculation. The advantage of having the myriad of options available to the analyst is, however, that it improves and optimizes the design process if the appropriate ones are selected. Unfortunately, the optimum choices are not always apparent and only through the process of elimination or prior extensive experience can the optimum choices or combination of choices be selected. The knowledge of expert analysts could be integrated into a fuzzy ``front-end`` rule-based package to optimize the design process. The use of logic to capture the heuristic and human knowledge for selecting optimum solution strategies sets the framework for these proposed strategies.
Multiphase poroelastic finite element models for soft tissue structure
Simon, B.R.
1992-06-01
During the last two decades. biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains-, and may swell or shrink when tissue ionic concentrations are altered. Given the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law and a total Lagrangian view for the formulation. The associated FEMS are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested.
Multiphase poroelastic finite element models for soft tissue structures
Simon, B.R.
1992-12-01
During the last two decades, biological structures with soft tissue components have been modeled using poroelastic or mixture-based constitutive laws, i.e., the material is viewed as a deformable (porous) solid matrix that is saturated by mobile tissue fluid. These structures exhibit a highly nonlinear, history-dependent material behavior; undergo finite strains; and may swell or shrink when tissue ionic concentrations are altered. Give the geometric and material complexity of soft tissue structures and that they are subjected to complicated initial and boundary conditions, finite element models (FEMs) have been very useful for quantitative structural analyses. This paper surveys recent applications of poroelastic and mixture-based theories and the associated FEMs for the study of the biomechanics of soft tissues, and indicates future directions for research in this area. Equivalent finite-strain poroelastic and mixture continuum biomechanical models are presented. Special attention is given to the identification of material properties using a porohyperelastic constitutive law ans a total Lagrangian view for the formulation. The associated FEMs are then formulated to include this porohyperelastic material response and finite strains. Extensions of the theory are suggested in order to include inherent viscoelasticity, transport phenomena, and swelling in soft tissue structures. A number of biomechanical research areas are identified, and possible applications of the porohyperelastic and mixture-based FEMs are suggested. 62 refs., 11 figs., 3 tabs.
Finite element stress analysis of a compression mold. Final report. [Using SASL and WILSON codes
Watterson, C.E.
1980-03-01
Thermally induced stresses occurring in a compression mold during production molding were evaluated using finite element analysis. A complementary experimental stress analysis, including strain gages and thermocouple arrays, verified the finite element model under typical loading conditions.
IFEMS, an Interactive Finite Element Modeling System Using a CAD/CAM System
NASA Technical Reports Server (NTRS)
Mckellip, S.; Schuman, T.; Lauer, S.
1980-01-01
A method of coupling a CAD/CAM system with a general purpose finite element mesh generator is described. The three computer programs which make up the interactive finite element graphics system are discussed.
Finite-element methods for spatially resolved mesoscopic electron transport
NASA Astrophysics Data System (ADS)
Kramer, Stephan
2013-09-01
A finite-element method is presented for calculating the quantum conductance of mesoscopic two-dimensional electron devices of complex geometry attached to semi-infinite leads. For computational purposes, the leads must be cut off at some finite length. To avoid spurious, unphysical reflections, this is modeled by transparent boundary conditions. We introduce the Hardy space infinite-element technique from acoustic scattering as a way of setting up transparent boundary conditions for transport computations spanning the range from the quantum mechanical to the quasiclassical regime. These boundary conditions are exact even for wave packets and thus are especially useful in the limit of high energies with many excited modes. Yet, they possess a memory-friendly sparse matrix representation. In addition to unbounded domains, Hardy space elements allow us to truncate those parts of the computational domain which are irrelevant for the calculation of the transport properties. Thus, the computation can be done only on the region that is essential for a physically meaningful simulation of the scattering states. The benefits of the method are demonstrated by three examples. The convergence properties are tested on the transport through a quasi-one-dimensional quantum wire. It is shown that higher-order finite elements considerably improve current conservation and establish the correct phase shift between the real and the imaginary parts of the electron wave function. The Aharonov-Bohm effect demonstrates that characteristic features of quantum interference can be assessed. A simulation of electron magnetic focusing exemplifies the capability of the computational framework to study the crossover from quantum to quasiclassical behavior.
3D finite element simulations of high velocity projectile impact
NASA Astrophysics Data System (ADS)
Ožbolt, Joško; İrhan, Barış; Ruta, Daniela
2015-09-01
An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Probabilistic finite elements for fracture and fatigue analysis
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Lawrence, M.; Besterfield, G. H.
1989-01-01
The fusion of the probabilistic finite element method (PFEM) and reliability analysis for probabilistic fracture mechanics (PFM) is presented. A comprehensive method for determining the probability of fatigue failure for curved crack growth was developed. The criterion for failure or performance function is stated as: the fatigue life of a component must exceed the service life of the component; otherwise failure will occur. An enriched element that has the near-crack-tip singular strain field embedded in the element is used to formulate the equilibrium equation and solve for the stress intensity factors at the crack-tip. Performance and accuracy of the method is demonstrated on a classical mode 1 fatigue problem.
Progress on hybrid finite element methods for scattering by bodies of revolution
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Volakis, John L.
1992-01-01
Progress on the development and implementation of hybrid finite element methods for scattering by bodies of revolution are described. It was found that earlier finite element-boundary integral formulations suffered from convergence difficulties when applied to large and thin bodies of revolution. An alternative implementation is described where the finite element method is terminated with an absorbing termination boundary. In addition, an alternative finite element-boundary integral implementation is discussed for improving the convergence of the original code.
A triangular thin shell finite element: Nonlinear analysis. [structural analysis
NASA Technical Reports Server (NTRS)
Thomas, G. R.; Gallagher, R. H.
1975-01-01
Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.
Large-eddy simulation using the finite element method
McCallen, R.C.; Gresho, P.M.; Leone, J.M. Jr.; Kollmann, W.
1993-10-01
In a large-eddy simulation (LES) of turbulent flows, the large-scale motion is calculated explicitly (i.e., approximated with semi-empirical relations). Typically, finite difference or spectral numerical schemes are used to generate an LES; the use of finite element methods (FEM) has been far less prominent. In this study, we demonstrate that FEM in combination with LES provides a viable tool for the study of turbulent, separating channel flows, specifically the flow over a two-dimensional backward-facing step. The combination of these methodologies brings together the advantages of each: LES provides a high degree of accuracy with a minimum of empiricism for turbulence modeling and FEM provides a robust way to simulate flow in very complex domains of practical interest. Such a combination should prove very valuable to the engineering community.
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.
Least-squares finite element methods for quantum chromodynamics
Ketelsen, Christian; Brannick, J; Manteuffel, T; Mccormick, S
2008-01-01
A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.
Improved inhomogeneous finite elements for fabric reinforced composite mechanics analysis
NASA Technical Reports Server (NTRS)
Foye, R. L.
1992-01-01
There is a need to do routine stress/failure analysis of fabric reinforced composite microstructures to provide additional confidence in critical applications and guide materials development. Conventional methods of 3-D stress analysis are time consuming to set up, run and interpret. A need exists for simpler methods of modeling these structures and analyzing the models. The principal difficulty is the discrete element mesh generation problem. Inhomogeneous finite elements are worth investigating for application to these problems because they eliminate the mesh generation problem. However, there are penalties associated with these elements. Their convergence rates can be slow compared to homogeneous elements. Also, there is no accepted method for obtaining detailed stresses in the constituent materials of each element. This paper shows that the convergence rate can be significantly improved by a simple device which substitutes homogeneous elements for the inhomogeneous ones. The device is shown to work well in simple one and two dimensional problems. However, demonstration of the application to more complex two and three dimensional problems remains to be done. Work is also progressing toward more realistic fabric microstructural geometries.
Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms
NASA Technical Reports Server (NTRS)
Prosser, W. H.; Hamstad, M. A.; Gary, J.; OGallagher, A.
1998-01-01
A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.
NASA Technical Reports Server (NTRS)
Ko, William L.; Olona, Timothy; Muramoto, Kyle M.
1990-01-01
Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.
Binary tree eigen solver in finite element analysis
Akl, F.A.; Janetzke, D.C.; Kiraly, L.J.
1993-01-01
This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling. 5 refs.
Finite-element impact response of debonded composite turbine blades
NASA Astrophysics Data System (ADS)
Dey, Sudip; Karmakar, Amit
2014-02-01
This paper investigates on the transient behavior of debonded composite pretwisted rotating shallow conical shells which could be idealized as turbine blades subjected to low velocity normal impact using finite-element method. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and the moderate rotational speeds are considered neglecting the Coriolis effect. An eight-noded isoparametric plate bending element is employed in the finite element formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. The modified Hertzian contact law which accounts for permanent indentation is utilized to compute the impact parameters. The time-dependent equations are solved by using Newmark's time integration scheme. Parametric studies are performed to investigate the effects of triggering parameters like angle of twist, rotational speed, laminate configuration and location of debonding considering low velocity normal impact at the center of eight-layered graphite-epoxy composite cantilevered conical shells with bending stiff ([0o2/{±} 30o]s), torsion stiff ([45°/-45°/-45°/45°]s) and cross-ply ([0°/90°/0°/90°]s) laminate configurations.
Finite element analysis of heat transport in a hydrothermal zone
Bixler, N.E.; Carrigan, C.R.
1987-01-01
Two-phase heat transport in the vicinity of a heated, subsurface zone is important for evaluation of nuclear waste repository design and estimation of geothermal energy recovery, as well as prediction of magma solidification rates. Finite element analyses of steady, two-phase, heat and mass transport have been performed to determine the relative importance of conduction and convection in a permeable medium adjacent to a hot, impermeable, vertical surface. The model includes the effects of liquid flow due to capillarity and buoyancy and vapor flow due to pressure gradients. Change of phase, with its associated latent heat effects, is also modeled. The mechanism of capillarity allows for the presence of two-phase zones, where both liquid and vapor can coexist, which has not been considered in previous investigations. The numerical method employs the standard Galerkin/finite element method, using eight-node, subparametric or isoparametric quadrilateral elements. In order to handle the extreme nonlinearities inherent in two-phase, nonisothermal, porous-flow problems, steady-state results are computed by integrating transients out to a long time (a method that is highly robust).
Merging of intersecting triangulations for finite element modeling.
Cebral, J R; Löhner, R; Choyke, P L; Yim, P J
2001-06-01
Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a background grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured grid. In a first step, a regular background mesh is constructed. For each point of the background grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the background grid elements. The resulting surface models are used as support surfaces to generate three-dimensional grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well. PMID:11470121
Regularised finite element model updating using measured incomplete modal data
NASA Astrophysics Data System (ADS)
Chen, Hua-Peng; Maung, Than Soe
2014-10-01
This paper presents an effective approach for directly updating finite element model from measured incomplete vibration modal data with regularised algorithms. The proposed method is based on the relationship between the perturbation of structural parameters such as stiffness change and the modal data measurements of the tested structure such as measured mode shape readings. In order to adjust structural parameters at detailed locations, structural updating parameters will be selected at critical point level to reflect the modelling errors at the connections of structural elements. These updating parameters are then evaluated by an iterative or a direct solution procedure, which gives optimised solutions in the least squares sense without requiring an optimisation technique. In order to reduce the influence of modal measurement uncertainty, the Tikhonov regularisation method incorporating the L-curve criterion is employed to produce reliable solutions for the chosen updating parameters. Numerical simulation investigations and experimental studies for the laboratory tested space steel frame structure are undertaken to verify the accuracy and effectiveness of the proposed methods for adjusting the stiffness at the joints of structural members. The results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.
