Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
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
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.
Nonlinear finite element analysis: An alternative formulation
NASA Technical Reports Server (NTRS)
Merazzi, S.; Stehlin, P.
1980-01-01
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.
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.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
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 a 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.
Modal Substructuring of Geometrically Nonlinear Finite-Element Models
Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.
2015-12-21
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 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.
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.
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.
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.
Probabilistic finite elements for transient analysis in nonlinear continua
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Nonlinear Finite Element Analysis of Sandwich Composites.
1981-03-01
to the element midsurface z - z(x,y) at all points. An additional coordinate r is used to describe the distance away from the midsurface at any point...It is assumed that on the element level, the shell is shallow, so that z2 2 (56) ,y everywhere. The unit vector normal to the shell midsurface at a...relations above do not involve the orientation of the displaced midsurface normal, and, therefore, apply to arbitrarily large displacements and rotations
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.
Finite element model calibration of a nonlinear perforated plate
NASA Astrophysics Data System (ADS)
Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.
2017-03-01
This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.
Nonlinear analysis of structures. [within framework of finite element method
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.
1974-01-01
The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.
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.
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.
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.
Finite element methods for the nonlinear motion of flexible aircraft
NASA Astrophysics Data System (ADS)
Yang, Victor P.
Conventional strategies in aeroelasticity and flight dynamics for studying aircraft involve making broad assumptions based more on analytical or computational convenience rather than on physical reality. Typically in aeroelastic analyses, the study of the interaction between aircraft flexibility and aerodynamic forces, the aircraft or structural component in question is constrained in a way that is not representative of realistic flight conditions. In flight dynamics, the study of the maneuvering of aircraft, it is common to consider the vehicle as perfectly rigid. In both disciplines it is well known that such contrivances can produce incorrect results. To address these shortcomings, a finite element formulation is developed for analyzing the dynamics of flexible aircraft undergoing arbitrarily large rotation and translation. The formulation is derived in a set of body-attached axes, a frame of reference conducive to analyzing the motion and control of aircraft, and considers the structure as a whole. Several implementation issues are addressed and mitigated, including finite element interpolating functions, the use of eigenvectors as the basis for nonlinear deformation, inclusion of geometrically nonlinear effects in the strain energy, and enforcement of kinematic constraints. Numerical examples illustrate the capabilities of the latter two aspects, and a free-flying aeroelastic model problem demonstrates the overall potential of the proposed formulation. The development is approached in a general way so that the methodology can be applied to any structure that may be modeled by finite elements.
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.
Nonlinear finite-element analysis of nanoindentation of viral capsids
NASA Astrophysics Data System (ADS)
Gibbons, Melissa M.; Klug, William S.
2007-03-01
Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .
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.
Parameter sampling and metamodel generation for nonlinear finite element simulations
Cundy, A. L.; Schultze, J. F.; Hemez, F. M.; Doebling, S. W.; Hylok, J. E.; Bingham, D.
2002-01-01
This research addresses the problem of analyzing the nonlinear transient response of a structural dynamics simulation. A threaded joint assembly's response to impulse loading has been studied. Twelve parameters relating to the input level, preloads of the joint and friction between components are thought to influence the acceleration response of the structure. Due to the high cost of physical testing and large amount of computation time to run numerical models a fastrunning metamodel is being developed. In this case, a metamodel is a statistically developed surrogate to the physics-based finite element model and can be evaluated in minutes on a single processor desktop computer. An unreasonable number of runs is required (312>500,000) to generate a three level full factorial design with 12 parameters for metamodel creation. Some manner of down-selecting or variable screening is needed in order to determine which of the parameters most affect the response and should be retained in subsequent models. A comparision of screening methods to general sensitivity analysis was conducted. A significant effects methodology, which involves a design of experiments technique has been examined. In this method, all parameters were first included in the model and then eliminated on the basis of statistical contributions associated with each parameter. Bayesian variable screening techniques, in which probabilities of effects are generated and updated, have also been explored, Encouraging results have been obtained, as the two methods yield similar sets of statistically significant parameters. Both methods have been compared to general sensitivity analysis (GSA). The resulting compact metamodel can then be explored at more levels to appropriately capture the underlying physics of the threaded assembly with a much smaller set of simulations.
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C.
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
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.
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 general purpose nonlinear rigid body mass finite element for application to rotary wing dynamics
NASA Technical Reports Server (NTRS)
Hamilton, B. K.; Straub, F. K.; Ruzicka, G. C.
1991-01-01
The Second Generation Comprehensive Helicopter Analysis System employs the present formulation of the general-purpose nonlinear rigid body mass finite element, which represents the hub masses, blade tip masses, and pendulum vibration absorbers. The rigid body mass element has six degrees of freedom, and accounts for gravitational as well as dynamic effects. A consequence of deriving the element's equations from various physical principles is that, prior to the transformation which couples the rigid body mass element to the rotor blade finite element, the forces obtained for each element are fundamentally different; this is true notwithstanding the degrees-of-freedom of each element are parameterized using the same coordinates.
Nonlinear dynamics of planetary gears using analytical and finite element models
NASA Astrophysics Data System (ADS)
Ambarisha, Vijaya Kumar; Parker, Robert G.
2007-05-01
Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.
Richins, W.D.; Miller, G.K.
1995-12-01
Large displacement, non-linear finite element analyses were performed to evaluate a swaging process used to fabricate connections between plates in the fuel elements for a test reactor at the Idaho National Engineering Laboratory. The force required to pull the fuel plate from the connection is referred to as the strength of the connection. Assurance that the integrity of the connections is maintained through reactor operation is provided by establishing a minimum acceptance requirement for this strength. Analysis results were used to assess the sensitivity of the strength of the swaged connections to variations in several manufacturing process parameters. The predicted strengths correlated well with results from tests where sample swaged connections were loaded to failure. Results from these investigations were used to assess the adequacy and need for various fabrication, testing, and quality control requirements.
PLANS; a finite element program for nonlinear analysis of structures. Volume 2: User's manual
NASA Technical Reports Server (NTRS)
Pifko, A.; Armen, H., Jr.; Levy, A.; Levine, H.
1977-01-01
The PLANS system, rather than being one comprehensive computer program, is a collection of finite element programs used for the nonlinear analysis of structures. This collection of programs evolved and is based on the organizational philosophy in which classes of analyses are treated individually based on the physical problem class to be analyzed. Each of the independent finite element computer programs of PLANS, with an associated element library, can be individually loaded and used to solve the problem class of interest. A number of programs have been developed for material nonlinear behavior alone and for combined geometric and material nonlinear behavior. The usage, capabilities, and element libraries of the current programs include: (1) plastic analysis of built-up structures where bending and membrane effects are significant, (2) three dimensional elastic-plastic analysis, (3) plastic analysis of bodies of revolution, and (4) material and geometric nonlinear analysis of built-up structures.
CUERVO: A finite element computer program for nonlinear scalar transport problems
Sirman, M.B.; Gartling, D.K.
1995-11-01
CUERVO is a finite element code that is designed for the solution of multi-dimensional field problems described by a general nonlinear, advection-diffusion equation. The code is also applicable to field problems described by diffusion, Poisson or Laplace equations. The finite element formulation and the associated numerical methods used in CUERVO are outlined here; detailed instructions for use of the code are also presented. Example problems are provided to illustrate the use of the code.
Nonlinear finite element analysis of solids and structures. Volume 1: Essentials
Crisfield, M.A.
1991-12-31
This book is written for the practicing engineer. It is an attempt to bring together various strands of work on nonlinear finite elements. The developments in the book are related to computer applications; there are a number of Fortran listings, and many flow charts, for solving parts of nonlinear finite element problems. (Floppy disks with the Fortran source and data files are available from the publisher). This book takes an engineering rather than a mathematical approach to nonlinear finite elements. The first three chapters deal with truss elements. The author introduces basic concepts of nonlinear finite element analysis for simple truss systems with one degree of freedom. The solution schemes considered include an incremental (Euler), an iterative (Newton-Raphson), and a combined incremental and iteration approach (full or modified Newton-Raphson or the initial stress method). In chapter 2, the author introduces the shallow truss theory of chapter 1 to derive the finite element equations for a shallow truss slement with four degrees of freedom. A set of Fortran subroutines is given to solve simple bar-spring problems; some flowcharts are also provided. This chapter also contains data and solutions from a number of bar-spring problems.
1992-09-01
the 3D isoparametric family of elements, and using a Total Lagrangian formulation and implicit integration of the global equations of motion. The...to be observed. NLDFEP, a NonLinear Dynamic Finite Element Program, is designed around the I three dimensional isoparametric family of elements...implemented in NLDFEP are the 8 and 20 node bricks. The program is structured so that additional elements, such as the 27 node brick or another family of
Cost Considerations in Nonlinear Finite-Element Computing
NASA Technical Reports Server (NTRS)
Utku, S.; Melosh, R. J.; Islam, M.; Salama, M.
1985-01-01
Conference paper discusses computational requirements for finiteelement analysis using quasi-linear approach to nonlinear problems. Paper evaluates computational efficiency of different computer architecturtural types in terms of relative cost and computing time.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen
2012-05-01
A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
NASA Technical Reports Server (NTRS)
Thornton, Earl A.; Dechaumphai, Pramote
1985-01-01
A Taylor-Galerkin finite element solution algorithm for transient nonlinear thermal-structural analysis of large, complex structural problems subjected to rapidly applied thermal-structural loads is described. The two-step Taylor-Galerkin algorithm is an application of an algorithm recently developed for problems in compressible fluid dynamics. The element integrals that appear in the algorithm can be evaluated in closed form for two and three dimensional elements.
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Muravyov, Alexander A.
2002-01-01
Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
An approach for verification of finite-element analysis in nonlinear elasticity under large strains
NASA Astrophysics Data System (ADS)
Zingerman, K. M.; Vershinin, A. V.; Levin, V. A.
2016-11-01
An approach to verification of finite-element calculations of stress-strain state of nonlinear elastic bodies under large deformations is suggested. The problems that may be reduced to one-dimensional ones using a semi-inverse method are taken as test problems. An example of such a test problem is the Lame problem for a cylinder. Generally, this problem for compressible hyperelastic materials has no exact analytical solution, but it can be reduced to a boundary value problem for an ordinary second-order nonlinear differential equation, and in some cases - to the Cauchy problem. A numerical solution of this problem can be used as a test one for finite element calculations carried out in three-dimensional statement. Some results of such verification (finite element calculations were performed using the Fidesys CAE-system) are presented.
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.
A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1991-01-01
The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
A Taylor-Galerkin finite element algorithm for transient nonlinear thermal-structural analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.
1986-01-01
A Taylor-Galerkin finite element method for solving large, nonlinear thermal-structural problems is presented. The algorithm is formulated for coupled transient and uncoupled quasistatic thermal-structural problems. Vectorizing strategies ensure computational efficiency. Two applications demonstrate the validity of the approach for analyzing transient and quasistatic thermal-structural problems.
Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer
NASA Technical Reports Server (NTRS)
Pifko, A. B.; Ogilvie, P. L.
1978-01-01
The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.
Finite-Element Analysis of a Mach-8 Flight Test Article Using Nonlinear Contact Elements
NASA Technical Reports Server (NTRS)
Richards, W. Lance
1997-01-01
A flight test article, called a glove, is required for a Mach-8 boundary-layer experiment to be conducted on a flight mission of the air-launched Pegasus(reg) space booster. The glove is required to provide a smooth, three-dimensional, structurally stable, aerodynamic surface and includes instrumentation to determine when and where boundary-layer transition occurs during the hypersonic flight trajectory. A restraint mechanism has been invented to attach the glove to the wing of the space booster. The restraint mechanism securely attaches the glove to the wing in directions normal to the wing/glove interface surface, but allows the glove to thermally expand and contract to alleviate stresses in directions parallel to the interface surface. A finite-element analysis has been performed using nonlinear contact elements to model the complex behavior of the sliding restraint mechanism. This paper provides an overview of the glove design and presents details of the analysis that were essential to demonstrate the flight worthiness of the wing-glove test article. Results show that all glove components are well within the allowable stress and deformation requirements to satisfy the objectives of the flight research experiment.
NASA Astrophysics Data System (ADS)
Singh, Gajbir; Venkateswara Rao, G.; Iyengar, N. G. R.
1995-03-01
The influence of finite amplitudes on the free flexural vibration response of moderately thick laminated plates is investigated. For this purpose, a simple higher order theory involving only four unknowns and satisfying the stress free conditions at the top and bottom surface of the composite plate is proposed. The proposed theory eliminates the use of shear correction factors which are otherwise required in Mindlin's plate theory. A rectangular four-node[formula]continuous finite element is developed based on this theory. The non-linear finite element equations are reduced to two non-linear ordinary differential equations governing the response of positive and negative deflection cycles. Direct numerical integration method is then employed to obtain the periods or non-linear frequencies. The finite element developed and the direct numerical integration method employed are validated for the case of isotropic rectangular plates. It is found that unsymmetrically laminated rectangular plates with hinged-hinged edge conditions oscillate with different amplitudes in the positive and negative deflection cycles. Furthermore, such plates would oscillate with a frequency less than the fundamental frequency for finite small amplitudes of oscillation. It is shown that this behaviour is strongly influenced by the boundary conditions. Results are presented for many configurations of composite plates.
Nonlinear Finite Element Analysis of a General Composite Shell
1988-12-01
strain I Poisson’s ratio ix I I iI I I 1 Total potential energy a Normal stress rShear stress Rotational terms Distance from midsurface e ,Y ,0 Rotations...respectively 0 0 Subscript "e" indicates element reference Subscript "g" indicates global reference Superscript "o" indicates midsurface values...surface strains and rotations are small, and displacements away from the midsurface are restricted by the Kirchhoff-Love hypotheses [3]. With these
Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint
Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.
2014-01-01
This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.
Research of carbon composite material for nonlinear finite element method
NASA Astrophysics Data System (ADS)
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2012-04-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
Research of carbon composite material for nonlinear finite element method
NASA Astrophysics Data System (ADS)
Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon
2011-11-01
Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
NASA Astrophysics Data System (ADS)
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2016-11-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1 -continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0 -continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1 -continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
A simple triangular finite element for nonlinear thin shells: statics, dynamics and anisotropy
NASA Astrophysics Data System (ADS)
Viebahn, Nils; Pimenta, Paulo M.; Schröder, Jörg
2017-02-01
This work presents a simple finite element implementation of a geometrically exact and fully nonlinear Kirchhoff-Love shell model. Thus, the kinematics are based on a deformation gradient written in terms of the first- and second-order derivatives of the displacements. The resulting finite element formulation provides C^1-continuity using a penalty approach, which penalizes the kinking at the edges of neighboring elements. This approach enables the application of well-known C^0-continuous interpolations for the displacements, which leads to a simple finite element formulation, where the only unknowns are the nodal displacements. On the basis of polyconvex strain energy functions, the numerical framework for the simulation of isotropic and anisotropic thin shells is presented. A consistent plane stress condition is incorporated at the constitutive level of the model. A triangular finite element, with a quadratic interpolation for the displacements and a one-point integration for the enforcement of the C^1-continuity at the element interfaces leads to a robust shell element. Due to the simple nature of the element, even complex geometries can be meshed easily, which include folded and branched shells. The reliability and flexibility of the element formulation is shown in a couple of numerical examples, including also time dependent boundary value problems. A plane reference configuration is assumed for the shell mid-surface, but initially curved shells can be accomplished if one regards the initial configuration as a stress-free deformed state from the plane position, as done in previous works.
Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam
NASA Technical Reports Server (NTRS)
Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.
1991-01-01
The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.
NASA Astrophysics Data System (ADS)
Fisher, Aaron C.
We have developed a mixed Vector Finite Element Method (VFEM) for Maxwell's equations with third order polarization terms. The method allows for discretization of complicated device geometries with arbitrary order representations of the B and E fields, and up to 4th order accurate time discretization. Additionally we have implemented a series of computational optimizations that significantly increase the scale of simulations that can be performed with this method. Among these optimizations is a new generalized mass lumping method that we developed which reduces the computational cost of the finite element system solve by a factor of 10x. In this dissertation we will present the Vector Finite Element Method, and the computational optimizations that we employed. Additionally, we will present a series of analyses and simulations that were performed to validate the method. Finally, we will present some production runs using this method, including nonlinear mode mixing in waveguides and supercontinuum generation in a photonic crystal fiber.
Multiple-mode nonlinear free and forced vibrations of beams using finite element method
NASA Technical Reports Server (NTRS)
Mei, Chuh; Decha-Umphai, Kamolphan
1987-01-01
Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.
NASA Astrophysics Data System (ADS)
Vismara, S. O.; Ricci, S.; Bellini, M.; Trittoni, L.