Simplified Finite Element Modelling of Acoustically Treated Structures
NASA Astrophysics Data System (ADS)
Carfagni, M.; Citti, P.; Pierini, M.
1997-07-01
The application of non-optimized damping and phono-absorbent materials to automotive systems has not proved fully satisfactory in abating noise and vibration. The objective of this work was to develop a simple finite element modelling procedure that would allow optimizing structures such as a car body-in-white in terms of vibroacoustic behavior from the design stage. A procedure was developed to determine the modifications to be made in the mass, stiffness and damping characteristics in the finite element (FE) modelling of a metal structure meshed with shell elements so that the model would describe the behavior of the acoustically treated structure. To validate the modifications, a numerical-experimental comparison of the velocities on the vibrating surface was carried out, followed by a numerical-experimental comparison of the sound pressures generated by the vibrating plate. In the comparison a simple monopole model was used, in which each area of vibrating surface could be likened to a point source. The simulation and experimental procedures, previously validated for the metal structure, were then applied to multi-layered panels. Good agreement between the experimental and simulated velocities and sound pressures resulted for all the multi-layered panel configurations examined.
Binary tree eigen solver in finite element analysis
NASA Technical Reports Server (NTRS)
Akl, F. A.; Janetzke, D. C.; Kiraly, L. J.
1993-01-01
This paper presents a transputer-based binary tree eigensolver for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on the method of recursive doubling, which parallel implementation of a number of associative operations on an arbitrary set having N elements is of the order of o(log2N), compared to (N-1) steps if implemented sequentially. The hardware used in the implementation of the binary tree consists of 32 transputers. The algorithm is written in OCCAM which is a high-level language developed with the transputers to address parallel programming constructs and to provide the communications between processors. The algorithm can be replicated to match the size of the binary tree transputer network. Parallel and sequential finite element analysis programs have been developed to solve for the set of the least-order eigenpairs using the modified subspace method. The speed-up obtained for a typical analysis problem indicates close agreement with the theoretical prediction given by the method of recursive doubling.
Numerical algorithms for finite element computations on arrays of microprocessors
NASA Technical Reports Server (NTRS)
Ortega, J. M.
1981-01-01
The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
Evaluation of a Kinematically-Driven Finite Element Footstrike Model.
Hannah, Iain; Harland, Andy; Price, Dan; Schlarb, Heiko; Lucas, Tim
2016-06-01
A dynamic finite element model of a shod running footstrike was developed and driven with 6 degree of freedom foot segment kinematics determined from a motion capture running trial. Quadratic tetrahedral elements were used to mesh the footwear components with material models determined from appropriate mechanical tests. Model outputs were compared with experimental high-speed video (HSV) footage, vertical ground reaction force (GRF), and center of pressure (COP) excursion to determine whether such an approach is appropriate for the development of athletic footwear. Although unquantified, good visual agreement to the HSV footage was observed but significant discrepancies were found between the model and experimental GRF and COP readings (9% and 61% of model readings outside of the mean experimental reading ± 2 standard deviations, respectively). Model output was also found to be highly sensitive to input kinematics with a 120% increase in maximum GRF observed when translating the force platform 2 mm vertically. While representing an alternative approach to existing dynamic finite element footstrike models, loading highly representative of an experimental trial was not found to be achievable when employing exclusively kinematic boundary conditions. This significantly limits the usefulness of employing such an approach in the footwear development process. PMID:26671721
Automated Finite Element Analysis of Elastically-Tailored Plates
NASA Technical Reports Server (NTRS)
Jegley, Dawn C. (Technical Monitor); Tatting, Brian F.; Guerdal, Zafer
2003-01-01
A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.
Curved Thermopiezoelectric Shell Structures Modeled by Finite Element Analysis
NASA Technical Reports Server (NTRS)
Lee, Ho-Jun
2000-01-01
"Smart" structures composed of piezoelectric materials may significantly improve the performance of aeropropulsion systems through a variety of vibration, noise, and shape-control applications. The development of analytical models for piezoelectric smart structures is an ongoing, in-house activity at the NASA Glenn Research Center at Lewis Field focused toward the experimental characterization of these materials. Research efforts have been directed toward developing analytical models that account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. Current work revolves around implementing thermal effects into a curvilinear-shell finite element code. This enhances capabilities to analyze curved structures and to account for coupling effects arising from thermal effects and the curved geometry. The current analytical model implements a unique mixed multi-field laminate theory to improve computational efficiency without sacrificing accuracy. The mechanics can model both the sensory and active behavior of piezoelectric composite shell structures. Finite element equations are being implemented for an eight-node curvilinear shell element, and numerical studies are being conducted to demonstrate capabilities to model the response of curved piezoelectric composite structures (see the figure).
A viscoelastic higher-order beam finite element
NASA Technical Reports Server (NTRS)
Johnson, Arthur R.; Tressler, Alexander
1996-01-01
A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.
Massively parallel computation of RCS with finite elements
NASA Technical Reports Server (NTRS)
Parker, Jay
1993-01-01
One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary
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
2016-07-01
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.
Galerkin finite-element simulation of a geothermal reservoir
Mercer, J.W., Jr.; Pinder, G.F.
1973-01-01
The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development. ?? 1973.
Finite element analysis of the stiffness of fabric reinforced composites
NASA Technical Reports Server (NTRS)
Foye, R. L.
1992-01-01
The objective of this work is the prediction of all three dimensional elastic moduli of textile fabric reinforced composites. The analysis is general enough for use with complex reinforcing geometries and capable of subsequent improvements. It places no restrictions on fabric microgeometry except that the unit cell be determinate and rectangular. The unit cell is divided into rectangular subcells in which the reinforcing geometries are easier to define and analyze. The analysis, based on inhomogeneous finite elements, is applied to a variety of weave, braid, and knit reinforced composites. Some of these predictions are correlated to test data.
Space-time formulation for finite element modeling of superconductors
Ashworth, Stephen P; Grilli, Francesco; Sirois, Frederic; Laforest, Marc
2008-01-01
In this paper we present a new model for computing the current density and field distributions in superconductors by means of a periodic space-time formulation for finite elements (FE). By considering a space dimension as time, we can use a static model to solve a time dependent problem. This allows overcoming one of the major problems of FE modeling of superconductors: the length of simulations, even for relatively simple cases. We present our first results and compare them to those obtained with a 'standard' time-dependent method and with analytical solutions.
Finite-element simulation of thermoemission electron guns
NASA Astrophysics Data System (ADS)
Greenfield, D.
2006-05-01
The peculiarity of the numeric simulation of the thermoemission electron guns consists in the principal necessity of taking into account the contribution of the electrons' charge into the potential distribution in the beam formation region. Ths fact makes the mathematical model essentially nonlinear especially in the high-perveance operation mode. Moreover, the charge density is extremely high in the vicinity of emitting surfaces, rising infinitely in the limit of zero initial velocities. A special semi-analytical approach has been applied to deal with the charge singularity. Being combined with traditional finite-element numerical techniques, this approach provides an efficient way to simulate thermoemission electron guns.
Analysis of Waveguide Junction Discontinuities Using Finite Element Method
NASA Technical Reports Server (NTRS)
Deshpande, Manohar D.
1997-01-01
A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. An H-plane discontinuity, an E-plane ridge discontinuity, and a step discontinuity in a concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained by the present method are in excellent agreement with the earlier published results. The numerical results obtained by the FEM are compared with the numerical results obtained using the Mode Matching Method (MMM) and also with the measured data.
Dual Formulations of Mixed Finite Element Methods with Applications
Gillette, Andrew; Bajaj, Chandrajit
2011-01-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841
Finite element analysis of thumb carpometacarpal joint implants
Nielsen, C.
1995-11-01
The thumb carpometacarpal joint is frequently replaced in women who have developed severe osteoarthritis of the hand. A new, privately developed implant design consists of two components, trapezial and metacarpal, each with a saddle-shaped articulating surface. A three dimensional finite element model of this implant has been developed to analyze stresses on the device. The first simulations using the model involve loading the implant with forces normal to the trapezial component. Preliminary results show contact stress distributions at the particulating surfaces of the implant.
Finite element computer model of microwave heated ceramics
Liqiu Zhou; Gang Liu; Jian Zhou
1995-12-31
In this paper, a 3-D finite element model to simulate the heating pattern during microwave sintering of ceramics in a TE{sub 10}{sup n} single mode rectangular cavity is described. A series of transient temperature profiles and heating rates of the ceramic cylinder and cubic sample were calculated versus different parameters such as thermal conductivity, dielectric loss factor, microwave power level, and microwave energy distribution. These numerical solutions may provide a better understanding of thermal runaway and solutions to microwave sintering of ceramics.
Finite element analysis of laminated plates and shells, volume 1
NASA Technical Reports Server (NTRS)
Seide, P.; Chang, P. N. H.
1978-01-01
The finite element method is used to investigate the static behavior of laminated composite flat plates and cylindrical shells. The analysis incorporates the effects of transverse shear deformation in each layer through the assumption that the normals to the undeformed layer midsurface remain straight but need not be normal to the mid-surface after deformation. A digital computer program was developed to perform the required computations. The program includes a very efficient equation solution code which permits the analysis of large size problems. The method is applied to the problem of stretching and bending of a perforated curved plate.
Recent experiences using finite-element-based structural optimization
NASA Technical Reports Server (NTRS)
Paul, B. K.; Mcconnell, J. C.; Love, Mike H.
1989-01-01
Structural optimization has been available to the structural analysis community as a tool for many years. The popular use of displacement method finite-element techniques to analyze linearly elastic structures has resulted in an ability to calculate the weight and constraint gradients inexpensively for numerical optimization of structures. Here, recent experiences in the investigation and use of structural optimization are discussed. In particular, experience with the commercially available ADS/NASOPT code is addressed. An overview of the ADS/NASOPT procedure and how it was implemented is given. Two example problems are also discussed.
Symbolic derivation of material property matrices in finite element analysis
NASA Technical Reports Server (NTRS)
Tan, H. Q.
1988-01-01
The principles and operation of MMAX, a symbolic-computation program which automates the process of generating property matrices for structural materials, are briefly described and illustrated with sample analyses of a rubberlike material and an elastoplastic material. MMAX is written in LISP under the symbolic finite-element generator FINGER and the general symbolic manipulator MACSYMA; it first derives the formulas required by mathematical manipulation, and then translates the formulas into FORTRAN code, adapted to the particular type of machine to be used for the numerical calculations. This approach is shown to combine efficiently the advantages of symbolic and numerical computation for engineering applications.
Finite element modelling of a rotating piezoelectric ultrasonic motor.
Frangi, A; Corigliano, A; Binci, M; Faure, P
2005-10-01
The evaluation of the performance of ultrasonic motors as a function of input parameters such as the driving frequency, voltage input and pre-load on the rotor is of key importance to their development and is here addressed by means of a finite element three-dimensional model. First the stator is simulated as a fully deformable elastic body and the travelling wave dynamics is accurately reproduced; secondly the interaction through contact between the stator and the rotor is accounted for by assuming that the rotor behaves as a rigid surface. Numerical results for the whole motor are finally compared to available experimental data. PMID:15975618
Specialty three-dimensional finite element analysis codes
NASA Technical Reports Server (NTRS)
Lackney, Joseph J.
1988-01-01
General purpose finite element computer codes that can model inelastic material behavior have been available for more than a decade. However, these codes have not been accurate enough for use in analyzing hot section engine components. To correct this problem, General Electric developed a series of nine new stand-alone computer codes for NASA. Because of the large temperature excursions associated with hot section engine components, these codes have been designed to accommodate broad variations in material behavior, including plasticity and creep. The capabilities of these computer codes are summarized.
Efficient finite element method for grating profile reconstruction
NASA Astrophysics Data System (ADS)
Zhang, Ruming; Sun, Jiguang
2015-12-01
This paper concerns the reconstruction of grating profiles from scattering data. The inverse problem is formulated as an optimization problem with a regularization term. We devise an efficient finite element method (FEM) and employ a quasi-Newton method to solve it. For the direct problems, the FEM stiff and mass matrices are assembled once at the beginning of the numerical procedure. Then only minor changes are made to the mass matrix at each iteration, which significantly saves the computation cost. Numerical examples show that the method is effective and robust.
Finite element modeling and experimentation of bone drilling forces
NASA Astrophysics Data System (ADS)
Lughmani, W. A.; Bouazza-Marouf, K.; Ashcroft, I.
2013-07-01
Bone drilling is an essential part of many orthopaedic surgery procedures, including those for internal fixation and for attaching prosthetics. Estimation and control of bone drilling forces are critical to prevent drill breakthrough, excessive heat generation, and mechanical damage to the bone. This paper presents a 3D finite element (FE) model for prediction of thrust forces experienced during bone drilling. The model incorporates the dynamic characteristics involved in the process along with the accurate geometrical considerations. The average critical thrust forces and torques obtained using FE analysis, for set of machining parameters are found to be in good agreement with the experimental results.
Vector algorithms for geometrically nonlinear 3D finite element analysis
NASA Technical Reports Server (NTRS)
Whitcomb, John D.
1989-01-01
Algorithms for geometrically nonlinear finite element analysis are presented which exploit the vector processing capability of the VPS-32, which is closely related to the CYBER 205. By manipulating vectors (which are long lists of numbers) rather than individual numbers, very high processing speeds are obtained. Long vector lengths are obtained without extensive replication or reordering by storage of intermediate results in strategic patterns at all stages of the computations. Comparisons of execution times with those from programs using either scalar or other vector programming techniques indicate that the algorithms presented are quite efficient.
Finite element analysis of advanced neutron source fuel plates
Luttrell, C.R.
1995-08-01
The proposed design for the Advanced Neutron Source reactor core consists of closely spaced involute fuel plates. Coolant flows between the plates at high velocities. It is vital that adjacent plates do not come in contact and that the coolant channels between the plates remain open. Several scenarios that could result in problems with the fuel plates are studied. Finite element analyses are performed on fuel plates under pressure from the coolant flowing between the plates at a high velocity, under pressure because of a partial flow blockage in one of the channels, and with different temperature profiles.
Visualizing Higher Order Finite Elements: FY05 Yearly Report.
Thompson, David; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elementsinto regions appropriate for isosurfacing and proves the conditions under which thealgorithm will terminate. Finite elements are used to create piecewise polynomialapproximants to the solution of partial differential equations for which no analyticalsolution exists. These polynomials represent fields such as pressure, stress, and mo-mentim. In the past, these polynomials have been linear in each parametric coordinate.Each polynomial coefficient must be uniquely determined by a simulation, and thesecoefficients are called degrees of freedom. When there are not enough degrees of free-dom, simulations will typically fail to produce a valid approximation to the solution.Recent work has shown that increasing the number of degrees of freedom by increas-ing the order of the polynomial approximation (instead of increasing the number offinite elements, each of which has its own set of coefficients) can allow some typesof simulations to produce a valid approximation with many fewer degrees of freedomthan increasing the number of finite elements alone. However, once the simulation hasdetermined the values of all the coefficients in a higher-order approximant, tools donot exist for visual inspection of the solution.This report focuses on a technique for the visual inspection of higher-order finiteelement simulation results based on decomposing each finite element into simplicialregions where existing visualization algorithms such as isosurfacing will work. Therequirements of the isosurfacing algorithm are enumerated and related to the placeswhere the partial derivatives of the polynomial become zero. The original isosurfacingalgorithm is then applied to each of these regions in turn.3 AcknowledgementThe authors would like to thank David Day and Louis Romero for their insight into poly-nomial system solvers and the LDRD Senior Council for the opportunity to pursue thisresearch. The authors were
Slender Compressed Plate in Component Based Finite Element Model
NASA Astrophysics Data System (ADS)
Kurejková, M.; Wald, F.; Kabeláč, J.; Šabatka, L.
2015-11-01
The paper presents an advance design model of a slender plate in the structural steel joint. Finite element methods and material models are described and design procedure for slender plates in numerical models of steel joints is proposed. The design procedure is demonstrated on examples. The results are verified with an analytical model according to European standards. A compressed beam with slender web and beam-to-column joint are studied by numerical analysis, buckling resistances are determined and results verified. The verification shows very good agreement.
Finite Element Analysis of 2-D Elastic Contacts Involving FGMs
NASA Astrophysics Data System (ADS)
Abhilash, M. N.; Murthy, H.
2014-05-01
The response of elastic indenters in contact with Functionally Graded Material (FGM) coated homogeneous elastic half space has been presented in the current paper. Finite element analysis has been used due to its ability to handle complex geometry, material, and boundary conditions. Indenters of different typical surface profiles have been considered and the problem has been idealized as a two-dimensional (2D) plane strain problem considering only normal loads. Initially, indenters were considered to be rigid and the results were validated with the solutions presented in the literature. The analysis has then been extended to the case of elastic indenters on FGM-coated half spaces and the results are discussed.
SPAR data set contents. [finite element structural analysis system
NASA Technical Reports Server (NTRS)
Cunningham, S. W.
1981-01-01
The contents of the stored data sets of the SPAR (space processing applications rocket) finite element structural analysis system are documented. The data generated by each of the system's processors are stored in a data file organized as a library. Each data set, containing a two-dimensional table or matrix, is identified by a four-word name listed in a table of contents. The creating SPAR processor, number of rows and columns, and definitions of each of the data items are listed for each data set. An example SPAR problem using these data sets is also presented.
A finite-element analysis model of orbital biomechanics.
Schutte, Sander; van den Bedem, Sven P W; van Keulen, Fred; van der Helm, Frans C T; Simonsz, Huibert J
2006-05-01
To reach a better understanding of the suspension of the eye in the orbit, an orbital mechanics model based upon finite-element analysis (FEA) has been developed. The FEA model developed contains few prior assumptions or constraints (e.g., the position of the eye in the orbit), allowing modeling of complex three-dimensional tissue interactions; unlike most current models of eye motility. Active eye movements and forced ductions were simulated and showed that the supporting action of the orbital fat plays an important role in the suspension of the eye in the orbit and in stabilization of rectus muscle paths. PMID:16413594
Finite element analysis of periodic transonic flow problems
NASA Technical Reports Server (NTRS)
Fix, G. J.
1978-01-01
Flow about an oscillating thin airfoil in a transonic stream was considered. It was assumed that the flow field can be decomposed into a mean flow plus a periodic perturbation. On the surface of the airfoil the usual Neumman conditions are imposed. Two computer programs were written, both using linear basis functions over triangles for the finite element space. The first program uses a banded Gaussian elimination solver to solve the matrix problem, while the second uses an iterative technique, namely SOR. The only results obtained are for an oscillating flat plate.
Finite element model of thermal processes in retinal photocoagulation
NASA Astrophysics Data System (ADS)
Sramek, Christopher; Paulus, Yannis M.; Nomoto, Hiroyuki; Huie, Phil; Palanker, Daniel
2009-02-01
Short duration (< 20 ms) pulses are desirable in patterned scanning laser photocoagulation to confine thermal damage to the photoreceptor layer, decrease overall treatment time and reduce pain. However, short exposures have a smaller therapeutic window (defined as the ratio of rupture threshold power to that of light coagulation). We have constructed a finite-element computational model of retinal photocoagulation to predict spatial damage and improve the therapeutic window. Model parameters were inferred from experimentally measured absorption characteristics of ocular tissues, as well as the thresholds of vaporization, coagulation, and retinal pigment epithelial (RPE) damage. Calculated lesion diameters showed good agreement with histological measurements over a wide range of pulse durations and powers.
Assessing performance and validating finite element simulations using probabilistic knowledge
Dolin, Ronald M.; Rodriguez, E. A.
2002-01-01
Two probabilistic approaches for assessing performance are presented. The first approach assesses probability of failure by simultaneously modeling all likely events. The probability each event causes failure along with the event's likelihood of occurrence contribute to the overall probability of failure. The second assessment method is based on stochastic sampling using an influence diagram. Latin-hypercube sampling is used to stochastically assess events. The overall probability of failure is taken as the maximum probability of failure of all the events. The Likelihood of Occurrence simulation suggests failure does not occur while the Stochastic Sampling approach predicts failure. The Likelihood of Occurrence results are used to validate finite element predictions.
A Best Approximation Evaluation of a Finite Element Calculation
ROBINSON, ALLEN C.; ROBINSON, DONALD W.
1999-09-29
We discuss an electrostatics problem whose solution must lie in the set S of all real n-by-n symmetric matrices with all row sums equal to zero. With respect to the Frobenius norm, we provide an algorithm that finds the member of S which is closest to any given n-by-n matrix, and determines the distance between the two. This algorithm makes it practical to find the distances to S of finite element approximate solutions of the electrostatics problem, and to reject those which are not sufficiently close.
[Finite Element Analysis of Intravascular Stent Based on ANSYS Software].
Shi, Gengqiang; Song, Xiaobing
2015-10-01
This paper adopted UG8.0 to bulid the stent and blood vessel models. The models were then imported into the finite element analysis software ANSYS. The simulation results of ANSYS software showed that after endothelial stent implantation, the velocity of the blood was slow and the fluctuation of velocity was small, which meant the flow was relatively stable. When blood flowed through the endothelial stent, the pressure gradually became smaller, and the range of the pressure was not wide. The endothelial shear stress basically unchanged. In general, it can be concluded that the endothelial stents have little impact on the flow of blood and can fully realize its function. PMID:26964302
Implementation of reflex loops in a biomechanical finite element model.