2016-06-01
The objective of the present paper is to describe a procedure to identify and model the non-linear behaviour of structural elements. The procedure herein applied can be divided into two main steps: the system identification and the finite element model updating. The application of the restoring force surface method as a strategy to characterize and identify localized non-linearities has been investigated. This method, which works in the time domain, has been chosen because it has `built-in' characterization capabilities, it allows a direct non-parametric identification of non-linear single-degree-of-freedom systems and it can easily deal with sine-sweep excitations. Two different application examples are reported. At first, a numerical test case has been carried out to investigate the modelling techniques in the case of non-linear behaviour based on the presence of a free-play in the model. The second example concerns the flap of the Intermediate eXperimental Vehicle that successfully completed its 100-min mission on 11 February 2015. The flap was developed under the responsibility of Thales Alenia Space Italia, the prime contractor, which provided the experimental data needed to accomplish the investigation. The procedure here presented has been applied to the results of modal testing performed on the article. Once the non-linear parameters were identified, they were used to update the finite element model in order to prove its capability of predicting the flap behaviour for different load levels.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-01-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn
1994-01-01
This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
NASA Astrophysics Data System (ADS)
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN
NASA Technical Reports Server (NTRS)
Sheerer, T. J.
1986-01-01
The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.
Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature
Rudd, R E; Broughton, J Q
2005-05-30
Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.
NASA Astrophysics Data System (ADS)
Brünig, M.
The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent finite strain analysis of solids undergoing large elastic-plastic deformations. The formulation relies on the introduction of a mixed-variant metric transformation tensor which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure whose rate is shown to be additively decomposed into elastic and plastic strain rate tensors. The mixed-variant logarithmic elastic strain tensor provides a basis for the definition of a local isotropic hyperelastic stress response in the elastic-plastic solid. Additionally, the plastic material behavior is assumed to be governed by a generalized J2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain tensors is based on 1st and higher order Padé approximations. Estimates of the stress and strain histories are obtained via a highly stable and accurate explicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step. The development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency of the algorithm.
Hoffelner, J; Landes, H; Kaltenbacher, M; Lerch, R
2001-05-01
A recently developed finite element method (FEM) for the numerical simulation of nonlinear sound wave propagation in thermoviscous fluids is presented. Based on the nonlinear wave equation as derived by Kuznetsov, typical effects associated with nonlinear acoustics, such as generation of higher harmonics and dissipation resulting from the propagation of a finite amplitude wave through a thermoviscous medium, are covered. An efficient time-stepping algorithm based on a modification of the standard Newmark method is used for solving the non-linear semidiscrete equation system. The method is verified by comparison with the well-known Fubini and Fay solutions for plane wave problems, where good agreement is found. As a practical application, a high intensity focused ultrasound (HIFU) source is considered. Impedance simulations of the piezoelectric transducer and the complete HIFU source loaded with air and water are performed and compared with measured data. Measurements of radiated low and high amplitude pressure pulses are compared with corresponding simulation results. The obtained good agreement demonstrates validity and applicability of the nonlinear FEM.
Simulation of Aircraft Landing Gears with a Nonlinear Dynamic Finite Element Code
NASA Technical Reports Server (NTRS)
Lyle, Karen H.; Jackson, Karen E.; Fasanella, Edwin L.
2000-01-01
Recent advances in computational speed have made aircraft and spacecraft crash simulations using an explicit, nonlinear, transient-dynamic, finite element analysis code more feasible. This paper describes the development of a simple landing gear model, which accurately simulates the energy absorbed by the gear without adding substantial complexity to the model. For a crash model, the landing gear response is approximated with a spring where the force applied to the fuselage is computed in a user-written subroutine. Helicopter crash simulations using this approach are compared with previously acquired experimental data from a full-scale crash test of a composite helicopter.
Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains
NASA Astrophysics Data System (ADS)
Yang, Z.; Yuan, Z.; Nie, Y.; Wang, J.; Zhu, X.; Liu, F.
2017-02-01
In this paper, we consider two-dimensional Riesz space fractional diffusion equations with nonlinear source term on convex domains. Applying Galerkin finite element method in space and backward difference method in time, we present a fully discrete scheme to solve Riesz space fractional diffusion equations. Our breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help us to deal with space fractional terms on any convex domain. The stability and convergence of the scheme are also discussed. Numerical examples are given to verify accuracy and stability of our scheme.
Nonlinear, three-dimensional finite-element analysis of air-cooled gas turbine blades
NASA Technical Reports Server (NTRS)
Kaufman, A.; Gaugler, R. E.
1980-01-01
Cyclic stress-strain states in cooled turbine blades were calculated for a simulated mission of an advanced-technology commercial aircraft engine. The MARC, nonlinear, finite-element computer program was used for the analysis of impingement-cooled airfoils, with and without leading-edge film cooling. Creep was the predominant damage mode (ignoring hot corrosion), particularly artund film-cooling holes. Radially angled holes exhibited less creep than holes with axes normal to the surface. Beam-theory analyses of all-impingement-cooled airfoils gave fair agreement with MARC results for initial creep.
NASA Astrophysics Data System (ADS)
Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.
2015-03-01
This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.
Finite element simulation of non-linear acoustic generation in a horn loudspeaker
NASA Astrophysics Data System (ADS)
Tsuchiya, T.; Kagawa, Y.; Doi, M.; Tsuji, T.
2003-10-01
The loudspeaker is an electro-acoustic device for sound reproduction which requires the distortion as small as possible. The distortion may arise from the magnetic non-linearity of the york, the uneven magnetic field distribution, the mechanical non-linearity at the diaphragm suspension and the acoustic non-linearity due to the high sound pressure and velocity in the duct-radiation system. A horn is sometimes provided in front of the vibrating diaphragm radiator, which plays an important role to increase the efficiency by matching the acoustic impedance between the radiator and the ambient medium. The horn is in many cases folded twice or three times to shorten the length, which further degrades the reproduction quality. The sound intensity and velocity are apt to attain very high in the small cross-sectional area in the throat and in the folded regions, which may cause the distortion due to the non-linear effect of the medium. The present paper is to investigate the frequency characteristics of the loudspeaker numerically evaluating the generation of the harmonics and sub-harmonics. An axisymmetric folded horn is considered for which the wave equation with the non-linear term retained is solved by the finite element method. The solution is made in time domain in which the sound pressure calculated at the opening end of the horn is Fourier-transformed to the frequency domain to evaluate the distortion, while the wave marching in the horn is visualized.
On nonlinear finite element analysis in single-, multi- and parallel-processors
NASA Technical Reports Server (NTRS)
Utku, S.; Melosh, R.; Islam, M.; Salama, M.
1982-01-01
Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.
Fracture prediction for the proximal femur using finite element models: Part II--Nonlinear analysis.
Lotz, J C; Cheal, E J; Hayes, W C
1991-11-01
In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.
NASA Technical Reports Server (NTRS)
Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter
2014-01-01
The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously
Finite Element Procedures Applicable to Nonlinear Analysis of Reinforced Concrete Shell Structures.
1984-09-01
details. 1- 4-9 Section 4: FINITE-ELEMENT IMPLEMENTATION 4-10 4.3.2 9-Node Elements The Heterosis element [10], which combines Lagrange (biquadratic...M., "The ’ Heterosis ’ Family of Plate Finite Elements," Proc. ASCE Electronic Computations Conference, St. Louis, MO, August 6-8, 1979. 1111 Kraus H
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1989-01-01
A computational procedure is presented for the nonlinear dynamic analysis of unsymmetric structures on vector multiprocessor systems. The procedure is based on a novel hierarchical partitioning strategy in which the response of the unsymmetric and antisymmetric response vectors (modes), each obtained by using only a fraction of the degrees of freedom of the original finite element model. The three key elements of the procedure which result in high degree of concurrency throughout the solution process are: (1) mixed (or primitive variable) formulation with independent shape functions for the different fields; (2) operator splitting or restructuring of the discrete equations at each time step to delineate the symmetric and antisymmetric vectors constituting the response; and (3) two level iterative process for generating the response of the structure. An assessment is made of the effectiveness of the procedure on the CRAY X-MP/4 computers.
NASA Astrophysics Data System (ADS)
Hamim, Salah Uddin Ahmed
Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.
PLANS: A finite element program for nonlinear analysis of structures. Volume 1: Theoretical manual
NASA Technical Reports Server (NTRS)
Pifko, A.; Levine, H. S.; Armen, H., Jr.
1975-01-01
The PLANS system is described which is a finite element program for nonlinear analysis. The system represents a collection of special purpose computer programs each associated with a distinct physical problem class. Modules of PLANS specifically referenced and described in detail include: (1) REVBY, for the plastic analysis of bodies of revolution; (2) OUT-OF-PLANE, for the plastic analysis of 3-D built-up structures where membrane effects are predominant; (3) BEND, for the plastic analysis of built-up structures where bending and membrane effects are significant; (4) HEX, for the 3-D elastic-plastic analysis of general solids; and (5) OUT-OF-PLANE-MG, for material and geometrically nonlinear analysis of built-up structures. The SATELLITE program for data debugging and plotting of input geometries is also described. The theoretical foundations upon which the analysis is based are presented. Discussed are the form of the governing equations, the methods of solution, plasticity theories available, a general system description and flow of the programs, and the elements available for use.
Non-linear rotation-free shell finite-element models for aortic heart valves.
Gilmanov, Anvar; Stolarski, Henryk; Sotiropoulos, Fotis
2017-01-04
Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves.
Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis
NASA Astrophysics Data System (ADS)
Yue, Zhihua
2005-11-01
The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step. A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error. In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems
Slave finite elements for nonlinear analysis of engine structures, volume 1
NASA Technical Reports Server (NTRS)
Gellin, S.
1991-01-01
A 336 degrees of freedom slave finite element processing capability to analyze engine structures under severe thermomechanical loading is presented. Description of the theoretical development and demonstration of that element is presented in this volume.
NASA Astrophysics Data System (ADS)
Hammerand, Daniel C.
Over the past several decades, the use of composite materials has grown considerably. Typically, fiber-reinforced polymer-matrix composites are modeled as being linear elastic. However, it is well-known that polymers are viscoelastic in nature. Furthermore, the analysis of complex structures requires a numerical approach such as the finite element method. In the present work, a triangular flat shell element for linear elastic composites is extended to model linear viscoelastic composites. Although polymers are usually modeled as being incompressible, here they are modeled as compressible. Furthermore, the macroscopic constitutive properties for fiber-reinforced composites are assumed to be known and are not determined using the matrix and fiber properties along with the fiber volume fraction. Hygrothermo-rheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log time scale, in addition to the usual hygrothermal loads. Both the temperature and moisture are taken to be prescribed. Hence, the heat energy generated by the viscoelastic deformations is not considered. When the deformations and rotations are small under an applied load history, the usual engineering stress and strain measures can be used and the time history of a viscoelastic deformation process is determined using the original geometry of the structure. If, however, sufficiently large loads are applied, the deflections and rotations will be large leading to changes in the structural stiffness characteristics and possibly the internal loads carried throughout the structure. Hence, in such a case, nonlinear effects must be taken into account and the appropriate stress and strain measures must be used. Although a geometrically-nonlinear finite element code could always be used to compute geometrically-linear deformation processes, it is inefficient to use such a code for small deformations, due to
Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis
NASA Technical Reports Server (NTRS)
Bibel, G. D.; Kumar, A.; Reddy, S.; Handschuh, R.
1993-01-01
A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.
NASA Astrophysics Data System (ADS)
Griebel, Matt; Buleri, Christine; Baylor, Andrew; Gunnels, Steve; Hull, Charlie; Palunas, Povilas; Phillips, Mark
2016-07-01
The Magellan Telescopes are a set of twin 6.5 meter ground based optical/near-IR telescopes operated by the Carnegie Institution for Science at the Las Campanas Observatory (LCO) in Chile. The primary mirrors are f/1.25 paraboloids made of borosilicate glass and a honeycomb structure. The secondary mirror provides both f/11 and f/5 focal lengths with two Nasmyth, three auxiliary, and a Cassegrain port on the optical support structure (OSS). The telescopes have been in operation since 2000 and have experienced several small earthquakes with no damage. Measurement of in situ response of the telescopes to seismic events showed significant dynamic amplification, however, the response of the telescopes to a survival level earthquake, including component level forces, displacements, accelerations, and stresses were unknown. The telescopes are supported with hydrostatic bearings that can lift up under high seismic loading, thus causing a nonlinear response. For this reason, the typical response spectrum analysis performed to analyze a survival level seismic earthquake is not sufficient in determining the true response of the structure. Therefore, a nonlinear transient finite element analysis (FEA) of the telescope structure was performed to assess high risk areas and develop acceleration responses for future instrument design. Several configurations were considered combining different installed components and altitude pointing directions. A description of the models, methodology, and results are presented.
Potential of minicomputer/array-processor system for nonlinear finite-element analysis
NASA Technical Reports Server (NTRS)
Strohkorb, G. A.; Noor, A. K.
1983-01-01
The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.
NASA Astrophysics Data System (ADS)
Huard, Steven Roger
The work involves the magnetic modeling of a variable reluctance and a hybrid stepping motor. The model combines two traditional methods for creating a magnetic model. Nonlinear two dimensional finite element analysis is combined with nonlinear lumped element modeling to create a three dimension lumped model. The two dimensional finite element analysis is used to numerically calculate the effective reluctance function of the motor tooth region. After the finite element analysis is completed, a two terminal tooth region reluctance element that is a function of both rotor angle and tooth region flux density results. The two terminal lumped element is then used to represent the tooth region of the motor in a lumped parameter model. The process by which the tooth region finite element field solution is transformed into the two terminal lumped reluctance is a new modeling approach; and, it is the foundation of the modeling method in this dissertation. Torque, back EMF, and inductance are some of the more important motor parameters predicted by the modeling method. The model predictions are compared to experimental data in the dissertation. The final motor parameter predictions from the model correlated quite well with experimental data. Also included in the dissertation is a unique derivation which defines the constraints that a region must satisfy such that a general three dimensional region of non-homogenous material can be modeled as a two terminal lumped reluctance element. The final restrictions imposed on the general three dimensional region are quite liberal. A method for solving any arbitrarily connected network of nonlinear lumped reluctances and sources is shown in detail. The method was developed specifically for use in this dissertation research, however, it is general enough to be applied to a wide variety of lumped element magnetic problems. The method explains how a Newton-Raphson iteration loop can be used to solve the nonlinear matrix equation created
Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method.
Syngellakis, S; Arnold, M A; Rassoulian, H
2000-01-01
The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element program is subsequently applied to the simulation of a series of tests designed to investigate the relation between AFO trimline location and stiffness for moderate and large rotations. Through careful consideration and identification of key modelling parameters, the developed finite element solution proves to be a reliable and effective alternative means of assessing variations of a typical plastic AFO design so that particular patient requirements could be met, in the long term.
Technology Transfer Automated Retrieval System (TEKTRAN)
Axisymmetric finite element (FE) method was developed using a commercial computer program to simulate cone penetration process in layered granular soil. Soil was considered as a non-linear elastic plastic material which was modeled using variable elastic parameters of Young’s Modulus and Poisson’s r...
NASA Technical Reports Server (NTRS)
Robinson, J. C.
1979-01-01
Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.
NASA Astrophysics Data System (ADS)
Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; Ortensi, Javier; Baker, Benjamin; Laboure, Vincent; Wang, Congjian; DeHart, Mark; Martineau, Richard
2017-06-01
This work presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the SN transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form is based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. While NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in
Glass, Micheal W.; Hogan, Roy E., Jr.; Gartling, David K.
2010-03-01
The need for the engineering analysis of systems in which the transport of thermal energy occurs primarily through a conduction process is a common situation. For all but the simplest geometries and boundary conditions, analytic solutions to heat conduction problems are unavailable, thus forcing the analyst to call upon some type of approximate numerical procedure. A wide variety of numerical packages currently exist for such applications, ranging in sophistication from the large, general purpose, commercial codes, such as COMSOL, COSMOSWorks, ABAQUS and TSS to codes written by individuals for specific problem applications. The original purpose for developing the finite element code described here, COYOTE, was to bridge the gap between the complex commercial codes and the more simplistic, individual application programs. COYOTE was designed to treat most of the standard conduction problems of interest with a user-oriented input structure and format that was easily learned and remembered. Because of its architecture, the code has also proved useful for research in numerical algorithms and development of thermal analysis capabilities. This general philosophy has been retained in the current version of the program, COYOTE, Version 5.0, though the capabilities of the code have been significantly expanded. A major change in the code is its availability on parallel computer architectures and the increase in problem complexity and size that this implies. The present document describes the theoretical and numerical background for the COYOTE program. This volume is intended as a background document for the user's manual. Potential users of COYOTE are encouraged to become familiar with the present report and the simple example analyses reported in before using the program. The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction problems
NASA Technical Reports Server (NTRS)
Atluri, S. N.; Nakagaki, M.; Kathiresan, K.
1980-01-01
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
NASA Technical Reports Server (NTRS)
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
NASA Astrophysics Data System (ADS)
Segura, Christopher L.