Salin, Dorian; Arnoux, Pierre-Jean; Kayvantash, Kambiz; Behr, Michel
2016-11-01
In the field of biomechanics, the offer of models which are more and more realistic requires to integrate a physiological response, in particular, the controlled muscle bracing and the reflexes. The following work aims to suggest a unique methodology which couples together a sensory and motor loop with a finite element model. Our method is applied to the study of the oscillation of the elbow in the case of a biceps brachial stretch reflex. The results obtained are promising in the purpose of the development of reactive human body models. PMID:27108871
Modelling the viscoelasticity of ceramic tiles by finite element
NASA Astrophysics Data System (ADS)
Pavlovic, Ana; Fragassa, Cristiano
2016-05-01
This research details a numerical method aiming at investigating the viscoelastic behaviour of a specific family of ceramic material, the Grès Porcelain, during an uncommon transformation, known as pyroplasticity, which occurs when a ceramic tile bends under a combination of thermal stress and own weight. In general, the theory of viscoelasticity can be considered extremely large and precise, but its application on real cases is particularly delicate. A time-depending problem, as viscoelasticity naturally is, has to be merged with a temperature-depending situation. This paper investigates how the viscoelastic response of bending ceramic materials can be modelled by commercial Finite Elements codes.
Finite element calculations for eddy current interactions with collinear slots
Atherton, D.L.; Czura, W. . Dept. of Physics)
1994-01-01
The results of finite element calculations detailing the interactions of eddy currents with fine collinear slots in nonferromagnetic and ferromagnetic conductors are presented. These are applicable to both remote field eddy current inspection tools and conventional reflected impedance eddy current probes. The calculations show that, while fine slots have little interaction with collinear induced currents in nonferromagnetic conductors, there are much larger effects in ferromagnetic conductors. This is due to magnetic field interactions. The term eddy current inspection' is therefore somewhat restrictive and the much broader term electromagnetic inspection' is proposed.
Turbomachinery flow calculation on unstructured grids using finite element method
NASA Astrophysics Data System (ADS)
Koschel, W.; Vornberger, A.
An explicit finite-element scheme based on a two-step Taylor-Galerkin algorithm allows the solution of the Euler and Navier-Stokes equations on unstructured grids. Mesh generation methods for unstructured grids are described which lead to efficient flow calculations. Turbulent flow is calculated by using an algebraic turbulence model. To test the numerical accuracy, a laminar and turbulent flow over a flat plate and the supersonic flow in a corner has been calculated. For validation the method is applied to the simulation of the inviscid flow through a transonic turbine cascade and the viscous flow through a subsonic turbine cascade.
Finite Element Analysis of Brain Injury due to Head Impact
NASA Astrophysics Data System (ADS)
Suh, Chang Min; Kim, Sung Ho; Goldsmith, Werner
Traumatic Brain Injury (TBI) due to head impact by external impactor was analyzed using Finite Element Method (FEM). Two-dimensiona modeling was performed according to Magnetic Resonance Imaging (MRI) data of Mongolian subject. Pressure variation in a cranium due to external impact was analyzed in order to simulate Nahum et al.'s cadaver test.6 And, analyzed results were compared with Nahum et al.'s experimental data.6 As results, stress and strain behaviors of the brain during impact were accorded with experimental data qualitatively even though there were some differences in quantitative values. In addition, they were accorded with other references about brain injury as well.
Finite Element Simulation of Diametral Strength Test of Hydroxyapatite
Ozturk, Fahrettin; Toros, Serkan; Evis, Zafer
2011-01-17
In this study, the diametral strength test of sintered hydroxyapatite was simulated by the finite element software, ABAQUS/Standard. Stress distributions on diametral test sample were determined. The effect of sintering temperature on stress distribution of hydroxyapatite was studied. It was concluded that high sintering temperatures did not reduce the stress on hydroxyapatite. It had a negative effect on stress distribution of hydroxyapatite after 1300 deg. C. In addition to the porosity, other factors (sintering temperature, presence of phases and the degree of crystallinity) affect the diametral strength of the hydroxyapatite.
Nonlinear structural finite element model updating and uncertainty quantification
NASA Astrophysics Data System (ADS)
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Finite Element Modeling Techniques for Analysis of VIIP
NASA Technical Reports Server (NTRS)
Feola, Andrew J.; Raykin, J.; Gleason, R.; Mulugeta, Lealem; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian C.; Ethier, C. Ross
2015-01-01
Visual Impairment and Intracranial Pressure (VIIP) syndrome is a major health concern for long-duration space missions. Currently, it is thought that a cephalad fluid shift in microgravity causes elevated intracranial pressure (ICP) that is transmitted along the optic nerve sheath (ONS). We hypothesize that this in turn leads to alteration and remodeling of connective tissue in the posterior eye which impacts vision. Finite element (FE) analysis is a powerful tool for examining the effects of mechanical loads in complex geometries. Our goal is to build a FE analysis framework to understand the response of the lamina cribrosa and optic nerve head to elevations in ICP in VIIP.
Investigation of the Finite Element Software Packages at KSC
NASA Technical Reports Server (NTRS)
Lu, Chu-Ho
1991-01-01
The useful and powerful features of NASTRAN and three real world problems for the testing of the capabilities of different NASTRAN versions are discussed. The test problems involve direct transient analysis, nonlinear analysis, and static analysis. The experiences in using graphics software packages are also discussed. It was found that MSC/XL can be more useful if it can be improved to generate picture files of the analysis results and to extend its capabilities to support finite element codes other than MSC/NASTRAN. It was found that the current version of SDRC/I-DEAS (version VI) may have bugs in the module 'Data Loader'.
Comparison of finite difference and finite element solutions to the variably saturated flow equation
NASA Astrophysics Data System (ADS)
Simpson, M. J.; Clement, T. P.
2003-01-01
Numerical solutions to the equation governing variably saturated flow are usually obtained using either the finite difference (FD) method or the finite element (FE) method. A detailed comparison of these methods shows that the main difference between them is in how the numerical schemes spatially average the variation of material properties. Further differences are also observed in the way that flux boundaries are represented in FE and FD methods. A modified finite element (MFE) algorithm is used to explore the significance of these differences. The MFE algorithm enables a direct comparison with a typical FD solution scheme, and explicitly demonstrates the differences between FE and FD methods. The MFE algorithm provides an improved approximation to the partial differential equation over the usual FD approach while being computationally simpler to implement than the standard FE solution. One of the main limitations of the MFE algorithm is that the algorithm was developed by imposing several restrictions upon the more general FE solution; however, the MFE is shown to be preferable over the usual FE and FD solutions for some of the test problems considered in this study. The comparison results show that the FE (or MFE) solution can avoid the erroneous results encountered in the FD solution for coarsely discretized problems. The improvement in the FE solution is attributed to the broader hydraulic conductivity averaging and differences in the representation of flux type boundaries.
Ateshian, Gerard A.; Maas, Steve; Weiss, Jeffrey A.
2010-01-01
Background This study formulates and implements a finite element contact algorithm for solid-fluid (biphasic) mixtures, accommodating both finite deformation and sliding. The finite element source code is made available to the general public. Methods The algorithm uses a penalty method regularized with an augmented Lagrangian method to enforce the continuity of contact traction and normal component of fluid flux across the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. The formulation addresses the need to automatically enforce free-draining conditions outside of the contact interface. Results The accuracy of the implementation is verified using contact problems for which exact solutions are obtained by alternative analyses. Illustrations are also provided that demonstrate large deformations and sliding under configurations relevant to biomechanical applications such as articular contact. Conclusions This study addresses an important computational need in the biomechanics of porous-permeable soft tissues. Placing the source code in the public domain provides a useful resource to the biomechanics community. PMID:20887031
NASA Technical Reports Server (NTRS)
Clark, J. H.; Kalinowski, A. J.; Wagner, C. A.
1983-01-01
An analysis is given using finite element techniques which addresses the propagaton of a uniform incident pressure wave through a finite diameter axisymmetric tapered plate immersed in a fluid. The approach utilized in developing a finite element solution to this problem is based upon a technique for axisymmetric fluid structure interaction problems. The problem addressed is that of a 10 inch diameter axisymmetric fixed plate totally immersed in a fluid. The plate increases in thickness from approximately 0.01 inches thick at the center to 0.421 inches thick at a radius of 5 inches. Against each face of the tapered plate a cylindrical fluid volume was represented extending five wavelengths off the plate in the axial direction. The outer boundary of the fluid and plate regions were represented as a rigid encasement cylinder as was nearly the case in the physical problem. The primary objective of the analysis is to determine the form of the transmitted pressure distribution on the downstream side of the plate.
Finite-element model of the active organ of Corti.
Ni, Guangjian; Elliott, Stephen J; Baumgart, Johannes
2016-02-01
The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivity is thought to be the result of an active biomechanical process within the sensory auditory organ, the organ of Corti. Although imaging techniques are developing rapidly, it is not currently possible, in a fully active cochlea, to obtain detailed measurements of the motion of individual elements within a cross section of the organ of Corti. This motion is predicted using a two-dimensional finite-element model. The various solid components are modelled using elastic elements, the outer hair cells (OHCs) as piezoelectric elements and the perilymph and endolymph as viscous and nearly incompressible fluid elements. The model is validated by comparison with existing measurements of the motions within the passive organ of Corti, calculated when it is driven either acoustically, by the fluid pressure or electrically, by excitation of the OHCs. The transverse basilar membrane (BM) motion and the shearing motion between the tectorial membrane and the reticular lamina are calculated for these two excitation modes. The fully active response of the BM to acoustic excitation is predicted using a linear superposition of the calculated responses and an assumed frequency response for the OHC feedback. PMID:26888950
Higher order finite element analysis of thick composite laminates
NASA Technical Reports Server (NTRS)
Goering, J.; Kim, H. J.
1992-01-01
A higher order, sub-parametric, laminated, 3D solid finite element was used for the analysis of very thick laminated composite plates. The geometry of this element is defined by four nodes in the X-Y plane which define a prism of material through the thickness of the laminate. There are twenty-four degrees of freedom at each node; translations at the upper and lower surfaces of the laminate in each of the three coordinate directions, and the derivatives of these translations with respect to each coordinate. This choice of degrees of freedom leads to displacement and strain compatibility at the corners. Stacking sequence effects are accounted for by explicitly integrating the strain energy density through the thickness of the element. The laminated solid element was combined with a gap-contact element to analyze thick laminated composite lugs loaded through flexible pins. The resulting model accounts for pin bending effects that produce non-uniform bearing stresses through the thickness of the lug. A thick composite lug experimental test program was performed, and provided data that was used to validate the analytical model. Two lug geometries and three stacking sequences were tested.