Numerical simulation tools capable of modeling nonlinear material and geometric behavior are important to structural engineers concerned with approximating the strength and deformation capacity of a structure. While structures are typically designed to behave linear elastic when subjected to building code design loads, exceedance of the linear elastic range is often an important consideration, especially with regards to structural response during hazard level events (i.e. earthquakes, hurricanes, floods), where collapse prevention is the primary goal. This thesis addresses developments made to Mercury, a nonlinear finite element program developed in MATLAB for numerical simulation and in C++ for real time hybrid simulation. Developments include the addition of three new constitutive models to extend Mercury's lumped plasticity modeling capabilities, a constitutive driver tool for testing and implementing Mercury constitutive models, and Mercury pre and post-processing tools. Mercury has been developed as a tool for transient analysis of distributed plasticity models, offering accurate nonlinear results on the material level, element level, and structural level. When only structural level response is desired (collapse prevention), obtaining material level results leads to unnecessarily lengthy computational time. To address this issue in Mercury, lumped plasticity capabilities are developed by implementing two lumped plasticity flexural response constitutive models and a column shear failure constitutive model. The models are chosen for implementation to address two critical issues evident in structural testing: column shear failure and strength and stiffness degradation under reverse cyclic loading. These tools make it possible to model post-peak behavior, capture strength and stiffness degradation, and predict global collapse. During the implementation process, a need was identified to create a simple program, separate from Mercury, to simplify the process of
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region.
NASA Technical Reports Server (NTRS)
Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.
1982-01-01
Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.
Gartling, D.K.
1996-05-01
The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.
Explicit Nonlinear Finite Element Geometric Analysis of Parabolic Leaf Springs under Various Loads
Kong, Y. S.; Omar, M. Z.; Chua, L. B.; Abdullah, S.
2013-01-01
This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and passenger safety. In this study, the explicit nonlinear dynamic finite element (FE) method is implemented because of the complexity of experimental testing A series of load cases; namely, vertical push, wind-up, and suspension roll are introduced for the simulations. The vertical stiffness of the parabolic leaf springs is related to the vehicle load-carrying capability, whereas the wind-up stiffness is associated with vehicle braking. The roll stiffness of the parabolic leaf springs is correlated with the vehicle roll stability. To obtain a better bus performance, two new parabolic leaf spring designs are proposed and simulated. The stress level during the loadings is observed and compared with its design limit. Results indicate that the newly designed high vertical stiffness parabolic spring provides the bus a greater roll stability and a lower stress value compared with the original design. Bus safety and stability is promoted, as well as the load carrying capability. PMID:24298209
Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J
2014-06-01
Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds.
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
2015-01-01
SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355
NASA Astrophysics Data System (ADS)
Chiroux, Robert Charles
The objective of this research was to produce a three dimensional, non-linear, dynamic simulation of the interaction between a hyperelastic wheel rolling over compactable soil. The finite element models developed to produce the simulation utilized the ABAQUS/Explicit computer code. Within the simulation two separate bodies were modeled, the hyperelastic wheel and a compactable soil-bed. Interaction between the bodies was achieved by allowing them to come in contact but not to penetrate the contact surface. The simulation included dynamic loading of a hyperelastic, rubber tire in contact with compactable soil with an applied constant angular velocity or torque, including a tow load, applied to the wheel hub. The constraints on the wheel model produced a straight and curved path. In addition the simulation included a shear limit between the tire and soil allowing for the introduction of slip. Soil properties were simulated using the Drucker-Prager, Cap Plasticity model available within the ABAQUS/Explicit program. Numerical results obtained from the three dimensional model were compared with related experimental data and showed good correlation for similar conditions. Numerical and experimental data compared well for both stress and wheel rut formation depth under a weight of 5.8 kN and a constant angular velocity applied to the wheel hub. The simulation results provided a demonstration of the benefit of three-dimensional simulation in comparison to previous two-dimensional, plane strain simulations.
Maker, B.N.
1995-04-14
This report provides a user`s manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.
NASA Astrophysics Data System (ADS)
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.
2017-02-01
This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic
Haverkort, J.W.; Blank, H.J. de; Huysmans, G.T.A.; Pratt, J.; Koren, B.
2016-07-01
Numerical simulations form an indispensable tool to understand the behavior of a hot plasma that is created inside a tokamak for providing nuclear fusion energy. Various aspects of tokamak plasmas have been successfully studied through the reduced magnetohydrodynamic (MHD) model. The need for more complete modeling through the full MHD equations is addressed here. Our computational method is presented along with measures against possible problems regarding pollution, stability, and regularity. The problem of ensuring continuity of solutions in the center of a polar grid is addressed in the context of a finite element discretization of the full MHD equations. A rigorous and generally applicable solution is proposed here. Useful analytical test cases are devised to verify the correct implementation of the momentum and induction equation, the hyperdiffusive terms, and the accuracy with which highly anisotropic diffusion can be simulated. A striking observation is that highly anisotropic diffusion can be treated with the same order of accuracy as isotropic diffusion, even on non-aligned grids, as long as these grids are generated with sufficient care. This property is shown to be associated with our use of a magnetic vector potential to describe the magnetic field. Several well-known instabilities are simulated to demonstrate the capabilities of the new method. The linear growth rate of an internal kink mode and a tearing mode are benchmarked against the results of a linear MHD code. The evolution of a tearing mode and the resulting magnetic islands are simulated well into the nonlinear regime. The results are compared with predictions from the reduced MHD model. Finally, a simulation of a ballooning mode illustrates the possibility to use our method as an ideal MHD method without the need to add any physical dissipation.
Nonlinear finite element analysis of mechanical characteristics on CFRP composite pressure vessels
NASA Astrophysics Data System (ADS)
Liu, Dong-xia; Liang, Li; Li, Ming
2010-06-01
CFRP(Carbon Fibre Reinforced Plastic) composite pressure vessel was calculated using finite element program of ANSYS for their mechanical characteristics in this paper. The elastic-plastic model and elements of Solid95 were selected for aluminium alloys of gas cylinder. Also liner-elastic model and layer elements of Shell99 were adopted for carbon fibre/epoxy resin. The stress state of CFRP composite pressure vessel was calculated under different internal pressures include pre-stressing pressures, working pressures, test hydraulic pressures, minimum destructive pressures etcetera to determine the size of gas cylinder and layer parameter of carbon fibre. The mechanical characteristics CFRP composite vessel could were using to design and test of gas cylinder. Numerical results showed that finite element model and calculating method were efficient for study of CFRP gas cylinder and useful for engineering design.
Nasedkina, A.A.; Nasedkin, A.V.; Iovane, G.
2009-07-15
The paper discusses modeling of a multi-layer coal seam under hydrodynamic action based on the coupled equations of poroelasticity and filtration with the nonlinear relationship of permeability and porous pressure. The calculations by the finite element method use correspondence between the poroelasticity and thermoelasticity equations. The influence of input data on the size of a degassing hole area is analyzed for the couple problem and pure filtration problem.
Fission-Fusion Adaptivity in Finite Elements for Nonlinear Dynamics of Shells
1988-11-30
where mesh refinement will prove useful. In fact, the deviation of a bilinear element from a smooth shell midsurface can be related to the angle between...comparisons with nonadaptive meshes. Conclusions and further discussions are given in Section 6. -5- 2. FINITE ELEMENT FORMULATION The shape of the midsurface ...8217 22 , and e3 is defined so that e, and e2 are tangent to the midsurface and rotate with the element; 2. for each node, a triad b i is defined so that
Linear and nonlinear finite element analysis of laminated composite structures at high temperatures
NASA Astrophysics Data System (ADS)
Wilt, Thomas Edmund
The use of composite materials in aerospace applications, particularly engine components, is becoming more prevalent due to the materials high strength, yet low weight. In addition to thermomechanical deformation response, life prediction and damage modeling analysis is also required to assess the component's service life. These complex and computationally intensive analyses require the development of simple, efficient and robust finite element analysis capabilities. A simple robust finite element which can effectively model the multi-layer composite material is developed. This will include thermal gradient capabilities necessary for a complete thermomechanical analysis. In order to integrate the numerically stiff rate dependent viscoplastic equations, efficient, stable numerical algorithms are developed. In addition, consistent viscoplastic/plastic tangent matrices will also be formulated. The finite element is formulated based upon a generalized mixed variational principle with independently assumed displacements and layer number independent strains. A unique scheme utilizing nodal temperatures is used to model a linear thermal gradient through the thickness of the composite. The numerical integration algorithms are formulated in the context of a fully implicit backward Euler scheme. The consistent tangent matrices arise directly from the formulation. The multi-layer composite finite element demonstrates good performance in terms of static displacement and stress predictions, and dynamic response. Also, the element appears to be relatively insensitive to mesh distortions. The robustness and efficiency of the fully implicit integration algorithms is effectively demonstrated in the numerical results. That is, large time steps and a significant reduction in global iterations, as a direct result of utilizing the consistent tangent matrices, is shown.
Zaslawsky, M.
1987-04-01
A two-dimensional plane strain model of the SSC magnet (cold mass) was developed to determine the stresses and deflections under a variety of conditions. Cool down from room temperature to 4.35 K and the effects of quench in the coils were calculated using the computer code TACO -- a finite element heat transfer code. Pre-assembly loads, energization to 6.6 tesla, pressure due to liquid helium, Lorentz Forces on the copper plated beam tube, were incorporated in NIKE2D -- 2-D vectorized implicit finite element code. The model for material behavior was treated as thermo-elastic plastic which required material properties as a function of temperature. The programs were run remotely on the Cray computers in Livermore via the Vax computers at Berkeley.
Matsuura, Yusuke; Kuniyoshi, Kazuki; Suzuki, Takane; Ogawa, Yasufumi; Sukegawa, Koji; Rokkaku, Tomoyuki; Thoreson, Andrew Ryan; An, Kai-Nan; Takahashi, Kazuhisa
2015-01-01
The feasibility of a user-specific finite element model for predicting the in situ strength of the radius after implantation of bone plates for open fracture reduction was established. The effect of metal artifact in CT imaging was characterized. The results were verified against biomechanical test data. Fourteen cadaveric radii were divided into two groups: (1) intact radii for evaluating the accuracy of radial diaphysis strength predictions with finite element analysis and (2) radii with a locking plate affixed for evaluating metal artifact. All bones were imaged with CT. In the plated group, radii were first imaged with the plates affixed (for simulating digital plate removal). They were then subsequently imaged with the locking plates and screws removed (actual plate removal). Fracture strength of the radius diaphysis under axial compression was predicted with a three-dimensional, specimen-specific, nonlinear finite element analysis for both the intact and plated bones (bones with and without the plate captured in the scan). Specimens were then loaded to failure using a universal testing machine to verify the actual fracture load. In the intact group, the physical and predicted fracture loads were strongly correlated. For radii with plates affixed, the physical and predicted (simulated plate removal and actual plate removal) fracture loads were strongly correlated. This study demonstrates that our specimen-specific finite element analysis can accurately predict the strength of the radial diaphysis. The metal artifact from CT imaging was shown to produce an overestimate of strength.
Closed form expressions for a consistent stress material nonlinear finite element
NASA Astrophysics Data System (ADS)
Knipe, Richard Lee
Finite element expressions for two dimensional elasto-plasticity problems were implemented in closed form. These closed form expressions are based upon a distribution of the elasto-plastic constitutive relationship that is consistent with the interpolating functions used for the displacement. Closed form expressions for the element tangent stiffness matrix and initial stress nodal load vector were developed for the non hierarchic constant, linear, and quadratic strain triangle. Decreased solution times were obtained when using the closed form expressions instead of expressions based on numerical integration. The quality of the solutions obtained from the closed form expressions was measured against published solutions for two dimensional elasto-plasticity problems.
Christen, David; Zwahlen, Alexander; Müller, Ralph
2014-01-01
Finite element (FE) simulations based on high-resolution peripheral quantitative computed-tomography (HRpQCT) measurements provide an elegant and direct way to estimate bone strength. Parallel solvers for nonlinear FE simulations allow the assessment not only of the initial linear elastic behavior of the bone but also materially and geometrically nonlinear effects. The reproducibility of HRpQCT measurements, as well as their analysis of microarchitecture using linear-elastic FE simulations with a homogeneous elastic modulus has been investigated before. However, it is not clear to which extent density-derived and nonlinear FE simulations are reproducible. In this study, we introduced new mechanical indices derived from nonlinear FE simulations that describe the onset of yielding and the behavior at maximal load. Using 14 embalmed forearms that were imaged three times, we found that in general the in vitro reproducibility of the nonlinear FE simulations is as good as the reproducibility of linear FE. For the nonlinear simulations precision errors (PEs) ranged between 0.4 and 3.2% and intraclass correlation coefficients were above 0.9. In conclusion, nonlinear FE simulations with density derived material properties contain important additional information that is independent from the results of the linear simulations.
Looking-Free Mixed hp Finite Element Methods for Linear and Geometrically Nonlinear Elasticity
1997-06-09
element method. Particu- lar areas of interest : hp versions, mixed methods , nearly incompressible materials, curvilinear domains, nonlinear elasticity...1 Introduction 1 2 Preliminaries 10 2.1 The Standard and Mixed Methods for Linear Elasticity .......... 10 2.2 Locking...be used to denote pressure, we use k to denote polynomial degree. 4 Mixed methods have also been used to avoid locking. In these methods, an aux
Horowitz, A; Sheinman, I; Lanir, Y; Perl, M; Sideman, S
1988-02-01
A two-dimensional incompressible plane-stress finite element is formulated for the simulation of the passive-state mechanics of thin myocardial strips. The formulation employs a total Lagrangian and materially nonlinear approach, being based on a recently proposed structural material law, which is derived from the histological composition of the tissue. The ensuing finite element allows to demonstrate the mechanical properties of a single myocardial layer containing uniformly directed fibers by simulating various loading cases such as tension, compression and shear. The results of these cases show that the fiber direction is considerably stiffer than the cross-fiber direction, that there is significant coupling between these two directions, and that the shear stiffness of the tissue is lower than its tensile and compressive stiffness.
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.
NASA Astrophysics Data System (ADS)
Lafontaine, N. M.; Rossi, R.; Cervera, M.; Chiumenti, M.
2015-03-01
Low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.
Shestakov, A I; Milovich, J L; Noy, A
2000-12-27
The nonlinear Poisson-Boltzmann (PB) equation is solved using Pseudo Transient Continuation. The PB solver is constructed by modifying the nonlinear diffusion module of a 3D, massively parallel, unstructured-grid, finite element, radiation-hydrodynamics code. The solver also computes the electrostatic energy and evaluates the force on a user-specified contour. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or linearizes conditions ''regulating'' the surface charge. The code may be run in either Cartesian, cylindrical, or spherical coordinates. The potential and force due to a conical probe interacting with a flat plate is computed and the result compared with direct force measurements by chemical force microscopy.
Tariq, S.M.
1987-05-01
This study presents results of finite-element modeling of steady-state flow in perforated natural completions. Use of a mesh chosen carefully by grid sensitivity analysis permits evaluation of flow with more precision than that achieved by previous investigators. Also, for the first time, flow characteristics of perforated completions are evaluated with the non-Darcy effect resulting form converging flow around the perforation taken into account. The results indicate confirmation of Locke's results qualitatively but 5 to 10% overprediction by the nomograph, the importance of angular phasing between adjacent perforations, the uncertainty in generally accepted severe permeability impairment in the compacted zone, and a significant reduction in productivity owing to a non-Darcy effect around the perforation for high-rate gas wells.
Tariq, S.M.
1984-04-01
This study presents results of finite element modelling of steady-state flow in perforated natural completions. Use of a carefully chosen mesh based on grid sensitivity analysis permits evaluation of flow with more precision than achieved by previous investigators. Also, for the first time, evaluation of flow characterstics of perforated completion is made taking into account the non-Darcy effect due to converging flow around the perforation. The results indicate: (1) confirmation of Locke's findings qualitatively but 5-10% overprediction by the nomograph (2) importance of angular phasing between adjacent perforations, (3) untenability of generally accepted severe permeability impairment in the compacted zone, and (4) significant reduction in productivity due to non-Darcy effect around the perforation for high-rate wells.
NASA Technical Reports Server (NTRS)
Padovan, J.; Adams, M.; Lam, P.; Fertis, D.; Zeid, I.
1982-01-01
Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.
Sun, Wei; Chaikof, Elliot L; Levenston, Marc E
2008-12-01
Finite element (FE) implementations of nearly incompressible material models often employ decoupled numerical treatments of the dilatational and deviatoric parts of the deformation gradient. This treatment allows the dilatational stiffness to be handled separately to alleviate ill conditioning of the tangent stiffness matrix. However, this can lead to complex formulations of the material tangent moduli that can be difficult to implement or may require custom FE codes, thus limiting their general use. Here we present an approach, based on work by Miehe (Miehe, 1996, "Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large Strain Computational Inelasticity," Comput. Methods Appl. Mech. Eng., 134, pp. 223-240), for an efficient numerical approximation of the tangent moduli that can be easily implemented within commercial FE codes. By perturbing the deformation gradient, the material tangent moduli from the Jaumann rate of the Kirchhoff stress are accurately approximated by a forward difference of the associated Kirchhoff stresses. The merit of this approach is that it produces a concise mathematical formulation that is not dependent on any particular material model. Consequently, once the approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and accuracy of this approach is first demonstrated with a simple neo-Hookean material. Subsequently, a fiber-reinforced structural model is applied to analyze the pressure-diameter curve during blood vessel inflation. Implementation of this approach will facilitate the incorporation of novel hyperelastic material models for a soft tissue behavior into commercial FE software.
Mohanty, Subhasish; Majumdar, Saurindranath
2015-01-01
Irradiation creep plays a major role in the structural integrity of the graphite components in high temperature gas cooled reactors. Finite element procedures combined with a suitable irradiation creep model can be used to simulate the time-integrated structural integrity of complex shapes, such as the reactor core graphite reflector and fuel bricks. In the present work a comparative study was undertaken to understand the effect of linear and nonlinear irradiation creep on results of finite element based stress analysis. Numerical results were generated through finite element simulations of a typical graphite reflector.
Nonlinear visco-elastic finite element analysis of different porcelain veneers configuration.
Sorrentino, Roberto; Apicella, Davide; Riccio, Carlo; Gherlone, Enrico; Zarone, Fernando; Aversa, Raffaella; Garcia-Godoy, Franklin; Ferrari, Marco; Apicella, Antonio
2009-11-01
This study is aimed at evaluating the biomechanical behavior of feldspathic versus alumina porcelain veneers. A 3D numerical model of a maxillary central incisor, with the periodontal ligament (PDL) and the alveolar bone was generated. Such model was made up of four main volumes: dentin, enamel, cement layer and veneer. Incisors restored with alumina and feldspathic porcelain veneers were compared with a natural sound tooth (control). Enamel, cementum, cancellous and cortical bone were considered as isotropic elastic materials; on the contrary, the tubular structure of dentin was designed as elastic orthotropic. The nonlinear visco-elatic behavior of the PDL was considered. The veneer volumes were coupled with alumina and feldspathic porcelain mechanical properties. The adhesive layers were modeled in the FE environment using spring elements. A 50N load applied at 60 degrees angle with tooth longitudinal axis was applied and validated. Compressive stresses were concentrated on the external surface of the buccal side of the veneer close to the incisal margin; such phenomenon was more evident in the presence of alumina. Tensile stresses were negligible when compared to compressive ones. Alumina and feldspathic ceramic were characterized by a different biomechanical behavior in terms of elastic deformations and stress distributions. The ultimate strength of both materials was not overcome in the performed analysis.
NASA Astrophysics Data System (ADS)
Pérez-Aparicio, José L.; Sosa, Horacio
2004-06-01
Magnetostriction is a phenomenon observed in all ferromagnetic materials. It couples elastic, electric, magnetic and in some situations also thermal fields and is of great industrial interest for use in sensors, actuators, adaptive or functional structures, robotics, transducers and MEMS. In this work, the governing equations of the three-field problem (i.e., the interactions of elastic, electric and magnetic effects) are formulated in three dimensions, accounting for non-linear (through magnetic body forces represented by the Maxwell tensor) and dynamic effects, and with constitutive equations resembling those of piezoelectricity. Through manipulation of Maxwell equations it is possible to find suitable expressions for developing the numerical weak, Galerkin and matrix forms in a natural way, including seven residuals (one for each nodal degree of freedom) and non-symmetric tangent, 'capacity' and mass consistent matrices. Simple backward Euler and central difference schemes can be used for the time domain integration. The only assumption made in this work for simplification is that the time variation of electric induction is negligible. This is justified by the relatively low frequencies ({\\ll }1 GHz) under which magnetostrictive materials usually work. The principal feature of the equations is the use of a magnetic potential (without much physical meaning) that allows a complete 'displacement' finite element formulation: all elastic, electric and magnetic nodal unknowns are zero derivatives. This allows the algorithm to be treated in a standard way, and important effects such as eddy currents can be obtained naturally. The formulation is implemented in the research finite element code FEAP. Although seven degrees of freedom per node is computer expensive to solve (especially for 3D problems), the current trend in the performance of computers, even personal ones, makes it worthwhile to build complete finite elements following the well-established (in mechanics
Gwinner, J; Thalhammer, M
The convergence of full discretisations by implicit Runge-Kutta and nonconforming Galerkin methods applied to nonlinear evolutionary inequalities is studied. The scope of applications includes differential inclusions governed by a nonlinear operator that is monotone and fulfills a certain growth condition. A basic assumption on the considered class of stiffly accurate Runge-Kutta time discretisations is a stability criterion which is in particular satisfied by the Radau IIA and Lobatto IIIC methods. In order to allow nonconforming hp-finite element approximations of unilateral constraints, set convergence of convex subsets in the sense of Glowinski-Mosco-Stummel is utilised. An appropriate formulation of the fully discrete variational inequality is deduced on the basis of a characteristic example of use, a Signorini-type initial-boundary value problem. Under hypotheses close to the existence theory of nonlinear first-order evolutionary equations and inequalities involving a monotone main part, a convergence result for the piecewise constant in time interpolant is established.
Ojdrovic, N.P.
1988-01-01
A unified procedure for the analysis of reinforced, partially prestressed, and prestressed concrete frames was formulated. Reinforced concrete is treated as a special case of prestressed concrete with zero prestressing force. A large variety of structures can be analyzed, from simple reinforced concrete beams, to reinforced or prestressed concrete frames, to structures whose various parts are made of different materials. Pretensioning and posttensioning with bonded and unbonded tendons are considered. The finite-element method based on the displacement formulation is used to solve the system of nonlinear equilibrium equations. Geometric and material nonlinearities are considered. Large displacements are accounted for using an updated Lagrangian formulation. The nonlinear behavior of concrete in compression is modeled using the Hognestad's parabola. Reinforcing steel is modeled as an elastic-perfectly plastic materials. To account for tension stiffening, a new model for the stress-strain relationship for concrete in tension is proposed. Results obtained in the numerical analyses show good agreement with experiments, although the proposed stress-strain model is based on only one concrete parameter, compressive strength.
Wang, Jaw-Lin; Shirazi-Adl, Aboulfazl; Parnianpour, Mohamad
2005-10-01
The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2-L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.
NASA Astrophysics Data System (ADS)
Kang, Dong-Keun; Kim, Chang-Wan; Yang, Hyun-Ik
2017-01-01
In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain-displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection
NASA Astrophysics Data System (ADS)
Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao
2016-11-01
This paper focuses on the development and engineering applications of a new resolvent sampling based Rayleigh-Ritz method (RSRR) for solving large-scale nonlinear eigenvalue problems (NEPs) in finite element analysis. There are three contributions. First, to generate reliable eigenspaces the resolvent sampling scheme is derived from Keldysh's theorem for holomorphic matrix functions following a more concise and insightful algebraic framework. Second, based on the new derivation a two-stage solution strategy is proposed for solving large-scale NEPs, which can greatly enhance the computational cost and accuracy of the RSRR. The effects of the user-defined parameters are studied, which provides a useful guide for real applications. Finally, the RSRR and the two-stage scheme is applied to solve two NEPs in the FE analysis of viscoelastic damping structures with up to 1 million degrees of freedom. The method is versatile, robust and suitable for parallelization, and can be easily implemented into other packages.
Townsend, Molly T; Sarigul-Klijn, Nesrin
2016-01-01
Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.
NASA Astrophysics Data System (ADS)
Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao
2017-02-01
This paper focuses on the development and engineering applications of a new resolvent sampling based Rayleigh-Ritz method (RSRR) for solving large-scale nonlinear eigenvalue problems (NEPs) in finite element analysis. There are three contributions. First, to generate reliable eigenspaces the resolvent sampling scheme is derived from Keldysh's theorem for holomorphic matrix functions following a more concise and insightful algebraic framework. Second, based on the new derivation a two-stage solution strategy is proposed for solving large-scale NEPs, which can greatly enhance the computational cost and accuracy of the RSRR. The effects of the user-defined parameters are studied, which provides a useful guide for real applications. Finally, the RSRR and the two-stage scheme is applied to solve two NEPs in the FE analysis of viscoelastic damping structures with up to 1 million degrees of freedom. The method is versatile, robust and suitable for parallelization, and can be easily implemented into other packages.
NASA Astrophysics Data System (ADS)
Al-Rousan, R. Z.
2015-09-01
The main objective of this study was to assess the effect of the number and schemes of carbon-fiber-reinforced polymer (CFRP) sheets on the capacity of bending moment, the ultimate displacement, the ultimate tensile strain of CFRP, the yielding moment, concrete compression strain, and the energy absorption of RC beams and to provide useful relationships that can be effectively utilized to determine the required number of CFRP sheets for a necessary increase in the flexural strength of the beams without a major loss in their ductility. To accomplish this, various RC beams, identical in their geometric and reinforcement details and having different number and configurations of CFRP sheets, are modeled and analyzed using the ANSYS software and a nonlinear finite-element analysis.
NASA Astrophysics Data System (ADS)
Joglekar, D. M.; Mitra, M.
2015-11-01
A breathing crack, due to its bilinear stiffness characteristics, modifies the frequency spectrum of a propagating dual-frequency elastic wave, and gives rise to sidebands around the probing frequency. This paper presents an analytical-numerical method to investigate such nonlinear frequency mixing resulting from the modulation effects induced by a breathing crack in 1D waveguides, such as axial rods and the Euler-Bernoulli beams. A transverse edge-crack is assumed to be present in both the waveguides, and the local flexibility caused by the crack is modeled using an equivalent spring approach. A simultaneous treatment of both the waveguides, in the framework of the Fourier transform based spectral finite element method, is presented for analyzing their response to a dual frequency excitation applied in the form of a tone-burst signal. The intermittent contact between the crack surfaces is accounted for by introducing bilinear contact forces acting at the nodes of the damage spectral element. Subsequently, an iterative approach is outlined for solving the resulting system of nonlinear simultaneous equations. Applicability of the proposed method is demonstrated by considering several test cases. The existence of sidebands and the higher order harmonics is confirmed in the frequency domain response of both the waveguides under investigation. A qualitative comparison with the previous experimental observations accentuates the utility of the proposed solution method. Additionally, the influence of the two constituent frequencies in the dual frequency excitation is assessed by varying the relative strengths of their amplitudes. A brief parametric study is performed for bringing out the effects of the relative crack depth and crack location on the degree of modulation, which is quantified in terms of the modulation parameter. Results of the present investigation can find their potential use in providing an analytical-numerical support to the studies geared towards the
Singh, Ashish Kumar; Chen, Bo-Yang; Tan, Vincent B C; Tay, Tong-Earn; Lee, Heow-Pueh
2017-02-01
Linear ultrasonics methods based on the principle of reflection, transmission, dissipation of sound waves have been traditionally used to detect delaminations in composite structures. However, when the delamination is in very early stages such that it is almost closed, or closed due to a compressive load, the linear methods may fail to detect such cases of delaminations. Nonlinear acoustics/ultrasonics have shown potential to identify damages in composite structures which are difficult to detect using conventional linear ultrasonic methods. The nonlinear method involves exciting the structure with a sinusoidal signal of certain (or multiple) frequency and observing the vibrations of the structure. The vibrations of the damage region differ significantly from intact regions and can be used to identify the damage. However due to the complex and varying nature of the nonlinear phenomena created by the interaction between the exciting signal and the damage, there are many variables at play which can lead to success or failure of the method. While experiments lead to the establishment of the method to be used as a damage detection technique, numerical simulations can help to explain the various phenomena associated with nonlinearity. This work presents a quick approach to model the nonlinear behavior caused by closed delaminations. The model is validated with a previously available approach for nonlinear vibrations modeling and a comparison is made between the two. The local nature of the nonlinearity enables to map out the area of damage in the structure. Additionally, a few parametric studies are performed to study the effect of various parameters related to the nonlinear phenomenon.
NASA Astrophysics Data System (ADS)
Abd El Baky, Hussien
This research work is devoted to theoretical and numerical studies on the flexural behaviour of FRP-strengthened concrete beams. The objectives of this research are to extend and generalize the results of simple experiments, to recommend new design guidelines based on accurate numerical tools, and to enhance our comprehension of the bond performance of such beams. These numerical tools can be exploited to bridge the existing gaps in the development of analysis and modelling approaches that can predict the behaviour of FRP-strengthened concrete beams. The research effort here begins with the formulation of a concrete model and development of FRP/concrete interface constitutive laws, followed by finite element simulations for beams strengthened in flexure. Finally, a statistical analysis is carried out taking the advantage of the aforesaid numerical tools to propose design guidelines. In this dissertation, an alternative incremental formulation of the M4 microplane model is proposed to overcome the computational complexities associated with the original formulation. Through a number of numerical applications, this incremental formulation is shown to be equivalent to the original M4 model. To assess the computational efficiency of the incremental formulation, the "arc-length" numerical technique is also considered and implemented in the original Bazant et al. [2000] M4 formulation. Finally, the M4 microplane concrete model is coded in FORTRAN and implemented as a user-defined subroutine into the commercial software package ADINA, Version 8.4. Then this subroutine is used with the finite element package to analyze various applications involving FRP strengthening. In the first application a nonlinear micromechanics-based finite element analysis is performed to investigate the interfacial behaviour of FRP/concrete joints subjected to direct shear loadings. The intention of this part is to develop a reliable bond--slip model for the FRP/concrete interface. The bond
Output-only identification of civil structures using nonlinear finite element model updating
NASA Astrophysics Data System (ADS)
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-03-01
This paper presents a novel approach for output-only nonlinear system identification of structures using data recorded during earthquake events. In this approach, state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with Bayesian Inference method to estimate (i) time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure, and (ii) the time history of the earthquake ground motion. To validate the performance of the proposed framework, the simulated responses of a bridge pier to an earthquake ground motion is polluted with artificial output measurement noise and used to jointly estimate the unknown material parameters and the time history of the earthquake ground motion. This proof-of-concept example illustrates the successful performance of the proposed approach even in the presence of high measurement noise.
Shih, Kao-Shang; Hsu, Ching-Chi; Hsu, Tzu-Pin; Hou, Sheng-Mou; Liaw, Chen-Kun
2014-02-01
Femoral shaft fractures can be treated using retrograde interlocking nailing systems; however, fracture nonunion still occurs. Dynamic fixation techniques, which remove either the proximal or distal locking screws, have been used to solve the problem of nonunion. In addition, a surgical rule for dynamic fixation techniques has been defined based on past clinical reports. However, the biomechanical performance of the retrograde interlocking nailing systems with either the traditional static fixation technique or the dynamic fixation techniques has not been investigated by using nonlinear numerical modeling. Three-dimensional nonlinear finite element models were developed, and the implant strength, fixation stability, and contact area of the fracture surfaces were evaluated. Three types of femoral shaft fractures (a proximal femoral shaft fracture, a middle femoral shaft fracture, and a distal femoral shaft fracture) fixed by three fixation techniques (insertion of all the locking screws, removal of the proximal locking screws, or removal of the distal locking screws) were analyzed. The results showed that the static fixation technique resulted in sufficient fixation stability and that the dynamic fixation techniques decreased the failure risk of the implant and produced a larger contact area of the fracture surfaces. The outcomes of the current study could assist orthopedic surgeons in comprehending the biomechanical performances of both static and dynamic fixation techniques. In addition, the surgeons could also select a fixation technique based on the specific patient situation using the numerical outcomes of this study.
1997-10-31
and Monte Cristo , off the Italian western coast." It was Monday, when people went to work, they read this news very sadly. The jet airliner was the...domain monte carlo for nonlinear response and sonic fatigue". 13th AIAA Aeroacoustics Conference, Paper 90-3938, Tallahassee, FL, October 1990. 89
MAGNA (Materially and Geometrically Nonlinear Analysis). Part I. Finite Element Analysis Manual.
1982-12-01
6.11.5 Midsurface Circumferential Stress Profiles in Clamped Circular Plate. 6.11.7 6.12.1 Simply-Supported Sandwich Plate Under Compression Load...that the element has nodes at the upper and lower surfaces, not at the shell midsurface . Each node point is permitted three translational degrees of...shell element can be of variable thickness, and the lateral boundaries of the element need not lie along the normal to the shell midsurface . The
NASA Astrophysics Data System (ADS)
Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan
2016-09-01
In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.
Constitutive Models for Nonlinear Finite Element Analysis of Masonry Prisms and Infill Walls
2008-03-01
based on a hyperbolic function proposed by Lotfi and Shing (1994), and is capable of modeling damage accumulation at mortar joints under increasing...loading and the effect that damage accumulation has on the modeling of the masonry infills. The re- view presented here discusses models that consider...nonlinear, plastic be- havior and damage effects resulting from masonry infill as an isotropic or orthotropic brittle or quasi-brittle material and/or
NASA Astrophysics Data System (ADS)
Çelebi, E.; Göktepe, F.; Karahan, N.
2012-11-01
The objective of this paper focuses primarily on the numerical approach based on two-dimensional (2-D) finite element method for analysis of the seismic response of infinite soil-structure interaction (SSI) system. This study is performed by a series of different scenarios that involved comprehensive parametric analyses including the effects of realistic material properties of the underlying soil on the structural response quantities. Viscous artificial boundaries, simulating the process of wave transmission along the truncated interface of the semi-infinite space, are adopted in the non-linear finite element formulation in the time domain along with Newmark's integration. The slenderness ratio of the superstructure and the local soil conditions as well as the characteristics of input excitations are important parameters for the numerical simulation in this research. The mechanical behavior of the underlying soil medium considered in this prediction model is simulated by an undrained elasto-plastic Mohr-Coulomb model under plane-strain conditions. To emphasize the important findings of this type of problems to civil engineers, systematic calculations with different controlling parameters are accomplished to evaluate directly the structural response of the vibrating soil-structure system. When the underlying soil becomes stiffer, the frequency content of the seismic motion has a major role in altering the seismic response. The sudden increase of the dynamic response is more pronounced for resonance case, when the frequency content of the seismic ground motion is close to that of the SSI system. The SSI effects under different seismic inputs are different for all considered soil conditions and structural types.