An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations
Key, S.W.; Heinstein, M.W.; Stone, C.M.
1997-12-31
Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.
A mixed finite element/finite volume approach for solving biodegradation transport in groundwater
NASA Astrophysics Data System (ADS)
Gallo, Claudio; Manzini, Gianmarco
1998-03-01
A numerical model for the simulation of flow and transport of organic compounds undergoing bacterial oxygen- and nitrate-based respiration is presented. General assumptions regarding microbial population, bacteria metabolism and effects of oxygen, nitrogen and nutrient concentration on organic substrate rate of consumption are briefly described. The numerical solution techniques for solving both the flow and the transport are presented. The saturated flow equation is discretized using a high-order mixed finite element scheme, which provides a highly accurate estimation of the velocity field. The transport equation for a sorbing porous medium is approximated using a finite volume scheme enclosing an upwind TVD shock-capturing technique for capturing concentration-unsteady steep fronts. The performance and capabilities of the present approach in a bio-remediation context are assessed by considering a set of test problems. The reliability of the numerical results concerning solution accuracy and the computational efficiency in terms of cost and memory requirements are also estimated.
NASA Astrophysics Data System (ADS)
Arbatani, Siamak; Callejo, Alfonso; Kövecses, József; Kalantari, Masoud; Marchand, Nick R.; Dargahi, Javad
2016-03-01
Directional drilling is a popular technique for oil well drilling. Accurate prediction of the directional performance is critical in order to achieve the desired well profile. Simplified geometry methods are, to date, the industry standard for predicting directional performance. A comprehensive, high-fidelity method for the simulation of directional drilling is presented here. It consists of a detailed discretization of the actual geometry and a rigorous application of two modeling techniques: the finite element and the finite segment methods. By doing so, the dynamic problem is addressed from two different yet complementary perspectives: structural mechanics and rigid-body motion. Collision detection and contact dynamics algorithms are also presented. Results show that both methods agree in terms of the dynamic response, and that the build rate estimations are consistent with available experimental data. Owing to the framework efficiency and physics-based nature, the presented tools are very well-suited for design engineering and real-time simulation.
Finite element-finite difference thermal/structural analysis of large space truss structures
NASA Technical Reports Server (NTRS)
Warren, Andrew H.; Arelt, Joseph E.; Eskew, William F.; Rogers, Karen M.
1992-01-01
A technique of automated and efficient thermal-structural processing of truss structures that interfaces the finite element and finite difference method was developed. The thermal-structural analysis tasks include development of the thermal and structural math models, thermal analysis, development of an interface and data transfer between the models, and finally an evaluation of the thermal stresses and displacements in the structure. Consequently, the objective of the developed technique was to minimize the model development time, in order to assure an automatic transfer of data between the thermal and structural models as well as to minimize the computer resources needed for the analysis itself. The method and techniques described are illustrated on the thermal/structural analysis of the Space Station Freedom main truss.
NASA Astrophysics Data System (ADS)
Arbatani, Siamak; Callejo, Alfonso; Kövecses, József; Kalantari, Masoud; Marchand, Nick R.; Dargahi, Javad
2016-06-01
Directional drilling is a popular technique for oil well drilling. Accurate prediction of the directional performance is critical in order to achieve the desired well profile. Simplified geometry methods are, to date, the industry standard for predicting directional performance. A comprehensive, high-fidelity method for the simulation of directional drilling is presented here. It consists of a detailed discretization of the actual geometry and a rigorous application of two modeling techniques: the finite element and the finite segment methods. By doing so, the dynamic problem is addressed from two different yet complementary perspectives: structural mechanics and rigid-body motion. Collision detection and contact dynamics algorithms are also presented. Results show that both methods agree in terms of the dynamic response, and that the build rate estimations are consistent with available experimental data. Owing to the framework efficiency and physics-based nature, the presented tools are very well-suited for design engineering and real-time simulation.
NASA Astrophysics Data System (ADS)
Stupkiewicz, Stanisław
2009-10-01
Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.
Probabilistic finite elements for fatigue and fracture analysis
NASA Technical Reports Server (NTRS)
Belytschko, Ted; Liu, Wing Kam
1993-01-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
Dynamic Analysis of Geared Rotors by Finite Elements
NASA Technical Reports Server (NTRS)
Kahraman, A.; Ozguven, H. Nevzat; Houser, D. R.; Zakrajsek, J. J.
1992-01-01
A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of on shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
NPLOT: an Interactive Plotting Program for NASTRAN Finite Element Models
NASA Technical Reports Server (NTRS)
Jones, G. K.; Mcentire, K. J.
1985-01-01
The NPLOT (NASTRAN Plot) is an interactive computer graphics program for plotting undeformed and deformed NASTRAN finite element models. Developed at NASA's Goddard Space Flight Center, the program provides flexible element selection and grid point, ASET and SPC degree of freedom labelling. It is easy to use and provides a combination menu and command driven user interface. NPLOT also provides very fast hidden line and haloed line algorithms. The hidden line algorithm in NPLOT proved to be both very accurate and several times faster than other existing hidden line algorithms. A fast spatial bucket sort and horizon edge computation are used to achieve this high level of performance. The hidden line and the haloed line algorithms are the primary features that make NPLOT different from other plotting programs.
Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs
Mota, A; Knap, J; Ortiz, M
2006-10-18
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.
Finite element analysis of laminated composite paraboloid of revolution shells
NASA Astrophysics Data System (ADS)
Dey, A.; Bandyopadhyay, J. N.; Sinha, P. K.
1992-07-01
A generalized formulation for the doubly curved laminated composite shell is attempted using eight-noded curved quadratic isoparametric finite elements with all three radii of curvature. The formulation is also applied to the isotropic material as a special case. In the present investigation, only the paraboloid of revolution is taken up for computing the deflections and stress resultants. Various parametric studies are carried out and the current results for both isotropic and laminated composite shells are compared with those available in the published literature. The shape functions are obtained from interpolation polynomial and the element stiffness matrices are formed on the basis of macromechanical analysis of laminates using the principle of minimum potential energy.
Automation Tools for Finite Element Analysis of Adhesively Bonded Joints
NASA Technical Reports Server (NTRS)
Tahmasebi, Farhad; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.
3D unstructured mesh discontinuous finite element hydro
Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.
1995-07-01
The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D.
Finite element analysis for bearingless rotor blade aeroelasticity
NASA Technical Reports Server (NTRS)
Sivaneri, N. T.; Chopra, I.
1982-01-01
A conventional articulated rotor blade has mechanical flap and lag hinges, a lag damper, and a pitch bearing. In connection with an interest in designs of greater mechanical simplicity and increased maintainability, hingeless and bearingless rotors have been developed. A hingeless blade lacks the hinges and is cantilevered at the hub. It does have a pitch bearing for pitch control. A bearingless design eliminates the hinges and the pitch bearing as well. In the present investigation of bearingless rotor blade characteristics, finite element analysis has been successfully applied to determine the solutions of the nonlinear trim equations and the linearized flutter equations of multiple-load-path blades. The employed formulation is based on Hamilton's principle. The spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.
Finite element solution of optimal control problems with inequality constraints
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1990-01-01
A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.
Analysis of aircraft tires via semianalytic finite elements
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Kim, Kyun O.; Tanner, John A.
1990-01-01
A computational procedure is presented for the geometrically nonlinear analysis of aircraft tires. The tire was modeled by using a two-dimensional laminated anisotropic shell theory with the effects of variation in material and geometric parameters included. The four key elements of the procedure are: (1) semianalytic finite elements in which the shell variables are represented by Fourier series in the circumferential direction and piecewise polynomials in the meridional direction; (2) a mixed formulation with the fundamental unknowns consisting of strain parameters, stress-resultant parameters, and generalized displacements; (3) multilevel operator splitting to effect successive simplifications, and to uncouple the equations associated with different Fourier harmonics; and (4) multilevel iterative procedures and reduction techniques to generate the response of the shell.
Multigrid waveform relaxation on spatial finite element meshes
Janssen, J.; Vandewalle, S.
1994-12-31
The authors shall discuss the numerical solution of a parabolic partial differential equation {partial_derivative}u/{partial_derivative}t(x,t) = Lu(x,t) + f(x,t), x{element_of}{Omega}, t>0, (1) supplied with a boundary condition and given initial values. The spatial finite element discretization of (1) on a discrete grid {Omega}{sub h} leads to an initial value problem of the form B{dot u} + Au = f, u(0) = u{sub o}, t > 0, (2) with B a non-singular matrix. The waveform relaxation method is a method for solving ordinary differential equations. It differs from most standard iterative techniques in that it is a continuous-time method, iterating with functions in time, and thereby well-suited for parallel computation.
Dynamic analysis of geared rotors by finite elements
NASA Technical Reports Server (NTRS)
Kahraman, A.; Ozguven, H. N.; Houser, D. R.; Zakrajsek, J.
1989-01-01
The finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shaft to mass unbalances, geometric eccentricities of gears and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
Dynamic analysis of geared rotors by finite elements
NASA Technical Reports Server (NTRS)
Kahraman, Ahmet; Ozguven, H. Nevzat; Houser, Donald R.; Zakrajsek, James J.
1990-01-01
A finite-element model of a geared rotor system on flexible bearings was developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shaft to mass unbalances, geometric eccentricities of gears and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
An analytically enriched finite element method for cohesive crack modeling.
Cox, James V.
2010-04-01
Meaningful computational investigations of many solid mechanics problems require accurate characterization of material behavior through failure. A recent approach to fracture modeling has combined the partition of unity finite element method (PUFEM) with cohesive zone models. Extension of the PUFEM to address crack propagation is often referred to as the extended finite element method (XFEM). In the PUFEM, the displacement field is enriched to improve the local approximation. Most XFEM studies have used simplified enrichment functions (e.g., generalized Heaviside functions) to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. As such, the mesh had to be sufficiently fine for the FEM basis functions to capture these gradients.In this study enrichment functions based upon two analytical investigations of the cohesive crack problem are examined. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack with a relatively coarse mesh and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation are summarized. Analysis results for simple model problems are presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. A standard finite element solution with interface elements is used to provide the accurate reference solution, so the model problems are limited to a straight, mode I crack in plane stress. Except for the cohesive zone, the material model for the problems is homogenous, isotropic linear elasticity. The effects of mesh refinement, mesh orientation, and enrichment schemes that enrich a larger region around the cohesive crack are considered in the study. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are presented. The analysis
Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.
Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A
2016-03-21
Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037
A general algorithm using finite element method for aerodynamic configurations at low speeds
NASA Technical Reports Server (NTRS)
Balasubramanian, R.
1975-01-01
A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.