NASA Astrophysics Data System (ADS)
Mikhaylova, Alena
This study presents a comprehensive investigation of performance and behavior of steel-fiber reinforced concrete pipes (SFRCP). The main goal of this study is to develop the material constitutive model for steel fiber reinforced concrete used in dry-cast application. To accomplish this goal a range of pipe sizes varying from 15 in. (400 mm) to 48 in. (1200 mm) in diameter and fiber content of 0.17%, 0.25%, 0.33%, 0.5%, 0.67% and 83% by volume were produced. The pipes were tested in three-edge bearing condition to obtain the load-deformation response and overall performance of the pipe. The pipes were also subjected to hydrostatic joint and joint shear tests to evaluate the performance of the fiber-pipe joints for water tightness and under differential displacements, respectively. In addition, testing on hardened concrete was performed to obtain the basic mechanical material properties. High variation in the test results for material testing was identified as a part of experimental investigation. A three-dimensional non-linear finite element model of the pipe under the three edge bearing condition was developed to identify the constitutive material relations of fiber-concrete composite. A constitutive model of concrete implementing the concrete plasticity and continuum fracture mechanics was considered for defining the complex non-linear behavior of fiber-concrete. Three main concrete damage algorithms were examined: concrete brittle cracking, concrete damaged plasticity with adaptive meshing technique and concrete damaged plasticity with visco-plastic regularization. The latter was identified as the most robust and efficient to model the post-cracking behavior of fiber reinforced concrete and was used in the subsequent studies. The tension stiffening material constitutive law for composite concrete was determined by converging the FEM solution of load-deformation response with the results of experimental testing. This was achieved by iteratively modifying the non-linear
Finite elements for a beam system with nonlinear contact under periodic excitation
NASA Astrophysics Data System (ADS)
Hazim, H.; Rousselet, B.
Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each other; this may damage the structure. To prevent this, rubber snubbers are mounted at well chosen points of the structure; a prestress is applied to the snubber; but it is quite difficult to check the amount of prestress and the snubber may act only on one side; they will be modeled as one sided springs (see figure 2). In this article, some analysis for responses (displacements) in both time and frequency domains for a clamped-clamped Euler-Bernoulli beam model with a spring are presented. This spring can be unilateral or bilateral fixed at a point. The mounting (beam +spring) is fixed on a rigid support which has a sinusoidal motion of constant frequency. The system is also studied in the frequency domain by sweeping frequencies between two fixed values, in order to save the maximum of displacements corresponding to each frequency. Numerical results are compared with exact solutions in particular cases which already exist in the literature. On the other hand, a numerical and theoretical investigation of nonlinear normal mode (NNM) can be a new method to describe nonlinear behaviors, this work is in progress.
Horowitz, A; Sheinman, I; Lanir, Y
1988-02-01
A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.
2013-01-01
response (stress, internal state variables (ISVs)). The micromorphic continuum constitutive model will account for the inherent length scale of damaged ...2008, 56 (2), 297–335. 9. Regueiro, R. On finite strain micromorphic elastoplasticity . Int. J. Solids Struct. 2010, 47, 786–800. 10. Isbuga, V.; Regueiro
Thorvaldsen, Tom; Osnes, Harald; Sundnes, Joakim
2005-12-01
In this paper we present a mixed finite element method for modeling the passive properties of the myocardium. The passive properties are described by a non-linear, transversely isotropic, hyperelastic material model, and the myocardium is assumed to be almost incompressible. Single-field, pure displacement-based formulations are known to cause numerical difficulties when applied to incompressible or slightly compressible material cases. This paper presents an alternative approach in the form of a mixed formulation, where a separately interpolated pressure field is introduced as a primary unknown in addition to the displacement field. Moreover, a constraint term is included in the formulation to enforce (almost) incompressibility. Numerical results presented in the paper demonstrate the difficulties related to employing a pure displacement-based method, applying a set of physically relevant material parameter values for the cardiac tissue. The same problems are not experienced for the proposed mixed method. We show that the mixed formulation provides reasonable numerical results for compressible as well as nearly incompressible cases, also in situations of large fiber stretches. There is good agreement between the numerical results and the underlying analytical models.
Kulak, R. F.; Fiala, C.
1980-03-01
This report presents the formulations used in the NEPTUNE code. Specifically, it describes the finite-element formulation of a three-dimensional hexahedral element for simulating the behavior of either fluid or solid continua. Since the newly developed hexahedral element and the original triangular plate element are finite elements, they are compatible in the sense that they can be combined arbitrarily to simulate complex reactor components in three-dimensional space. Because rate-type constitutive relations are used in conjunction with a velocity-strain tensor, the formulation is applicable to large deformation problems. This development can be used to simulate (1) the fluid adjacent to reactor components and (2) the concrete fill found in large reactor head closures.
Finite elements and finite differences for transonic flow calculations
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley
1995-01-01
Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.
Puso, M; Maker, B N; Ferencz, R M; Hallquist, J O
2000-03-24
This report provides the NIKE3D user's manual update summary for changes made from version 3.0.0 April 24, 1995 to version 3.3.6 March 24,2000. The updates are excerpted directly from the code printed output file (hence the Courier font and formatting), are presented in chronological order and delineated by NIKE3D version number. NIKE3D is a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Thirty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a direct factorization method.
Finite element modeling and analysis of tires
NASA Technical Reports Server (NTRS)
Noor, A. K.; Andersen, C. M.
1983-01-01
Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.
Varga, Peter; Schwiedrzik, Jakob; Zysset, Philippe K; Fliri-Hofmann, Ladina; Widmer, Daniel; Gueorguiev, Boyko; Blauth, Michael; Windolf, Markus
2016-04-01
Osteoporotic proximal femur fractures are caused by low energy trauma, typically when falling on the hip from standing height. Finite element simulations, widely used to predict the fracture load of femora in fall, usually include neither mass-related inertial effects, nor the viscous part of bone׳s material behavior. The aim of this study was to elucidate if quasi-static non-linear homogenized finite element analyses can predict in vitro mechanical properties of proximal femora assessed in dynamic drop tower experiments. The case-specific numerical models of 13 femora predicted the strength (R(2)=0.84, SEE=540N, 16.2%), stiffness (R(2)=0.82, SEE=233N/mm, 18.0%) and fracture energy (R(2)=0.72, SEE=3.85J, 39.6%); and provided fair qualitative matches with the fracture patterns. The influence of material anisotropy was negligible for all predictions. These results suggest that quasi-static homogenized finite element analysis may be used to predict mechanical properties of proximal femora in the dynamic sideways fall situation.
Hoover, C G; DeGroot, A J; Sherwood, R J
2000-06-01
ParaDyn is a parallel version of the DYNA3D computer program, a three-dimensional explicit finite-element program for analyzing the dynamic response of solids and structures. The ParaDyn program has been used as a production tool for over three years for analyzing problems which range in size from a few tens of thousands of elements to between one-million and ten-million elements. ParaDyn runs on parallel computers provided by the Department of Energy Accelerated Strategic Computing Initiative (ASCI) and the Department of Defense High Performance Computing and Modernization Program. Preprocessing and post-processing software utilities and tools are designed to facilitate the generation of partitioned domains for processors on a massively parallel computer and the visualization of both resultant data and boundary data generated in a parallel simulation. This manual provides a brief overview of the parallel implementation; describes techniques for running the ParaDyn program, tools and utilities; and provides examples of parallel simulations.
NASA Technical Reports Server (NTRS)
Kaufman, A.; Laflen, J. H.; Lindholm, U. S.
1985-01-01
Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine components with particular application to isotropic materials used for high-pressure stage turbine blades and vanes. Forms or combinations of models independently proposed by Bodner and Walker were considered. These theories combine time-dependent and time-independent aspects of inelasticity into a continuous spectrum of behavior. This is in sharp contrast to previous classical approaches that partition inelastic strain into uncoupled plastic and creep components. Predicted stress-strain responses from these models were evaluated against monotonic and cyclic test results for uniaxial specimens of two cast nickel-base alloys, B1900+Hf and Rene' 80. Previously obtained tension-torsion test results for Hastelloy X alloy were used to evaluate multiaxial stress-strain cycle predictions. The unified models, as well as appropriate algorithms for integrating the constitutive equations, were implemented in finite-element computer codes.
NASA Technical Reports Server (NTRS)
Kaufman, A.; Laflen, J. H.; Lindholm, U. S.
1985-01-01
Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine components with particular application to isotropic materials used for high-pressure stage turbine blades and vanes. Forms or combinations of models independently proposed by Bodner and Walker were considered. These theories combine time-dependent and time-independent aspects of inelasticity into a continuous spectrum of behavior. This is in sharp contrast to previous classical approaches that partition inelastic strain into uncoupled plastic and creep components. Predicted stress-strain responses from these models were evaluated against monotonic and cyclic test results for uniaxial specimens of two cast nickel-base alloys, B1900+Hf and Rene 80. Previously obtained tension-torsion test results for Hastelloy X alloy were used to evaluate multiaxial stress-strain cycle predictions. The unified models, as well as appropriate algorithms for integrating the constitutive equations, were implemented in finite-element computer codes.
Klöppel, Thomas; Wall, Wolfgang A
2011-07-01
A novel finite element approach is presented to simulate the mechanical behavior of human red blood cells (RBC, erythrocytes). As the RBC membrane comprises a phospholipid bilayer with an intervening protein network, we propose to model the membrane with two distinct layers. The fairly complex characteristics of the very thin lipid bilayer are represented by special incompressible solid shell elements and an anisotropic viscoelastic constitutive model. Properties of the protein network are modeled with an isotropic hyperelastic third-order material. The elastic behavior of the model is validated with existing optical tweezers studies with quasi-static deformations. Employing material parameters consistent with literature, simulation results are in excellent agreement with experimental data. Available models in literature neglect either the surface area conservation of the RBC membrane or realistic loading conditions of the optical tweezers experiments. The importance of these modeling assumptions, that are both included in this study, are discussed and their influence quantified. For the simulation of the dynamic motion of RBC, the model is extended to incorporate the cytoplasm. This is realized with a monolithic fully coupled fluid-structure interaction simulation, where the fluid is described by the incompressible Navier-Stokes equations in an arbitrary Lagrangian Eulerian framework. It is shown that both membrane viscosity and cytoplasm viscosity have significant influence on simulation results. Characteristic recovery times and energy dissipation for varying strain rates in dynamic laser trap experiments are calculated for the first time and are found to be comparable with experimental data.
Adaptive finite element strategies for shell structures
NASA Technical Reports Server (NTRS)
Stanley, G.; Levit, I.; Stehlin, B.; Hurlbut, B.
1992-01-01
The present paper extends existing finite element adaptive refinement (AR) techniques to shell structures, which have heretofore been neglected in the AR literature. Specific challenges in applying AR to shell structures include: (1) physical discontinuities (e.g., stiffener intersections); (2) boundary layers; (3) sensitivity to geometric imperfections; (4) the sensitivity of most shell elements to mesh distortion, constraint definition and/or thinness; and (5) intrinsic geometric nonlinearity. All of these challenges but (5) are addressed here.
NASA Technical Reports Server (NTRS)
Ratcliffe, James G.; Krueger, Ronald
2006-01-01
One particular concern of polymer matrix composite laminates is the relatively low resistance to delamination cracking, in particular when the dominant type of failure is mode I opening. One method proposed for alleviating this problem involves the insertion pultruded carbon pins through the laminate thickness. The pins, known as z-pins, are inserted into the prepreg laminate using an ultrasonic hammer prior to the curing process, resulting in a field of pins embedded normal to the laminate plane as illustrated in Figure. 1. Pin diameters range between 0.28-mm to 0.5-mm and standard areal densities range from 0.5% to 4%. The z-pins are provided by the manufacturer, Aztex(Registered TradeMark) , in a low-density foam preform, which acts to stabilize orientation of the pins during the insertion process [1-3]. Typical pin materials include boron and carbon fibers embedded in a polymer matrix. A number of methods have been developed for predicting delamination growth in laminates reinforced with z-pins. During a study on the effect of z-pin reinforcement on mode I delamination resistance, finite element analyses of z-pin reinforced double cantilever beam (DCB) specimens were performed by Cartie and Partridge [4]. The z-pin bridging stresses were modeled by applying equivalent forces at the pin locations. Single z-pin pull-out tests were performed to characterize the traction law of the pins under mode I loading conditions. Analytical solutions for delamination growth in z-pin reinforced DCB specimens were independently derived by Robinson and Das [5] and Ratcliffe and O'Brien [6]. In the former case, pin bridging stresses were modeled using a distributed load and in the latter example the bridging stresses were discretely modeled by way of grounded springs. Additionally, Robinson and Das developed a data reduction strategy for calculating mode I fracture toughness, G(sub Ic), from a z-pin reinforced DCB specimen test [5]. In both cases a traction law similar to that
Zhang, Ning; Magland, Jeremy F.; Rajapakse, Chamith S.; Bhagat, Yusuf A.; Wehrli, Felix W.
2013-01-01
Purpose: Bone strength is the key factor impacting fracture risk. Assessment of bone strength from high-resolution (HR) images have largely relied on linear micro-finite element analysis (μFEA) even though failure always occurs beyond the yield point, which is outside the linear regime. Nonlinear μFEA may therefore be more informative in predicting failure behavior. However, existing nonlinear models applied to trabecular bone (TB) have largely been confined to micro-computed tomography (μCT) and, more recently, HR peripheral quantitative computed tomography (HR-pQCT) images, and typically have ignored evaluation of the post-yield behavior. The primary purpose of this work was threefold: (1) to provide an improved algorithm and program to assess TB yield as well as post-yield properties; (2) to explore the potential benefits of nonlinear μFEA beyond its linear counterpart; and (3) to assess the feasibility and practicality of performing nonlinear analysis on desktop computers on the basis of micro-magnetic resonance (μMR) images obtained in vivo in patients. Methods: A method for nonlinear μFE modeling of TB yield as well as post-yield behavior has been designed where material nonlinearity is captured by adjusting the tissue modulus iteratively according to the tissue-level effective strain obtained from linear analysis using a computationally optimized algorithm. The software allows for images at in vivo μMRI resolution as input with retention of grayscale information. Associations between axial stiffness estimated from linear analysis and yield as well as post-yield parameters from nonlinear analysis were investigated from in vivo μMR images of the distal tibia (N = 20; ages: 58–84) and radius (N = 20; ages: 50–75). Results: All simulations were completed in 1 h or less for 61 strain levels using a desktop computer (dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM). Although yield stress and ultimate stress correlated strongly (R2 > 0
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.
Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen; Ringler, Todd
2012-01-04
The numerical modeling of glacier and ice sheet evolution is a subject of growing interest, in part because of the potential for models to inform estimates of global sea level change. This paper focuses on the development of a numerical model that determines the velocity and pressure fields within an ice sheet. Our numerical model features a high-fidelity mathematical model involving the nonlinear Stokes system and combinations of no-sliding and sliding basal boundary conditions, high-order accurate finite element discretizations based on variable resolution grids, and highly scalable parallel solution strategies, all of which contribute to a numerical model that can achieve accurate velocity and pressure approximations in a highly efficient manner. We demonstrate the accuracy and efficiency of our model by analytical solution tests, established ice sheet benchmark experiments, and comparisons with other well-established ice sheet models.
Finite element shell instability analysis
NASA Technical Reports Server (NTRS)
1975-01-01
Formulation procedures and the associated computer program for finite element thin shell instability analysis are discussed. Data cover: (1) formulation of basic element relationships, (2) construction of solution algorithms on both the conceptual and algorithmic levels, and (3) conduction of numerical analyses to verify the accuracy and efficiency of the theory and related programs therein are described.
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.
1991-01-01
their midsurface counterparts due to the nature of the pin deflection and resulting load transfer. Linear elastic coupon radial stresses also followed... midsurface counterparts. The effects of the nonlinear elastic material behavior were quite evident when viewing the [(0/90)3,01, coupon intralaminar...to the midsurface of the coupon. The nonlinear elastic intralaminar shear stress-strain assumption acted to increase through thickness stresses
Improved finite element methodology for integrated thermal structural analysis
NASA Technical Reports Server (NTRS)
Dechaumphai, P.; Thornton, E. A.
1982-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.
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.
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.
Lundström, T; Jonas, T; Volkwein, A
2008-01-01
Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.
Jacobs, Nathan T; Cortes, Daniel H; Peloquin, John M; Vresilovic, Edward J; Elliott, Dawn M
2014-08-22
Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress-strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model's nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean ± 95% confidence interval) of the disc's nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc's full nonlinear response in multiple loading scenarios.
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
Whirley, R.G.; Engelmann, B.E.
1993-11-01
This report is the User Manual for the 1993 version of DYNA3D, and also serves as a User Guide. DYNA3D is a nonlinear, explicit, finite element code for analyzing the transient dynamic response of three-dimensional solids and structures. The code is fully vectorized and is available on several computer platforms. DYNA3D includes solid, shell, beam, and truss elements to allow maximum flexibility in modeling physical problems. Many material models are available to represent a wide range of material behavior, including elasticity, plasticity, composites, thermal effects, and rate dependence. In addition, DYNA3D has a sophisticated contact interface capability, including frictional sliding and single surface contact. Rigid materials provide added modeling flexibility. A material model driver with interactive graphics display is incorporated into DYNA3D to permit accurate modeling of complex material response based on experimental data. Along with the DYNA3D Example Problem Manual, this document provides the information necessary to apply DYNA3D to solve a wide range of engineering analysis problems.
Solution Techniques in Finite Element Analysis.
1983-05-01
CR 83.027 NAVAL CIVIL ENGINEERING LABORATORY Port Hueneme, California Sponsored by NAVAL FACILITIES ENGINEERING COMMAND ___ SOLUTION TECHNIQUES IN...CATALOG NUMBER CR 83.027 A bA/Z3 SZ *4 TITLE fori SoobIt, S TYPE F REP RT II PERIOD COVERED SOLUTION TECHNIQUES IN FINITE ELEMENT Not 192in Jna98 ANALYSIS...elements; nonlinear algebraic equations; numierical solution methods 20 ABSTRACT (Contlinue mI e.se mde It nc..Ac.. Wd ordonhifI, by block .- abe,) ,A
Harrison, Noel M; McDonnell, Pat; Mullins, Liam; Wilson, Niall; O'Mahoney, Denis; McHugh, Peter E
2013-04-01
Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage -1.16 %, tension damage 0.69 %, compression fracture -2.91 % and tension fracture 1.98 %. Ultimate strength and post-ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile-brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post-ultimate strength softening.
The Relation of Finite Element and Finite Difference Methods
NASA Technical Reports Server (NTRS)
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Finite element modeling of permanent magnet devices
NASA Astrophysics Data System (ADS)
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
Finite element concepts in computational aerodynamics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1978-01-01
Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.
NASA Technical Reports Server (NTRS)
Witkop, D. L.; Dale, B. J.; Gellin, S.
1991-01-01
The programming aspects of SFENES are described in the User's Manual. The information presented is provided for the installation programmer. It is sufficient to fully describe the general program logic and required peripheral storage. All element generated data is stored externally to reduce required memory allocation. A separate section is devoted to the description of these files thereby permitting the optimization of Input/Output (I/O) time through efficient buffer descriptions. Individual subroutine descriptions are presented along with the complete Fortran source listings. A short description of the major control, computation, and I/O phases is included to aid in obtaining an overall familiarity with the program's components. Finally, a discussion of the suggested overlay structure which allows the program to execute with a reasonable amount of memory allocation is presented.
Generic element processor (application to nonlinear analysis)
NASA Technical Reports Server (NTRS)
Stanley, Gary
1989-01-01
The focus here is on one aspect of the Computational Structural Mechanics (CSM) Testbed: finite element technology. The approach involves a Generic Element Processor: a command-driven, database-oriented software shell that facilitates introduction of new elements into the testbed. This shell features an element-independent corotational capability that upgrades linear elements to geometrically nonlinear analysis, and corrects the rigid-body errors that plague many contemporary plate and shell elements. Specific elements that have been implemented in the Testbed via this mechanism include the Assumed Natural-Coordinate Strain (ANS) shell elements, developed with Professor K. C. Park (University of Colorado, Boulder), a new class of curved hybrid shell elements, developed by Dr. David Kang of LPARL (formerly a student of Professor T. Pian), other shell and solid hybrid elements developed by NASA personnel, and recently a repackaged version of the workhorse shell element used in the traditional STAGS nonlinear shell analysis code. The presentation covers: (1) user and developer interfaces to the generic element processor, (2) an explanation of the built-in corotational option, (3) a description of some of the shell-elements currently implemented, and (4) application to sample nonlinear shell postbuckling problems.
A hybrid transfinite element approach for nonlinear transient thermal analysis
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
A new computational approach for transient nonlinear thermal analysis of structures is proposed. It is a hybrid approach which combines the modeling versatility of contemporary finite elements in conjunction with transform methods and classical Bubnov-Galerkin schemes. The present study is limited to nonlinearities due to temperature-dependent thermophysical properties. Numerical test cases attest to the basic capabilities and therein validate the transfinite element approach by means of comparisons with conventional finite element schemes and/or available solutions.
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.
SUPG Finite Element Simulations of Compressible Flows
NASA Technical Reports Server (NTRS)
Kirk, Brnjamin, S.
2006-01-01
The Streamline-Upwind Petrov-Galerkin (SUPG) finite element simulations of compressible flows is presented. The topics include: 1) Introduction; 2) SUPG Galerkin Finite Element Methods; 3) Applications; and 4) Bibliography.
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)
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.
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.
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
Linear and Nonlinear Finite Elements.
1983-12-01
1 ’’ wht ( ) d/d:- Two cat.us point jit egral ibn of n( C) i" (. .1) over the teth c eneent resuils ill the approximation 2 l - -’ -1 " 2 ’ ai ’ 4...free beam we set it in motion with the initial velocities i 0 =O and yo=a[cosAs+coshAs+a( sinAs +sinhAs) (36) where A = 4.7300408 and where sin A -sin-A
NASA Technical Reports Server (NTRS)
Aminpour, Mohammad
1995-01-01
The work reported here pertains only to the first year of research for a three year proposal period. As a prelude to this two dimensional interface element, the one dimensional element was tested and errors were discovered in the code for built-up structures and curved interfaces. These errors were corrected and the benchmark Boeing composite crown panel was analyzed successfully. A study of various splines led to the conclusion that cubic B-splines best suit this interface element application. A least squares approach combined with cubic B-splines was constructed to make a smooth function from the noisy data obtained with random error in the coordinate data points of the Boeing crown panel analysis. Preliminary investigations for the formulation of discontinuous 2-D shell and 3-D solid elements were conducted.
NASA Technical Reports Server (NTRS)
Aguirre-Ramirez, G.; Oden, J. T.
1969-01-01
Finite element method applied to heat conduction in solids with temperature dependent thermal conductivity, using nonlinear constitutive equation for heat ABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGHIABCDEFGH
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.
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.
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Biffle, J.H.
1993-02-01
JAC3D is a three-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equation. The method is implemented in a three-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. An eight-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic-plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; Rossi, Simone
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.
Scovazzi, Guglielmo; Carnes, Brian; Zeng, Xianyi; ...
2015-11-12
Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear andmore » nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.« less
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide).
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.
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
NASA Technical Reports Server (NTRS)
Arya, Vinod K.; Halford, Gary R.
1993-01-01
The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.
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.
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.
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Spilker, R. L.; Witmer, E. A.; French, S. E.; Rodal, J. J. A.
1980-01-01
Two computer programs are described for predicting the transient large deflection elastic viscoplastic responses of thin single layer, initially flat unstiffened or integrally stiffened, Kirchhoff-Lov ductile metal panels. The PLATE 1 program pertains to structural responses produced by prescribed externally applied transient loading or prescribed initial velocity distributions. The collision imparted velocity method PLATE 1 program concerns structural responses produced by impact of an idealized nondeformable fragment. Finite elements are used to represent the structure in both programs. Strain hardening and strain rate effects of initially isotropic material are considered.
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.
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.
Books and monographs on finite element technology
NASA Technical Reports Server (NTRS)
Noor, A. K.
1985-01-01
The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.
Finite element analysis for acoustic characteristics of a magnetostrictive transducer
NASA Astrophysics Data System (ADS)
Kim, Jaehwan; Jung, Eunmi
2005-12-01
This paper presents a finite element analysis for a magnetostrictive transducer by taking into account the nonlinear behavior of the magnetostrictive material and fluid interaction. A finite element formulation is derived for the coupling of magnetostrictive and elastic materials based upon a separated magnetic and displacement field calculation and a curve fitting technique of material properties. The fluid and structure coupled problem is taken into account based upon pressure and velocity potential fields formulation. Infinite wave envelope elements are introduced at an artificial boundary to deal with the infinite fluid domain. A finite element code for the analysis of a magnetostrictive transducer is developed. A magnetostrictive tonpilz transducer is taken as an example and verification for the developed program is made by comparing with a commercial code. The acoustic characteristics of the magnetostrictive tonpilz transducer are calculated in terms of radiation pattern and transmitted current response.
Differentiating a Finite Element Biodegradation Simulation Model for Optimal Control
NASA Astrophysics Data System (ADS)
Minsker, Barbara S.; Shoemaker, Christine A.
1996-01-01
An optimal control model for improving the design of in situ bioremediation of groundwater has been developed. The model uses a finite element biodegradation simulation model called Bio2D to find optimal pumping strategies. Analytical derivatives of the bioremediation finite element model are derived; these derivatives must be computed for the optimal control algorithm. The derivatives are complex and nonlinear; the bulk of the computational effort in solving the optimal control problem is required to calculate the derivatives. An overview of the optimal control and simulation model formulations is also given.
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.
Optimizing header strength utilizing finite element analyses
NASA Astrophysics Data System (ADS)
Burchett, S. N.
Finite element techniques have been successfully applied as a design tool in the optimization of high strength headers for pyrotechnic-driven actuators. These techniques have been applied to three aspects of the design process of a high strength header. The design process was a joint effort of experts from several disciplines including design engineers, material scientists, test engineers, manufacturing engineers, and structural analysts. Following material selection, finite element techniques were applied to evaluate the residual stresses due to manufacturing which were developed in the high strength glass ceramic-to-metal seal headers. Results from these finite element analyses were used to identify header designs which were manufacturable and had a minimum residual stress state. Finite element techniques were than applied to obtain the response of the header due to pyrotechnic burn. The results provided realistic upper bounds on the pressure containment ability of various preliminary header designs and provided a quick and inexpensive method of strengthening and refining the designs. Since testing of the headers was difficult and sometimes destructive, results of the analyses were also used to interpret test results and identify failure modes. In this paper, details of the finite element element techniques including the models used, material properties, material failure models, and loading will be presented. Results from the analyses showing the header failure process will also be presented. This paper will show that significant gains in capability and understanding can result when finite element techniques are included as an integral part of the design process of complicated high strength headers.
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.
Quadratic finite elements and incompressible viscous flows.
Dohrmann, Clark R.; Gartling, David K.
2005-01-01
Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.
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.
Stabilized Finite Elements in FUN3D
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
Nonlinear Conservation Laws and Finite Volume Methods
NASA Astrophysics Data System (ADS)
Leveque, Randall J.
Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
VALIDATION OF ANSYS FINITE ELEMENT ANALYSIS SOFTWARE
HAMM, E.R.
2003-06-27
This document provides a record of the verification and Validation of the ANSYS Version 7.0 software that is installed on selected CH2M HILL computers. The issues addressed include: Software verification, installation, validation, configuration management and error reporting. The ANSYS{reg_sign} computer program is a large scale multi-purpose finite element program which may be used for solving several classes of engineering analysis. The analysis capabilities of ANSYS Full Mechanical Version 7.0 installed on selected CH2M Hill Hanford Group (CH2M HILL) Intel processor based computers include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses and various types of field and coupled-field applications. The program contains many special features which allow nonlinearities or secondary effects to be included in the solution, such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and thermal radiation. The ANSYS program has been in commercial use since 1970, and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil and steel industries.
An iterative algorithm for finite element analysis
NASA Astrophysics Data System (ADS)
Laouafa, F.; Royis, P.
2004-03-01
In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the GMRES algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration.
Model Reduction of Viscoelastic Finite Element Models
NASA Astrophysics Data System (ADS)
Park, C. H.; Inman, D. J.; Lam, M. J.
1999-01-01
This paper examines a method of adding viscoelastic properties to finite element models by using additional co-ordinates to account for the frequency dependence usually associated with such damping materials. Several such methods exist and all suffer from an increase in order of the final finite model which is undesirable in many applications. Here we propose to combine one of these methods, the GHM (Golla-Hughes-McTavish) method, with model reduction techniques to remove the objection of increased model order. The result of combining several methods is an ability to add the effects of visoelastic components to finite element or other analytical models without increasing the order of the system. The procedure is illustrated by a numerical example. The method proposed here results in a viscoelastic finite element of a structure without increasing the order of the original model.
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 class of finite dimensional optimal nonlinear estimators
NASA Technical Reports Server (NTRS)
Marcus, S. I.; Willsky, A. S.
1974-01-01
Finite dimensional optimal nonlinear state estimators are derived for bilinear systems evolving on nilpotent and solvable Lie groups. These results are extended to other classes of systems involving polynomial nonlinearities. The concepts of exact differentials and path-independent integrals are used to derive optimal finite dimensional estimators for a further class of nonlinear systems.
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.
The GPRIME approach to finite element modeling
NASA Technical Reports Server (NTRS)
Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.
1983-01-01
GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data.
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.
Waveguide finite elements for curved structures
NASA Astrophysics Data System (ADS)
Finnveden, Svante; Fraggstedt, Martin
2008-05-01
A waveguide finite element formulation for the analysis of curved structures is introduced. The formulation is valid for structures that along one axis have constant properties. It is based on a modified Hamilton's principle valid for general linear viscoelastic motion, which is derived here. Using this principle, material properties such as losses may be distributed in the system and may vary with frequency. Element formulations for isoparametric solid elements and deep shell elements are presented for curved waveguides as well as for straight waveguides. In earlier works, the curved elements have successfully been used to model a passenger car tyre. Here a simple validation example and convergence study is presented, which considers a finite length circular cylinder and all four elements presented are used, in turn, to model this structure. Calculated results compare favourably to those in the literature.
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Exact finite elements for conduction and convection
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.
Zhang, Ning; Magland, Jeremy F.; Rajapakse, Chamith S.; Lam, ShingChun Benny
2013-01-01
Rationale and Objectives To assess the performance of a nonlinear micro-finite element model on predicting trabecular bone (TB) yield and post-yield behavior based on high-resolution in-vivo MR images via the serial reproducibility. Materials and Methods The nonlinear model captures material nonlinearity by iteratively adjusting tissue-level modulus based on tissue-level effective strain. It enables simulations of TB yield and post-yield behavior from micro-MR images at in-vivo resolution by solving a series of nonlinear systems via an iterative algorithm on a desktop computer. Measures of mechanical competence (yield strain/strength, ultimate strain/strength, modulus of resilience and toughness) were estimated at the distal radius of pre- and postmenopausal women (N=20; age 50–75) in whom osteoporotic fractures typically occur. Each subject underwent three scans (20.2±14.5 days). Serial reproducibility was evaluated via coefficients of variation (CV) and intra-class correlation coefficient (ICC). Results Nonlinear simulations were completed in an average of 14 minutes per 3D image data set involving analysis of 61 strain levels. The predicted yield strain/strength, ultimate strain/strength, modulus of resilience and toughness had a mean value of 0.78%, 3.09 MPa, 1.35%, 3.48 MPa, 14.30 kPa and 32.66 kPa, respectively, covering a substantial range by a factor of up to four. ICC ranged from 0.986 to 0.994 (average 0.991); CV ranged from 1.01% to 5.62% (average 3.6%), with yield strain and toughness having the lowest and highest CV values, respectively. Conclusion The data suggest that the yield and post-yield parameters have adequate reproducibility to evaluate treatment effects in interventional studies within short follow-up periods. PMID:24200486
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.
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 Analysis of Pipe Elbows.
1980-02-01
AD-AO81 077 DAVD TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/B 13/11 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS .(U) FE SO M S MARCUS, B C...TAYLOR NAVAL SHIP i RESEARCH AND DEVELOPMENT CENTER Bethesda, Md. 20084 4 FINITE ELEMENT ANALYSIS OF PIPE ELBOWS by 0 Melvyn S. Marcus and Gordon C...a 90-degree pipe elbow to determine principal stresses due to internal pressure, inplane bending, out-of-plane bending, and torsion moment loadings
Finite Element Model to Reduce Fire and Blast Vulnerability
2013-01-01
Finite Element Analysis FEM Finite Element Model NAVAIR...and probabilistic analysis are need to address these challenges. The objective of this effort is to develop a finite element model of a soldier to...UNCLASSIFIED FINITE ELEMENT MODEL TO REDUCE FIRE AND BLAST VULNERABILITY INTERIM REPORT TFLRF No. 439 by W. Loren Francis
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.
Life assessment of structural components using inelastic finite element analyses
NASA Technical Reports Server (NTRS)
Arya, Vinod K.; Halford, Gary R.
1993-01-01
The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.
Life assessment of structural components using inelastic finite element analyses
NASA Astrophysics Data System (ADS)
Arya, Vinod K.; Halford, Gary R.
1993-10-01
The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.