Accelerated finite element elastodynamic simulations using the GPU
Huthwaite, Peter
2014-01-15
An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia's CUDA. Of critical importance for this problem is the arrangement of nodes in memory, allowing data to be loaded efficiently and minimising communication between the independently executed blocks of threads. The initial stage of memory arrangement is partitioning the mesh; both a well established ‘greedy’ partitioner and a new, more efficient ‘aligned’ partitioner are investigated. A method is then developed to efficiently arrange the memory within each partition. The software is applied to three models from the fields of non-destructive testing, vibrations and geophysics, demonstrating a memory bandwidth of very close to the card's maximum, reflecting the bandwidth-limited nature of the algorithm. Comparison with Abaqus, a widely used commercial CPU equivalent, validated the accuracy of the results and demonstrated a speed improvement of around two orders of magnitude. A software package, Pogo, incorporating these developments, is released open source, downloadable from (http://www.pogo-fea.com/) to benefit the community. -- Highlights: •A novel memory arrangement approach is discussed for finite elements on the GPU. •The mesh is partitioned then nodes are arranged efficiently within each partition. •Models from ultrasonics, vibrations and geophysics are run. •The code is significantly faster than an equivalent commercial CPU package. •Pogo, the new software package, is released open source.
Finite Element Model Calibration Approach for Ares I-X
NASA Technical Reports Server (NTRS)
Horta, Lucas G.; Reaves, Mercedes C.; Buehrle, Ralph D.; Templeton, Justin D.; Lazor, Daniel R.; Gaspar, James L.; Parks, Russel A.; Bartolotta, Paul A.
2010-01-01
Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of nonconventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pre-test predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.
A nonlinear dynamic finite element approach for simulating muscular hydrostats.
Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A
2014-01-01
An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching. PMID:23025686
Finite Element Modeling of Magnetically-Damped Convection during Solidification
NASA Technical Reports Server (NTRS)
deGroh, H. C.; Li, B. Q.; Lu, X.
1998-01-01
A fully 3-D, transient finite element model is developed to represent the magnetic damping effects on complex fluid flow, heat transfer and electromagnetic field distributions in a Sn- 35.5%Pb melt undergoing unidirectional solidification. The model is developed based on our in- house finite element code for the fluid flow, heat transfer and electromagnetic field calculations. The numerical model is tested against numerical and experimental results for water as reported in literature. Various numerical simulations are carried out for the melt convection and temperature distribution with and without the presence of a transverse magnetic field. Numerical results show that magnetic damping can be effectively applied to stabilize melt flow, reduce turbulence and flow levels in the melt and over a certain threshold value a higher magnetic field resulted in a greater reduction in velocity. Also, for the study of melt flow instability, a long enough running time is needed to ensure the final fluid flow recirculation pattern. Moreover, numerical results suggest that there seems to exist a threshold value of applied magnetic field, above which magnetic damping becomes possible and below which the 0 convection in the melt is actually enhanced.
Finite element visualization in the cave virtual reality environment
Plaskacz, E.J.; Kuhn, M.A.
1996-03-01
Through the use of the post-processing software, Virtual Reality visualization (VRviz), and the Cave Automatic Virtual Environment (CAVE), finite element representations can be viewed as they would be in real life. VRviz is a program written in ANSI C to translate the mathematical results generated by finite element analysis programs into a virtual representation. This virtual representation is projected into the CAVE environment and the results are animated. The animation is fully controllable. A user is able to translate the image, rotate about any axis and scale the image at any time. The user is also able to freeze the animation at any time step and control the image update rate. This allows the user to navigate around, or even inside, the image in order to effectively analyze possible failure points and redesign as necessary. Through the use of the CAVE and the real life image that is being produced by VRviz, engineers are able to save considerable time, money, and effort in the design process.
Finite Element Model Calibration Approach for Area I-X
NASA Technical Reports Server (NTRS)
Horta, Lucas G.; Reaves, Mercedes C.; Buehrle, Ralph D.; Templeton, Justin D.; Gaspar, James L.; Lazor, Daniel R.; Parks, Russell A.; Bartolotta, Paul A.
2010-01-01
Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of non-conventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pretest predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.
Finite element simulation of food transport through the esophageal body
Yang, Wei; Fung, Tat Ching; Chian, Kerm Sim; Chong, Chuh Khiun
2007-01-01
The peristaltic transport of swallowed material in the esophagus is a neuro-muscular function involving the nerve control, bolus-structure interaction, and structure-mechanics relationship of the tissue. In this study, a finite element model (FEM) was developed to simulate food transport through the esophagus. The FEM consists of three components, i.e., tissue, food bolus and peristaltic wave, as well as the interactions between them. The transport process was simulated as three stages, i.e., the filling of fluid, contraction of circular muscle and traveling of peristaltic wave. It was found that the maximal passive intraluminal pressure due to bolus expansion was in the range of 0.8-10 kPa and it increased with bolus volume and fluid viscosity. It was found that the highest normal and shear stresses were at the inner surface of muscle layer. In addition, the peak pressure required for the fluid flow was predicted to be 1-15 kPa at the bolus tail. The diseases of systemic sclerosis or osteogenesis imperfecta, with the remodeled microstructures and mechanical properties, might induce the malfunction of esophageal transport. In conclusion, the current simulation was demonstrated to be able to capture the main characteristics in the intraluminal pressure and bolus geometry as measured experimentally. Therefore, the finite element model established in this study could be used to further explore the mechanism of esophageal transport in various clinical applications. PMID:17457965
Immersed finite element method and its applications to biological systems
Liu, Wing Kam; Liu, Yaling; Farrell, David; Zhang, Lucy; Wang, X. Sheldon; Fukui, Yoshio; Patankar, Neelesh; Zhang, Yongjie; Bajaj, Chandrajit; Lee, Junghoon; Hong, Juhee; Chen, Xinyu; Hsu, Huayi
2009-01-01
This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid–structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid–structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility. PMID:20200602
Aeroelastic Stability of Rotor Blades Using Finite Element Analysis
NASA Technical Reports Server (NTRS)
Chopra, I.; Sivaneri, N.
1982-01-01
The flutter stability of flap bending, lead-lag bending, and torsion of helicopter rotor blades in hover is investigated using a finite element formulation based on Hamilton's principle. The blade is divided into a number of finite elements. Quasi-steady strip theory is used to evaluate the aerodynamic loads. The nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The equations of motion are linearized assuming blade motion to be a small perturbation about the steady deflected shape. The normal mode method based on the coupled rotating natural modes is used to reduce the number of equations in the flutter analysis. First the formulation is applied to single-load-path blades (articulated and hingeless blades). Numerical results show very good agreement with existing results obtained using the modal approach. The second part of the application concerns multiple-load-path blades, i.e. bearingless blades. Numerical results are presented for several analytical models of the bearingless blade. Results are also obtained using an equivalent beam approach wherein a bearingless blade is modelled as a single beam with equivalent properties. Results show the equivalent beam model.
Adaptive Finite Element Methods for Continuum Damage Modeling
NASA Technical Reports Server (NTRS)
Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.
1995-01-01
The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.
Immersed finite element method and its applications to biological systems.
Liu, Wing Kam; Liu, Yaling; Farrell, David; Zhang, Lucy; Wang, X Sheldon; Fukui, Yoshio; Patankar, Neelesh; Zhang, Yongjie; Bajaj, Chandrajit; Lee, Junghoon; Hong, Juhee; Chen, Xinyu; Hsu, Huayi
2006-02-15
This paper summarizes the newly developed immersed finite element method (IFEM) and its applications to the modeling of biological systems. This work was inspired by the pioneering work of Professor T.J.R. Hughes in solving fluid-structure interaction problems. In IFEM, a Lagrangian solid mesh moves on top of a background Eulerian fluid mesh which spans the entire computational domain. Hence, mesh generation is greatly simplified. Moreover, both fluid and solid domains are modeled with the finite element method and the continuity between the fluid and solid subdomains is enforced via the interpolation of the velocities and the distribution of the forces with the reproducing Kernel particle method (RKPM) delta function. The proposed method is used to study the fluid-structure interaction problems encountered in human cardiovascular systems. Currently, the heart modeling is being constructed and the deployment process of an angioplasty stent has been simulated. Some preliminary results on monocyte and platelet deposition are presented. Blood rheology, in particular, the shear-rate dependent de-aggregation of red blood cell (RBC) clusters and the transport of deformable cells, are modeled. Furthermore, IFEM is combined with electrokinetics to study the mechanisms of nano/bio filament assembly for the understanding of cell motility. PMID:20200602
Distributed Finite Element Analysis Using a Transputer Network
NASA Technical Reports Server (NTRS)
Watson, James; Favenesi, James; Danial, Albert; Tombrello, Joseph; Yang, Dabby; Reynolds, Brian; Turrentine, Ronald; Shephard, Mark; Baehmann, Peggy
1989-01-01
The principal objective of this research effort was to demonstrate the extraordinarily cost effective acceleration of finite element structural analysis problems using a transputer-based parallel processing network. This objective was accomplished in the form of a commercially viable parallel processing workstation. The workstation is a desktop size, low-maintenance computing unit capable of supercomputer performance yet costs two orders of magnitude less. To achieve the principal research objective, a transputer based structural analysis workstation termed XPFEM was implemented with linear static structural analysis capabilities resembling commercially available NASTRAN. Finite element model files, generated using the on-line preprocessing module or external preprocessing packages, are downloaded to a network of 32 transputers for accelerated solution. The system currently executes at about one third Cray X-MP24 speed but additional acceleration appears likely. For the NASA selected demonstration problem of a Space Shuttle main engine turbine blade model with about 1500 nodes and 4500 independent degrees of freedom, the Cray X-MP24 required 23.9 seconds to obtain a solution while the transputer network, operated from an IBM PC-AT compatible host computer, required 71.7 seconds. Consequently, the $80,000 transputer network demonstrated a cost-performance ratio about 60 times better than the $15,000,000 Cray X-MP24 system.
Finite element analysis of phase-change storage media
Jabbar, M.; Najafi, M.
1995-12-31
The objective of this study is to predict the cooling curve for the storage tank of a clathrate (crystalline compounds made of gaseous refrigerant and water) thermal energy storage system using finite element analysis. The analysis involve modeling of a storage medium which changes its phase from liquid to solid within the storage tank. The solidification of the storage medium takes place during the storage tank`s heat extraction simulation process (charging process). The storage media in this study are Refrigerant 134a (R134a) clathrate and Refrigerant 12 (R12) clathrate. The enthalpy based standard approach is utilized to overcome the phase change discontinuities. The governing equations count for the phase change, two dimensional conduction, and convection modes. The cooling of the storage medium is simulated as energy loss from the storage tank contents. A set of algebraic discretized equations are obtained from the governing equations through the method of finite element formulation. These algebraic equations are solved using the common purpose computational fluid dynamics analysis package (FIDAP, 1991) to obtain the temperature distribution and consequently the cooling curve for the storage tank. The results for R12 clathrate are in good agreement with the experimental results obtained by Najafi and Schaetzle (1991). For R134a clathrate the results obtained follow a pattern similar to those of experimental work on R12 clathrate. The work of this study provides the necessary background for conducting experimental studies on R134a clathrate thermal energy storage system.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
Accurate optical CD profiler based on specialized finite element method
NASA Astrophysics Data System (ADS)
Carrero, Jesus; Perçin, Gökhan
2012-03-01
As the semiconductor industry is moving to very low-k1 patterning solutions, the metrology problems facing process engineers are becoming much more complex. Choosing the right optical critical dimension (OCD) metrology technique is essential for bridging the metrology gap and achieving the required manufacturing volume throughput. The critical dimension scanning electron microscope (CD-SEM) measurement is usually distorted by the high aspect ratio of the photoresist and hard mask layers. CD-SEM measurements cease to correlate with complex three-dimensional profiles, such as the cases for double patterning and FinFETs, thus necessitating sophisticated, accurate and fast computational methods to bridge the gap. In this work, a suite of computational methods that complement advanced OCD equipment, and enabling them to operate at higher accuracies, are developed. In this article, a novel method for accurately modeling OCD profiles is presented. A finite element formulation in primal form is used to discretize the equations. The implementation uses specialized finite element spaces to solve Maxwell equations in two dimensions.
3D Finite Element Trajectory Code with Adaptive Meshing
NASA Astrophysics Data System (ADS)
Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien
2004-11-01
Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.
Finite element formulation of biphasic poroviscoelastic model for articular cartilage.
Suh, J K; Bai, S
1998-04-01
The purpose of the present study was to develop a computationally efficient finite element model that could be useful for parametric analysis of the biphasic poroviscoelastic (BPVE) behavior of articular cartilage under various loading conditions. The articular cartilage was modeled as the BPVE mixture of a porous, linear viscoelastic, and incompressible solid and an inviscid and incompressible fluid. A finite element (FE) formulation of the BPVE model was developed using two different algorithms, the continuous and discrete spectrum relaxation functions for the viscoelasticity of the solid matrix. These algorithms were applied to the creep and stress relaxation responses to the confined compression of articular cartilage, and a comparison of their performances was made. It was found that the discrete spectrum algorithm significantly saved CPU time and memory, as compared to the continuous spectrum algorithm. The consistency analysis for the present FE formulation was performed in comparison with the IMSL, a commercially available numerical software package. It was found that the present FE formulation yielded consistent results in predicting model behavior, whereas the IMSL subroutine produced inconsistent results in the velocity field, and thereby in the strain calculation. PMID:10412380
Progress in Developing Finite Element Models Replicating Flexural Graphite Testing
Robert Bratton
2010-06-01
This report documents the status of flexural strength evaluations from current ASTM procedures and of developing finite element models predicting the probability of failure. This work is covered under QLD REC-00030. Flexural testing procedures of the American Society for Testing and Materials (ASTM) assume a linear elastic material that has the same moduli for tension and compression. Contrary to this assumption, graphite is known to have different moduli for tension and compression. A finite element model was developed and demonstrated that accounts for the difference in moduli tension and compression. Brittle materials such as graphite exhibit significant scatter in tensile strength, so probabilistic design approaches must be used when designing components fabricated from brittle materials. ASTM procedures predicting probability of failure in ceramics were compared to methods from the current version of the ASME graphite core components rules predicting probability of failure. Using the ASTM procedures yields failure curves at lower applied forces than the ASME rules. A journal paper was published in the Journal of Nuclear Engineering and Design exploring the statistical models of fracture in graphite.
Finite element shape optimization for biodegradable magnesium alloy stents.
Wu, W; Petrini, L; Gastaldi, D; Villa, T; Vedani, M; Lesma, E; Previtali, B; Migliavacca, F
2010-09-01
Biodegradable magnesium alloy stents (MAS) are a promising solution for long-term adverse events caused by interactions between vessels and permanent stent platforms of drug eluting stents. However, the existing MAS showed severe lumen loss after a few months: too short degradation time may be the main reason for this drawback. In this study, a new design concept of MAS was proposed and a shape optimization method with finite element analysis was applied on two-dimensional (2D) stent models considering four different magnesium alloys: AZ80, AZ31, ZM21, and WE43. A morphing procedure was utilized to facilitate the optimization. Two experiments were carried out for a preliminary validation of the 2D models with good results. The optimized designs were compared to an existing MAS by means of three-dimensional finite element analysis. The results showed that the final optimized design with alloy WE43, compared to the existing MAS, has an increased strut width by approximately 48%, improved safety properties (decreased the maximum principal stress after recoil with tissue by 29%, and decreased the maximum principal strain during expansion by 14%) and improved scaffolding ability (increased by 24%). Accordingly, the degradation time can be expected to extend. The used methodology provides a convenient and practical way to develop novel MAS designs. PMID:20446037
Finite element modeling of electrically rectified piezoelectric energy harvesters
NASA Astrophysics Data System (ADS)
Wu, P. H.; Shu, Y. C.
2015-09-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique.
Finite Element Modeling of the Posterior Eye in Microgravity
NASA Technical Reports Server (NTRS)
Feola, Andrew; Raykin, Julia; Mulugeta, Lealem; Gleason, Rudolph; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian; Ethier, C. Ross
2015-01-01
Microgravity experienced during spaceflight affects astronauts in various ways, including weakened muscles and loss of bone density. Recently, visual impairment and intracranial pressure (VIIP) syndrome has become a major concern for space missions lasting longer than 30 days. Astronauts suffering from VIIP syndrome have changes in ocular anatomical and visual impairment that persist after returning to earth. It is hypothesized that a cephalad fluid shift in microgravity may increase the intracranial pressure (ICP), which leads to an altered biomechanical environment of the posterior globe and optic nerve sheath (ONS).Currently, there is a lack of knowledge of how elevated ICP may lead to vision impairment and connective tissue changes in VIIP. Our goal was to develop a finite element model to simulate the acute effects of elevated ICP on the posterior eye and optic nerve sheath. We used a finite element (FE) analysis approach to understand the response of the lamina cribrosa and optic nerve to the elevations in ICP thought to occur in microgravity and to identify which tissue components have the greatest impact on strain experienced by optic nerve head tissues.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
NASA Technical Reports Server (NTRS)
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2011-01-01
Detailed two-dimensional finite element analyses of the cross-sections of a model CVI (chemical vapor infiltrated) SiC/SiC (silicon carbide fiber in a silicon carbide matrix) ceramic matrix composites are performed. High resolution images of the cross-section of this composite material are generated using serial sectioning of the test specimens. These images are then used to develop very detailed finite element models of the cross-sections using the public domain software OOF2 (Object Oriented Analysis of Material Microstructures). Examination of these images shows that these microstructures have significant variability and irregularity. How these variabilities manifest themselves in the variability in effective properties as well as the stress distribution, damage initiation and damage progression is the overall objective of this work. Results indicate that even though the macroscopic stress-strain behavior of various sections analyzed is very similar, each section has a very distinct damage pattern when subjected to in-plane tensile loads and this damage pattern seems to follow the unique architectural and microstructural details of the analyzed sections.
A Finite Element Model for Simulation of Carbon Dioxide Sequestration
Bao, Jie; Xu, Zhijie; Fang, Yilin
2015-07-23
We present a hydro-mechanical model, followed by stress, deformation, and shear-slip failure analysis for geological sequestration of carbon dioxide (CO2). The model considers the poroelastic effects by taking into account of the two-way coupling between the geomechanical response and the fluid flow process. Analytical solutions for pressure and deformation fields were derived for a typical geological sequestration scenario in our previous work. A finite element approach is introduced here for numerically solving the hydro-mechanical model with arbitrary boundary conditions. The numerical approach was built on an open-source finite element code Elmer, and results were compared to the analytical solutions. The shear-slip failure analysis was presented based on the numerical results, where the potential failure zone is identified. Information is relevant to the prediction of the maximum sustainable injection rate or pressure. The effects of caprock permeability on the fluid pressure, deformation, stress, and the shear-slip failure zone were also quantitatively studied. It was shown that a larger permeability in caprock and base rock leads to a larger uplift but a smaller shear-slip failure zone.
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
Finite Element Reconstruction of a Mandibular First Molar
Ehsani, Sara; Mirhashemi, Fatemeh Sadat; Asgary, Saeed
2013-01-01
Introduction Mandibular first molar is the most important tooth with complicated morphology. In finite element (FE) studies, investigators usually prefer to model anterior teeth with a simple and single straight root; it makes the results deviate from the actual case. The most complicated and time-consuming step in FE studies is modeling of the desired tooth, thus this study was performed to establish a finite element method (FEM) of reconstructing a mandibular first molar with the greatest precision. Materials and Methods An extracted mandibular first molar was digitized, and then radiographed from different aspects to achieve its outer and inner morphology. The solid model of tooth and root canals were constructed according to this data as well as the anatomy of mandibular first molar described in the literature. Result A three-dimensional model of mandibular first molar was created, giving special consideration to shape and root canal system dimensions. Conclusion This model may constitute a basis for investigating the effect of different clinical situations on mandibular first molars in vitro, especially on its root canal system. The method described here seems feasible and reasonably precise foundation for investigations. PMID:23717327
Finite element analysis of composites materials for aerospace applications
NASA Astrophysics Data System (ADS)
Nurhaniza, M.; Ariffin, M. K. A.; Ali, Aidy; Mustapha, F.; Noraini, A. W.
2010-05-01
Composites materials are intended to be used more extensively as an alternative of aluminum structure in aircraft and aerospace applications. This is due to their attractive properties as high strength-to-weight ratio and stiffness-to-weight ratio. Besides that it clarifies the growing interest for composites materials due to advantages of lightweight, high strength, high stiffness, superior fatigue life, tremendous corrosion resistance and low cost manufacturing. In this study, a finite element analysis (FEA) of fiberglass unidirectional E-type was analyzed in the framework of ABAQUS finite element commercial software. The analysis was done to quantify the mechanical properties and response of unidirectional E-glass in term of tensile, compression and thermal responses. From the analysis, the maximum and minimum values of stress and strain for E-glass 21xK43 Gevetex and Silenka E-glass 1200tex were obtained and stress-strain curve is presented. The ultimate load of failure, elastic behavior, tensile strength and other properties for each laminated plates under tensile and thermal-stress are determined from stress-strain curves. The simulation will run twice for each material where the first simulation based on orientation angles of 45° for ply-1, -45° for ply-2 and 90° for ply-3 while the second simulation, the orientation angles is 0° for all plies. The simulation is successfully conducted and verified by experimental data.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
NASA Technical Reports Server (NTRS)
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
The Mixed Finite Element Multigrid Method for Stokes Equations
Muzhinji, K.; Shateyi, S.; Motsa, S. S.