Finite element simulation of thick sheet thermoforming
NASA Astrophysics Data System (ADS)
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
NASA Astrophysics Data System (ADS)
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
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 wavelets with improved quantitative properties
NASA Astrophysics Data System (ADS)
Nguyen, Hoang; Stevenson, Rob
2009-08-01
In [W. Dahmen, R. Stevenson, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37 (1) (1999) 319-352 (electronic)], finite element wavelets were constructed on polygonal domains or Lipschitz manifolds that are piecewise parametrized by mappings with constant Jacobian determinants. The wavelets could be arranged to have any desired order of cancellation properties, and they generated stable bases for the Sobolev spaces Hs for (or s<=1 on manifolds). Unfortunately, it appears that the quantitative properties of these wavelets are rather disappointing. In this paper, we modify the construction from the above-mentioned work to obtain finite element wavelets which are much better conditioned.
Efficient linear and nonlinear heat conduction with a quadrilateral element
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.
1984-01-01
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
Finite element model for brittle fracture and fragmentation
Li, Wei; Delaney, Tristan J.; Jiao, Xiangmin; ...
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.
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.
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.
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.
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.
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.
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.
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 Heat & Mass Transfer Code
Trease, Lynn
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; and double porosity and double porosity/double permeability capabilities.
Finite Element Analysis of Piping Tees.
1980-06-01
Combustion Engineering, Inc., performed an experimental stress analysis3 on an ANSI B16.9 carbon steelt tee designated T-12. Pipe extensions were welded to...AD-ASS? 353 DAVID If TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE--ETC F/S 13/11 FINITE ELEENT ANALYSIS OF PIPING TEES.(U) JUN 8 A J QUEZON. S C...DAVID W. TAYLOR NAVAL SHIP SRESEARCH AND DEVELOPMENT CENTER Bethesa Md. 20084 FINITE ELEMENT ANALYSIS OF PIPING TEES by Antonio J. Quezon, Gordon C
Nonlinear/linear unified thermal stress formulations - Transfinite element approach
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
A new unified computational approach for applicability to nonlinear/linear thermal-structural problems is presented. Basic concepts of the approach including applicability to nonlinear and linear thermal structural mechanics are first described via general formulations. Therein, the approach is demonstrated for thermal stress and thermal-structural dynamic applications. The proposed transfinite element approach focuses on providing a viable hybrid computational methodology by combining the modeling versatility of contemporary finite element schemes in conjunction with transform techniques and the classical Bubnov-Galerkin schemes. Comparative samples of numerical test cases highlight the capabilities of the proposed concepts.
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.
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.
Discontinuous Galerkin finite element solution for poromechanics
NASA Astrophysics Data System (ADS)
Liu, Ruijie
This dissertation focuses on applying discontinuous Galerkin (DG) methods to poromechanics problems. A few challenges have been presented in traditional and popular continuous Galerkin (CG) finite element methods for solving complex coupled thermal, flow and solid mechanics. For example, nonphysical pore pressure oscillations often occur in CG solutions for poroelasticity problems with low permeability. A robust and practical numerical scheme for removing or alleviating the oscillation is not available. In modeling thermoporoelastoplasticity, CG methods require the use of very small time steps to obtain a convergent solution. The temperature profile predicted by CG methods in the fine mesh zones is often seriously polluted by large errors produced in coarse mesh zones in the case where the convection dominates the thermal process. The nonphysical oscillations in pore pressure and temperature solutions induced by CG methods at very early time stages seriously corrupt the solutions at longer time. We propose DG methods to handle these challenges because they are physics driven, provide local conservation of mass and momentum, have high stability and robustness, are locking-free, and because of their meshing and implementation capabilities. We first apply a family of DG methods, including Oden-Babuska-Baumann (OBB), Nonsymmetric Interior Penalty Galerkin (NIPG), Symmetric Interior Penalty Galerkin (SIPG) and Incomplete Interior Penalty Galerkin (IIPG), to 3D linear elasticity problems. This family of DG methods is tested and evaluated by using a cantilever beam problem with nearly incompressible materials. It is shown that DG methods are simple, robust and locking-free in dealing with nearly incompressible materials. Based on the success of DG methods in elasticity, we extend the DG theory into plasticity problems. A DG formulation has been implemented for solving 3D poroelasticity problems with low permeability. Numerical examples solved by DG methods demonstrate
Finite element modelling of SAW correlator
NASA Astrophysics Data System (ADS)
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
EC Vacuum Vessel Finite Element Analysis
Rudland, D.; Luther, R.; /Fermilab
1992-02-04
This Note contains a summary of the results of the finite element analysis of the EC Cryostat vacuum vessel performed by Dave Rudland in 1987. The results are used in the structural evaluation of the EC cryostats presented in Engineering Note 194. It should also be noted that the adequacy of the design of the vacuum vessels was reviewed and verified by the Battelle Memorial Institute. Battelle used a shell of revolution program to essentially duplicate the FEA analysis with similar results. It should be noted that no plots of the finite element mesh were retained from the analysis, and these can not be easily reproduced due to a change in the version of the ANSYS computer program shortly after the analysis was completed.
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
Sanford, L. A.; Hallquist, J. O.
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 forces 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.
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 Methods: Principles for Their Selection.
1983-02-01
the finite element methods. 39 Various statements in the literature that certain mixed methods work well inspite of the fact that the LBB (BB...method, displacement and mixed methods , various adaptive approaches, etc. The examples discussed in Sections 2 and 3 show that the same computational...performance and their relation to mixed methods , SIAM J. Num. Anal., to appear. 5. F. Brezzi, On the existence uniqueness and approximation of saddle-point
Finite Element Output Bounds for Hyperbolic Problems
Machiels, L.
2000-03-27
We propose a Neumann-subproblem a posteriori finite element error bound technique for linear stationary scalar advection problems. The method is similar in many respects to the previous output bound technique developed for elliptic problems. In the new approach, however, the primal residual is enhanced with a streamline diffusion term. We first formulate the bound algorithm, with particular emphasis on the proof of the bounding properties; then, we provide numerical results for an illustrative example.
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 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.
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.
Transient finite element method using edge elements for moving conductor
Tani, Koji; Nishio, Takayuki; Yamada, Takashi ); Kawase, Yoshihiro . Dept. of Information Science)
1999-05-01
For the next generation of high speed railway systems and automobiles new braking systems are currently under development. These braking systems take into account the eddy currents, which are produced by the movement of the conductor in the magnetic field. For their optimum design, it is necessary to know the distribution of eddy currents in the moving conductor. The finite element method (FEM) is often used to simulate them. Here, transient finite element method using edge elements for moving conductor is presented. Here the magnetic vector potential is interpolated at the upwind position and the time derivative term is discretized by the backward difference method. As a result, the system matrix becomes symmetric and the ICCG method is applicable to solve the matrix. This method is used to solve an eddy current rail brake system. The results demonstrate that this approach is suitable to solve transient problems involving movement.
Efficient linear and nonlinear heat conduction with a quadrilateral element
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.
1983-01-01
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2, and 1 for the normalized stabilization parameter lead to the 5-point, 9-point finite difference, and fully integrated finite element operators, respectively, for rectangular meshes and have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
Finite element modeling of lipid bilayer membranes
NASA Astrophysics Data System (ADS)
Feng, Feng; Klug, William S.
2006-12-01
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.
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.
Gauge finite element method for incompressible flows
NASA Astrophysics Data System (ADS)
E, Weinan; Liu, Jian-Guo
2000-12-01
A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J-G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher-order) finite elements. This method can achieve high-order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright
Edge-based finite element method for shallow water equations
NASA Astrophysics Data System (ADS)
Ribeiro, F. L. B.; Galeão, A. C.; Landau, L.
2001-07-01
This paper describes an edge-based implementation of the generalized residual minimum (GMRES) solver for the fully coupled solution of non-linear systems arising from finite element discretization of shallow water equations (SWEs). The gain in terms of memory, floating point operations and indirect addressing is quantified for semi-discrete and space-time analyses. Stabilized formulations, including Petrov-Galerkin models and discontinuity-capturing operators, are also discussed for both types of discretization. Results illustrating the quality of the stabilized solutions and the advantages of using the edge-based approach are presented at the end of the paper. Copyright
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.
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.
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.
Bounds on nonlinear motion for a finite time
Warnock, R.L.; Ruth, R.D.
1989-06-01
Recent improvements in numerical methods to compute canonical transformations make it feasible to set interesting bounds on the motion of nonlinear Hamiltonian systems over a finite interval of time. 7 refs.
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
NASA Technical Reports Server (NTRS)
Aberson, J. A.; Anderson, J. M.
1973-01-01
The recent introduction of special crack-tip singularity elements, usually referred to as cracked elements, has brought the power and flexibility of the finite-element method to bear much more effectively on fracture mechanics problems. This paper recalls the development of two cracked elements and presents the results of some applications proving their accuracy and economy. Judging from the available literature on numerical methods in fracture mechanics, it seems clear that the elements described have been used more extensively than any others in practical fracture mechanics applications.
Finite element analysis of hysteresis effects in piezoelectric transducers
NASA Astrophysics Data System (ADS)
Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard
2000-06-01
The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Tariqul Islam, Md.; Sturkell, Erik; Sigmundsson, Freysteinn; Drouin, Vincent Jean Paul B.; Ófeigsson, Benedikt G.
2014-05-01
Iceland is located on the mid Atlantic ridge, where the spreading rate is nearly 2 cm/yr. The high rate of magmatism in Iceland is caused by the interaction between the Iceland hotspot and the divergent mid-Atlantic plate boundary. Iceland hosts about 35 volcanoes or volcanic systems that are active. Most of these are aliened along the plate boundary. The best studied magma chamber of central volcanoes (e.g., Askja, Krafla, Grimsvötn, Katla) have verified (suggested) a shallow magma chamber (< 5 km), which has been model successfully with a Mogi source, using elastic and/or elastic-viscoelastic half-space. Maxwell and Newtonian viscosity is mainly considered for viscoelastic half-space. Therefore, rheology may be oversimplified. Our attempt is to study deformation of the Askja volcano together with plate spreading in Iceland using temperature-dependent non-linear rheology. It offers continuous variation of rheology, laterally and vertically from rift axis and surface. To implement it, we consider thermo-mechanic coupling models where rheology follows dislocation flow in dry condition based on a temperature distribution. Continuous deflation of the Askja volcanic system is associated with solidification of magma in the magma chamber and post eruption relaxation. A long time series of levelling data show its subsidence trend to exponentially. In our preliminary models, a magma chamber at 2.8 km depth with 0.5 km radius is introduced at the ridge axis as a Mogi source. Simultaneously far field of rift axis stretching by 18.4 mm/yr (measured during 2007 to 20013) is applied to reproduce plate spreading. Predicted surface deformation caused of combined effect of tectonic-volcanic activities is evaluated with GPS during 2003-2009 and RADARSAT InSAR data during 2000 to 2010. During 2003-2009, data from the GPS site OLAF (close to the centre of subsidence) shows average rate of subsidence 19±1 mm/yr relative to the ITRF2005 reference frame. The MASK (Mid ASKJA) site is
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.
NASA Technical Reports Server (NTRS)
Abdul-Aziz, Ali; Baaklini, George Y.; Zagidulin, Dmitri; Rauser, Richard W.
2000-01-01
Capabilities and expertise related to the development of links between nondestructive evaluation (NDE) and finite element analysis (FEA) at Glenn Research Center (GRC) are demonstrated. Current tools to analyze data produced by computed tomography (CT) scans are exercised to help assess the damage state in high temperature structural composite materials. A utility translator was written to convert velocity (an image processing software) STL data file to a suitable CAD-FEA type file. Finite element analyses are carried out with MARC, a commercial nonlinear finite element code, and the analytical results are discussed. Modeling was established by building MSC/Patran (a pre and post processing finite element package) generated model and comparing it to a model generated by Velocity in conjunction with MSC/Patran Graphics. Modeling issues and results are discussed in this paper. The entire process that outlines the tie between the data extracted via NDE and the finite element modeling and analysis is fully described.
A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations
NASA Technical Reports Server (NTRS)
Hu, Changqing; Shu, Chi-Wang
1998-01-01
In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.
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 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.
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 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.
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.
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.
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.
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.
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.
NASA Technical Reports Server (NTRS)
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
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.
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).
Patient-specific finite element modeling of bones.
Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A
2013-04-01
Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.
Efficient finite element modeling of elastodynamic scattering
NASA Astrophysics Data System (ADS)
Wilcox, Paul D.; Velichko, Alexander
2009-03-01
The scattering of elastic waves by defects is the physical basis of ultrasonic NDE. Although analytical models exist for some canonical problems, the general case of scattering from an arbitrarily-shaped defect requires numerical methods such as finite elements (FE). In this paper, a robust and efficient FE technique is presented that is based on the premise of meshing a relatively small domain sufficient to enclose the scatterer. Plane waves are then excited from a particular direction by a numerical implementation of the Helmholtz-Kirchhoff integral that uses an encircling array of uni-modal point sources. The scattered field displacements are recorded at the same points and the field decomposed into plane waves of different modes at different angles. By repeating this procedure for different incident angles it is possible to generate the scattering- or S-matrix for the scatterer. For a given size of scatterer, all the information in an S-matrix can be represented in the Fourier domain by a limited number of complex coefficients. Thus the complete scattering behavior of an arbitrary-shaped scatterer can be characterized by a finite number of complex coefficients, that can be obtained from a relatively small number of FE model executions.
Inversion of Robin coefficient by a spectral stochastic finite element approach
Jin Bangti Zou Jun
2008-03-01
This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.
Compressible seal flow analysis using the finite element method with Galerkin solution technique
NASA Technical Reports Server (NTRS)
Zuk, J.
1974-01-01
High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.
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.
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.
Adaptive finite element methods in electrochemistry.
Gavaghan, David J; Gillow, Kathryn; Süli, Endre
2006-12-05
In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.
Evaluation of the use of a singularity element in finite element analysis of center-cracked plates
NASA Technical Reports Server (NTRS)
Mendelson, A.; Gross, B.; Srawley, J., E.
1972-01-01
Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.
A finite element method for analysis of vibration induced by maglev trains
NASA Astrophysics Data System (ADS)
Ju, S. H.; Ho, Y. S.; Leong, C. C.
2012-07-01
This paper developed a finite element method to perform the maglev train-bridge-soil interaction analysis with rail irregularities. An efficient proportional integral (PI) scheme with only a simple equation is used to control the force of the maglev wheel, which is modeled as a contact node moving along a number of target nodes. The moving maglev vehicles are modeled as a combination of spring-damper elements, lumped mass and rigid links. The Newmark method with the Newton-Raphson method is then used to solve the nonlinear dynamic equation. The major advantage is that all the proposed procedures are standard in the finite element method. The analytic solution of maglev vehicles passing a Timoshenko beam was used to validate the current finite element method with good agreements. Moreover, a very large-scale finite element analysis using the proposed scheme was also tested in this paper.
NASA Technical Reports Server (NTRS)
Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.
1989-01-01
The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.
NASA Technical Reports Server (NTRS)
Chiang, C. K.; Xue, David Y.; Mei, Chuh
1993-01-01
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.
Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element
NASA Technical Reports Server (NTRS)
Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.
2010-01-01
Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and finite element results.
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.
Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications
NASA Technical Reports Server (NTRS)
Johnston, John D.; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.
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.
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.
Leukocyte deformability: finite element modeling of large viscoelastic deformation.
Dong, C; Skalak, R
1992-09-21
An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.
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.
Leapfrog/Finite Element Method for Fractional Diffusion Equation
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L 2-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis. PMID:24955431
Finite-difference and finite-volume methods for nonlinear standing ultrasonic waves in fluid media.
Vanhille, C; Conde, C; Campos-Pozuelo, C
2004-04-01
In the framework of the application of high-power ultrasonics in industrial processing in fluid media, the mathematical prediction of the acoustical parameters inside resonators should improve the development of practical systems. This can be achieved by the use of numerical tools able to treat the nonlinear acoustics involved in these phenomena. In particular, effects like nonlinear distortion and nonlinear attenuation are fundamental in applications. In this paper, three one-dimensional numerical models in the time domain for calculating the nonlinear acoustic field inside a one-dimensional resonant cavity are presented and compared. They are based on the finite-difference and the finite-volume methods. These different algorithms solve the differential equations, from the linear up to the strongly nonlinear case (including weak shock). Some physical results obtained from the modelling of ultrasonic waves and a comparison of the efficiency of the different algorithms are presented.
Finite element (MARC) solution technologies for viscoplastic analyses
NASA Technical Reports Server (NTRS)
Arya, V. K.; Thompson, Robert L.
1988-01-01
A need for development of realistic constitutive models for structural components operating at high temperatures, accompanied by appropriate solution technologies for stress/life analyses of these components is studied. Viscoplastic models provide a better description of inelastic behavior of materials, but their mathematical structure is very complex. The highly nonlinear and stiff nature of the constitutive equations makes analytical solutions difficult. Therefore, suitable solution, finite element or other numerical, technologies must be developed to make these models adaptable for better and rational designs of components. NASA-Lewis has developed several solution technologies and successfully applied them to the solution of a number of uniaxial and multiaxial problems. Some of these solution technologies are described along with the models and representative results. The solution technologies developed and presented encompass a wide range of models, such as, isotropic, anisotropic, metal matrix composites, and single crystal models.