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361
A Method of Modeling Fabric Shear using Finite Element Analysis
NASA Astrophysics Data System (ADS)
Chichani, Swapnil; Guha, Anirban
2015-04-01
Fabric modeling may be attempted by modeling fibres or yarns or small fabric units. The first is computationally intensive while the third does not allow relationships between the fabric's structure and its mechanical properties to be predicted. The second approach has been the most widely used so far. Out of the various ways in which this has been attempted, the finite element approach offers high flexibility while allowing the procedure to be relatively simple because of the availability of user-friendly softwares. This work explores a two-step finite element approach for modeling in-plane fabric shear. A major innovation of the modeling process was that the path of yarns in the fabric was allowed to evolve through the modeling process rather than being pre-defined. The relationship between shear angle and shear stress predicted by this model was compared with that obtained from a picture frame shear experiment. It was found that modeling the yarn with a set of anisotropic properties, gave very good correlation with experimental results.
The application of finite element analysis on polydimethylsiloxane
NASA Astrophysics Data System (ADS)
Halim, Siti Aisyah Abdul; Yahud, Shuhaida; Muhamad, Wan Zuki Azman Wan; Daud, Ruslizam; Zain, Noor Alia Md
2015-05-01
An artificial skin should have the similarities of the human skin in term of biomechanical properties. In this paper, Polydimethysiloxane (PDMS) have been chosen as artificial skin material. PDMS specimens were prepared and the hardness of the material will be altered by adding different percentages of diluents to the mixture of the base and a cross-linker component. It indicated that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio and strain rate. Tensile and compression test are conducted to find out the Hyperelastic (HE) coefficient and Young's modulus. These material coefficients will be used to define the constitutive model of PDMS for finite element analysis study. In this paper, three dimensional (3D) finite element (FE) stress and displacement analysis were used. Three types of models with different values of height were simulated in COMSOL MULTIPHYSICS. The analysis of the von Mises stress and surface deflection values revealed that maximum stress and maximum deflection concentration were located in the region near line load. PDMS polymer 10:1 is the softer product and can be commercialized as artificial skin material.
Validation of a finite element model of the human metacarpal.
Barker, D S; Netherway, D J; Krishnan, J; Hearn, T C
2005-03-01
Implant loosening and mechanical failure of components are frequently reported following metacarpophalangeal (MCP) joint replacement. Studies of the mechanical environment of the MCP implant-bone construct are rare. The objective of this study was to evaluate the predictive ability of a finite element model of the intact second human metacarpal to provide a validated baseline for further mechanical studies. A right index human metacarpal was subjected to torsion and combined axial/bending loading using strain gauge (SG) and 3D finite element (FE) analysis. Four different representations of bone material properties were considered. Regression analyses were performed comparing maximum and minimum principal surface strains taken from the SG and FE models. Regression slopes close to unity and high correlation coefficients were found when the diaphyseal cortical shell was modelled as anisotropic and cancellous bone properties were derived from quantitative computed tomography. The inclusion of anisotropy for cortical bone was strongly influential in producing high model validity whereas variation in methods of assigning stiffness to cancellous bone had only a minor influence. The validated FE model provides a tool for future investigations of current and novel MCP joint prostheses. PMID:15642506
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.
1990-01-01
An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.
Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector
NASA Technical Reports Server (NTRS)
Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)
2001-01-01
Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.
Finite Element Analysis of Drilling of Carbon Fibre Reinforced Composites
NASA Astrophysics Data System (ADS)
Isbilir, Ozden; Ghassemieh, Elaheh
2012-06-01
Despite the increased applications of the composite materials in aerospace due to their exceptional physical and mechanical properties, the machining of composites remains a challenge. Fibre reinforced laminated composites are prone to different damages during machining process such as delamination, fibre pull-out, microcracks, thermal damages. Optimization of the drilling process parameters can reduces the probability of these damages. In the current research, a 3D finite element (FE) model is developed of the process of drilling in the carbon fibre reinforced composite (CFC). The FE model is used to investigate the effects of cutting speed and feed rate on thrust force, torque and delamination in the drilling of carbon fiber reinforced laminated composite. A mesoscale FE model taking into account of the different oriented plies and interfaces has been proposed to predict different damage modes in the plies and delamination. For validation purposes, experimental drilling tests have been performed and compared to the results of the finite element analysis. Using Matlab a digital image analysis code has been developed to assess the delamination factor produced in CFC as a result of drilling.
Hierarchical flux-based thermal-structural finite element analysis method
NASA Technical Reports Server (NTRS)
Polesky, Sandra P.
1992-01-01
A hierarchical flux-based finite element method is developed for both a one and two dimensional thermal structural analyses. Derivation of the finite element equations is presented. The resulting finite element matrices associated with the flux based formulation are evaluated in a closed form. The hierarchical finite elements include additional degrees of freedom in the approximation of the element variable distributions by the use of nodeless variables. The nodeless variables offer increased solution accuracy without the need for defining actual nodes and rediscretizing the finite element model. Thermal and structural responses are obtained from a conventional linear finite element method and exact solutions. Results show that the hierarchical flux-based method can provide improved thermal and structural solution accuracy with fewer elements when compared to results for the conventional linear element method.
High-order finite element methods for cardiac monodomain simulations.
Vincent, Kevin P; Gonzales, Matthew J; Gillette, Andrew K; Villongco, Christopher T; Pezzuto, Simone; Omens, Jeffrey H; Holst, Michael J; McCulloch, Andrew D
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
Finite element analysis of (SA) mechanoreceptors in tactile sensing application
NASA Astrophysics Data System (ADS)
N, Syamimi; Yahud, S.
2015-05-01
This paper addresses the structural design of a fingertip model in order to analyse the sensory function of slow adapting (SA) mechanoreceptors by using the finite element analysis (FEA) method. A biologically inspired tactile sensor was designed to mimic a similar response of the human mechanoreceptors in the human glabrous skin. The simulation work was done by using COMSOL Multiphysics. The artificial skin was modelled as a solid square block of silicone elastomer with a semi cylinder protrusion on top. It was modelled as a nearly incompressible and linear hyperelastic material defined by Neo Hookean constitutive law. The sensing element on the other hand was modelled by using constantan alloy mimicking the SA1 receptor. Boundary loads of 1 N/m² to 4 N/m² with the increment of 1 N/m² were applied to the top surface of the protrusion in z and x-direction for normal and shear stress, respectively. The epidermal model base was constrained to maintain the same boundary conditions throughout all simulations. The changes of length experienced by the sensing element were calculated. The simulations result in terms of strain was identified. The simulated result was plotted in terms of sensing element strain against the boundary load and the graph should produce a linear response.
Finite element prediction of fatigue damage growth in cancellous bone.
Hambli, Ridha; Frikha, Sana; Toumi, Hechmi; Tavares, João Manuel R S
2016-01-01
Cyclic stresses applied to bones generate fatigue damage that affects the bone stiffness and its elastic modulus. This paper proposes a finite element model for the prediction of fatigue damage accumulation and failure in cancellous bone at continuum scale. The model is based on continuum damage mechanics and incorporates crack closure effects in compression. The propagation of the cracks is completely simulated throughout the damaged area. In this case, the stiffness of the broken element is reduced by 98% to ensure no stress-carrying capacities of completely damaged elements. Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. The proposed model suggests that damage evolves over a real physical time variable (cycles). In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. In this approach, the real number of cycles is reduced (divided) into equivalent blocks of cycles. Damage accumulation is computed over the cycle blocks and then extrapolated over the corresponding real cycles. The results show a clear difference between local tensile and compressive stresses on damage accumulation. Incorporating stiffness reduction also produces a redistribution of the peak stresses in the damaged region, which results in a delay in damage fracture. PMID:26077722
NASA Astrophysics Data System (ADS)
Borovkov, Alexei I.; Avdeev, Ilya V.; Artemyev, A.
1999-05-01
In present work, the stress, vibration and buckling finite element analysis of laminated beams is performed. Review of the equivalent single-layer (ESL) laminate theories is done. Finite element algorithms and procedures integrated into the original FEA program system and based on the classical laminated plate theory (CLPT), first-order shear deformation theory (FSDT), third-order theory of Reddy (TSDT-R) and third- order theory of Kant (TSDT-K) with the use of the Lanczos method for solving of the eigenproblem are developed. Several numerical tests and examples of bending, free vibration and buckling of multilayered and sandwich beams with various material, geometry properties and boundary conditions are solved. New effective higher-order hierarchical element for the accurate calculation of transverse shear stress is proposed. The comparative analysis of results obtained by the considered models and solutions of 2D problems of the heterogeneous anisotropic elasticity is fulfilled.
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.
Applications of finite element simulation in orthopedic and trauma surgery.
Herrera, Antonio; Ibarz, Elena; Cegoñino, José; Lobo-Escolar, Antonio; Puértolas, Sergio; López, Enrique; Mateo, Jesús; Gracia, Luis
2012-04-18
Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect correlation of the different structures, in any region of the human body. Authors have developed a mixed technique, joining the use of a three-dimensional laser scanner Roland Picza captured together with computed tomography (CT) and 3D CT images, to achieve a perfect reproduction of the anatomy. Finite element (FE) simulation lets us know the biomechanical changes that take place after hip prostheses or osteosynthesis implantation and biological responses of bone to biomechanical changes. The simulation models are able to predict changes in bone stress distribution around the implant, so allowing preventing future pathologies. The development of a FE model of lumbar spine is another interesting application of the simulation. The model allows research on the lumbar spine, not only in physiological conditions but also simulating different load conditions, to assess the impact on biomechanics. Different degrees of disc degeneration can also be simulated to determine the impact on adjacent anatomical elements. Finally, FE models may be useful to test different fixation systems, i.e., pedicular screws, interbody devices or rigid fixations compared with the dynamic ones. We have also developed models of lumbar spine and hip joint to predict the occurrence of osteoporotic fractures, based on densitometric determinations and specific biomechanical models, including approaches from damage and fracture mechanics. FE simulations also allow us to predict the behavior of orthopedic splints
NASA Astrophysics Data System (ADS)
Fan, Y.; Collet, M.; Ichchou, M.; Li, L.; Bareille, O.; Dimitrijevic, Z.
2016-01-01
This paper presents a rapid and accurate numerical tool for the energy flow evaluation in a periodic substructure from the near-field to the far-field domain. Here we suppose that the near-field part contains a point source characterized by the injected power in the structure. The near-field part is then modeled by Finite Element Method (FEM) while the periodic structure and the far-field part are regarded as waveguides and modeled by an enhanced Wave and Finite Element Method (WFEM). Enhancements are made on the eigenvalue scheme, the condensation of the unit cell and the consideration of a reduced wave basis. Efforts are made to adapt substructures modeled by different strategies in a multi-scale manner such that the final matrices dimensions of the built-up structure are largely reduced. The method is then validated numerically and theoretically. An application is presented, where a structural dynamical system coupled with periodic resistive piezoelectric shunts is discussed.
Effect of triangular element orientation on finite element solutions of the Helmholtz equation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1986-01-01
The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is examined. Nonsymmetric element patterns are found to give generally poor results in the model problems investigated, particularly for cases where standing waves exist. For a fixed number of vertical elements, the results showed that symmetric element patterns give much better agreement with corresponding exact analytical results. In laminated wave guide application, the symmetric pyramid pattern is convenient to use and is shown to give excellent results.