Multi-level adaptive finite element methods. 1: Variation problems
NASA Technical Reports Server (NTRS)
Brandt, A.
1979-01-01
A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.
Simulating dynamic plastic continuous neural networks by finite elements.
Joghataie, Abdolreza; Torghabehi, Omid Oliyan
2014-08-01
We introduce dynamic plastic continuous neural network (DPCNN), which is comprised of neurons distributed in a nonlinear plastic medium where wire-like connections of neural networks are replaced with the continuous medium. We use finite element method to model the dynamic phenomenon of information processing within the DPCNNs. During the training, instead of weights, the properties of the continuous material at its different locations and some properties of neurons are modified. Input and output can be vectors and/or continuous functions over lines and/or areas. Delay and feedback from neurons to themselves and from outputs occur in the DPCNNs. We model a simple form of the DPCNN where the medium is a rectangular plate of bilinear material, and the neurons continuously fire a signal, which is a function of the horizontal displacement.
HIFU Induced Heating Modelling by Using the Finite Element Method
NASA Astrophysics Data System (ADS)
Martínez, R.; Vera, A.; Leija, L.
High intensity focused ultrasound is a thermal therapy method used to treat malignant tumors and other medical conditions. Focused ultrasound concentrates acoustic energy at a focal zone. There, temperature rises rapidly over 56 °C to provoke tissue necrosis. Device performance depends on its fabrication placing computational modeling as a powerful tool to anticipate experimentation results. Finite element method allows modeling of multiphysics systems. Therefore, induced heating was modeled considering the acoustic field produced by a concave radiator excited with electric potentials from 5 V to 20 V. Nonlinear propagation was neglected and a linear response between the acoustic fields and pressure distribution was obtained. Finally, the results showed that acoustic propagation and heating models should be improved and validated with experimental measurements.
Adaptive Mesh Refinement Algorithms for Parallel Unstructured Finite Element Codes
Parsons, I D; Solberg, J M
2006-02-03
This project produced algorithms for and software implementations of adaptive mesh refinement (AMR) methods for solving practical solid and thermal mechanics problems on multiprocessor parallel computers using unstructured finite element meshes. The overall goal is to provide computational solutions that are accurate to some prescribed tolerance, and adaptivity is the correct path toward this goal. These new tools will enable analysts to conduct more reliable simulations at reduced cost, both in terms of analyst and computer time. Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems. Research issues that were considered include: effective error estimators for nonlinear structural mechanics; local meshing at irregular geometric boundaries; and constructing efficient software for parallel computing environments.
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.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
NASA Technical Reports Server (NTRS)
Arya, V. K.
1990-01-01
The viability of advanced viscoplastic models for nonlinear finite element analyses of structural components is investigated. Several uniaxial and a multiaxial problem are analyzed using the finite element implementation of Freed's viscoplastic model. Good agreement between the experimental and calculated uniaxial results validates the finite element implementation and gives confidence to apply it to more complex multiaxial problems. A comparison of results for a sample structural component (the cowl lip of a hypersonic engine inlet) with the earlier elastic, elastic-plastic, and elastic-plastic-creep analyses available in the literature shows that the elastic-viscoplastic analyses yield more reasonable stress and strain distributions. Finally, the versatility of the finite-element-based solution technology presented herein is demonstrated by applying it to another viscoplastic model.
Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)
NASA Technical Reports Server (NTRS)
Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.
2016-01-01
Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code.
Nonlinear susceptibilities of finite conjugated organic polymers
NASA Technical Reports Server (NTRS)
Beratan, David N.; Onuchic, Jose Nelson; Perry, Joseph W.
1987-01-01
Tight-binding calculations of the length dependence of the third-order molecular hyperpolarizability for polyenes and polyynes are reported. The pi-electron wave functions were determined by exploiting the limited translational symmetry of the molecules. Perturbation theory was used to calculate the longitudinal component of the electronic nonresonant hyperpolarizability. This is the first two-'band' calculation of third-order hyperpolarizabilities on finite pi-electron systems of varying length. In contrast to the results of the one-'band' models, the hyperpolarizability densities increase rapidly and then, after about 10-15 repeating units, approach an asymptotic value.
3-d finite element model development for biomechanics: a software demonstration
Hollerbach, K.; Hollister, A.M.; Ashby, E.
1997-03-01
Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models, using human hand and knee examples, and will demonstrate their software tools.
A composite nodal finite element for hexagons
Hennart, J.P.; Mund, E.H. |; Valle, E. Del
1997-10-01
A nodal algorithm for the solution of the multigroup diffusion equations in hexagonal arrays is analyzed. Basically, the method consists of dividing each hexagon into four quarters and mapping the hexagon quarters onto squares. The resulting boundary value problem on a quadrangular domain is solved in primal weak formulation. Nodal finite element methods like the Raviart-Thomas RTk schemes provide accurate analytical expansions of the solution in the hexagons. Transverse integration cannot be performed on the equations in the quadrangular domain as simply as it is usually done on squares because these equations have essentially variable coefficients. However, by considering an auxiliary problem with constant coefficients (on the same quadrangular domain) and by using a preconditioning approach, transverse integration can be performed as for rectangular geometry. A description of the algorithm is given for a one-group diffusion equation. Numerical results are presented for a simple model problem with a known analytical solution and for k{sub eff} evaluations of some benchmark problems proposed in the literature. For the analytical problem, the results indicate that the theoretical convergence orders of RTk schemes (k = 0,1) are obtained, yielding accurate solutions at the expense of a few preconditioning iterations.
Finite element modelling of fabric shear
NASA Astrophysics Data System (ADS)
Lin, Hua; Clifford, Mike J.; Long, Andrew C.; Sherburn, Martin
2009-01-01
In this study, a finite element model to predict shear force versus shear angle for woven fabrics is developed. The model is based on the TexGen geometric modelling schema, developed at the University of Nottingham and orthotropic constitutive models for yarn behaviour, coupled with a unified displacement-difference periodic boundary condition. A major distinction from prior modelling of fabric shear is that the details of picture frame kinematics are included in the model, which allows the mechanisms of fabric shear to be represented more accurately. Meso- and micro-mechanisms of deformation are modelled to determine their contributions to energy dissipation during shear. The model is evaluated using results obtained for a glass fibre plain woven fabric, and the importance of boundary conditions in the analysis of deformation mechanisms is highlighted. The simulation results show that the simple rotation boundary condition is adequate for predicting shear force at large deformations, with most of the energy being dissipated at higher shear angles due to yarn compaction. For small deformations, a detailed kinematic analysis is needed, enabling the yarn shear and rotation deformation mechanisms to be modelled accurately.
Finite element analysis of arc welding
Friedman, E.
1980-01-01
Analytical models of the gas tungsten-arc welding process into finite element computer programs provides a valuable tool for determining the welding thermal cycle, weld bead shape, and penetration characteristics, as well as for evaluating the stresses and distortions generated as a result of the temperature transients. The analysis procedures are applicable to planar or axisymmetric welds with arbitrary cross-sectional geometries, under quasistationary conditions. The method used for determining temperatures features an iteration procedure to accurately account for the latent heat absorbed during melting and liberated during solidification of the weld. By simulating the heat input from the arc to the workpiece by a normal distribution function, temperature transients, weld bead dimensions, and cooling rates are evaluated as functions of both the magnitude and distribution of heat input, weldment geometry, and weld speed (or duration of heating for stationary arcs). Modeling of the welding thermal cycle is a prerequisite to analytical treatments of metallurgical changes in weld metal and heat-affected zone material, residual stresses and distortions, and weld defects. A quasistationary formulation for moving welds enables temperatures to be calculated using a two-dimensional heat conduction computer program. The present limitation of high welding speed can, however, be relaxed without altering the two-dimensional framework of the procedure.
Intra Plate Stresses Using Finite Element Modelling
NASA Astrophysics Data System (ADS)
Jayalakshmi, S.; Raghukanth, S. T. G.
2016-10-01
One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo- Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma).
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)
Nonlinear evolution of Alfven waves in a finite beta plasma
Som, B.K. ); Dasgupta, B.; Patel, V.L. ); Gupta, M.R. )
1989-12-01
A general form of the derivative nonlinear Schroedinger (DNLS) equation, describing the nonlinear evolution of Alfven waves propagating parallel to the magnetic field, is derived by using two-fluid equations with electron and ion pressure tensors obtained from Braginskii (in {ital Reviews} {ital of} {ital Plasma Physics} (Consultants Bureau, New York, 1965), Vol. 1, p. 218). This equation is a mixed version of the nonlinear Schroedinger (NLS) equation and the DNLS, as it contains an additional cubic nonlinear term that is of the same order as the derivative of the nonlinear terms, a term containing the product of a quadratic term, and a first-order derivative. It incorporates the effects of finite beta, which is an important characteristic of space and laboratory plasmas.
Thermal-structural finite element analysis using linear flux formulation
NASA Technical Reports Server (NTRS)
Pandey, Ajay K.; Dechaumphai, Pramote; Wieting, Allan R.
1990-01-01
A linear flux approach is developed for a finite element thermal-structural analysis of steady state thermal and structural problems. The element fluxes are assumed to vary linearly in the same form as the element unknown variables, and the finite element matrices are evaluated in closed form. Since numerical integration is avoided, significant computational time saving is achieved. Solution accuracy and computational speed improvements are demonstrated by solving several two and three dimensional thermal-structural examples.
Tinianow, M.A.; Rotelli, R.L. Jr.; Baird, J.A.
1984-06-01
User instructions for the GEODYN Interactive Finite Element Computer Program are presented. The program is capable of performing the analysis of the three-dimensional transient dynamic response of a Polycrystalline Diamond Compact Bit - Bit Sub arising from the intermittent contact of the bit with the downhole rock formations. The program accommodates non-linear, time dependent, loading and boundary conditions.
Baird, J.A.; Apostal, M.C.; Rotelli, R.L. Jr.; Tinianow, M.A.; Wormley, D.N.
1984-06-01
The Theoretical Description for the GEODYN interactive finite-element computer program is presented. The program is capable of performing the analysis of the three-dimensional transient dynamic response of a Polycrystalline Diamond Compact Bit-Bit Sub arising from the intermittent contact of the bit with the downhole rock formations. The program accommodates nonlinear, time-dependent, loading and boundary conditions.
Finite area method for nonlinear conical flows
NASA Technical Reports Server (NTRS)
Sritharan, S. S.; Seebass, A. R.
1982-01-01
A fully conservative finite area method for the computation of steady inviscid flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell and a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding appropriate artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point lift off correctly. Results are compared with those of other investigations.
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.
Generating Finite-Element Models Of Composite Materials
NASA Technical Reports Server (NTRS)
Melis, M. E.
1993-01-01
Program starts at micromechanical level, from simple inputs supplied by user. COMGEN, COmposite Model GENerator, is interactive FORTRAN program used to create wide variety of finite-element models of continuous-fiber composite materials at micromechanical level. Quickly generates batch or "session files" to be submitted to finite-element preprocessor and postprocessor program, PATRAN. COMGEN requires PATRAN to complete model.
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 analysis of a weld-penetration problem
NASA Technical Reports Server (NTRS)
Rogge, T. R.
1977-01-01
The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.
TAURUS96. 3-D Finite Element Code Postprocessor
Brown, B.; Hallquist, J.O.; Spelce, T.E.
1993-11-30
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.
Practical Application of Finite Element Analysis to Aircraft Structural Design
1986-08-01
t] Cook, Robert D., "Concepts and Applications of Finite element Analysis," John Wiley & Sons, Inc., New York, 1981. [5] Rao, S. S., "The Finite...generation large-scale computer programs is discussed. V.P. Analysis of aircraft structure using applied fracture mechanics (AA) WILHEM , D. P. Northrop...Analytical, finite element for surface flaws, holes (AA) WILHEM , D. P. Northrop Corp., Hawthorne, Calif. (N5631231) Aircraft Group. In AGARD Fracture
NASA Technical Reports Server (NTRS)
Namburu, Raju R.; Tamma, Kumar K.
1993-01-01
An integrated finite element approach is presented for interdisciplinary thermal-structural problems. Of the various numerical approaches, finite element methods with direct time integration procedures are most widely used for these nonlinear problems. Traditionally, combined thermal-structural analysis is performed sequentially by transferring data between thermal and structural analysis. This approach is generally effective and routinely used. However, to solve the combined thermal-structural problems, this approach results in cumbersome data transfer, incompatible algorithmic representations, and different discretized element formulations. The integrated approach discussed in this paper effectively combines thermal and structural fields, thus overcoming the above major shortcomings. The approach follows Lax-Wendroff type finite element formulations with flux and stress based representations. As a consequence, this integrated approach uses common algorithmic representations and element formulations. Illustrative test examples show that the approach is effective for integrated thermal-structural problems.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Technical Reports Server (NTRS)
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Astrophysics Data System (ADS)
Cerro, J. A.; Scotti, S. J.
1991-07-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
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.
Solar Electric Generating System II finite element analysis
Dohner, J.L.; Anderson, J.R.
1994-04-01
On June 2, 1992, Landers` earthquake struck the Solar Electric Generating System II, located in Daggett, California. The 30 megawatt power station, operated by the Daggett Leasing Corporation (DLC), suffered substantial damage due to structural failures in the solar farm. These failures consisted of the separation of sliding joints supporting a distribution of parabolic glass mirrors. At separation, the mirrors fell to the ground and broke. It was the desire of the DLC and the Solar Thermal Design Assistance Center (STDAC) of Sandia National Laboratories (SNL) and to redesign these joints so that, in the event of future quakes, costly breakage will be avoided. To accomplish this task, drawings of collector components were developed by the STDAC, from which a detailed finite element computer model of a solar collector was produced. This nonlinear dynamic model, which consisted of over 8,560 degrees of freedom, underwent model reduction to form a low order nonlinear dynamic model containing only 40 degrees of freedom. This model was then used as a design tool to estimate joint dynamics. Using this design tool, joint configurations were modified, and an acceptable joint redesign determined. The results of this analysis showed that the implementation of metal stops welded to support shafts for the purpose of preventing joint separation is a suitable joint redesign. Moreover, it was found that, for quakes of Landers` magnitude, mirror breakage due to enhanced vibration in the trough assembly is unlikely.
Finite-element analysis of pipeline upheaval buckling
Shaw, P.K.; Bomba, J.G.
1994-12-31
It is well known that pipelines may buckle under axial compressive force created by severe temperature change and internal pressure loading conditions. Extensive work has been conducted in the past to understand the beam mode buckling behavior of the pipeline, its impact on pipeline design and, ultimately, the integrity of the pipeline. To fully describe this localized buckling behavior, both the upward and axial displacements of the pipeline need to be considered. This paper presents a large deflection finite-element analysis method with nonlinear material behavior to examine the pipeline response under upheaval buckling condition. The axial displacement caused by thermal expansion and the geometric change of the pipeline due to upheaval motion are examined to better define the pipeline buckling response. By combining both the nonlinear geometry and material effects, it is possible to characterize the extreme responses to determine potential severe damages. A pipeline with a potential for upheaval buckling from a recent North Sea field development was analyzed using the method to evaluate the buckling potential and the pipeline behavior beyond buckling.
Three dimensional inelastic finite element analysis of laminated composites
NASA Technical Reports Server (NTRS)
Griffin, O. H., Jr.; Kamat, M. P.
1980-01-01
Formulations of the inelastic response of laminated composites to thermal and mechanical loading are used as the basis for development of the computer NALCOM (Nonlinear Analysis of Laminated Composites) computer program which uses a fully three dimensional isoparametric finite element with 24 nodes and 72 degrees of freedom. An incremental solution is performed with nonlinearities introduced as pseudoloads computed for initial strains. Equilibrium iteration may be performed at every step. Elastic and elastic-plastic response of boron/epoxy and graphite/epoxy graphite/epoxy and problems of curing 0/90 sub s Gr/Ep laminates with and without circular holes are analyzed. Mechanical loading of + or - 45sub s Gr/Ep laminates is modeled and symmetry conditions which exist in angle-ply laminates are discussed. Results are compared to experiments and other analytical models when possible. All models are seen to agree reasonably well with experimetnal results for off-axis tensile coupons. The laminate analyses show the three dimensional effects which are present near holes and free corners.
NASA Technical Reports Server (NTRS)
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
1991-01-01
The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.
TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures
NASA Technical Reports Server (NTRS)
Thornton, E. A.
1976-01-01
The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.
Physical Constraint Finite Element Model for Medical Image Registration
Zhang, Jingya; Wang, Jiajun; Wang, Xiuying; Gao, Xin; Feng, Dagan
2015-01-01
Due to being derived from linear assumption, most elastic body based non-rigid image registration algorithms are facing challenges for soft tissues with complex nonlinear behavior and with large deformations. To take into account the geometric nonlinearity of soft tissues, we propose a registration algorithm on the basis of Newtonian differential equation. The material behavior of soft tissues is modeled as St. Venant-Kirchhoff elasticity, and the nonlinearity of the continuum represents the quadratic term of the deformation gradient under the Green- St.Venant strain. In our algorithm, the elastic force is formulated as the derivative of the deformation energy with respect to the nodal displacement vectors of the finite element; the external force is determined by the registration similarity gradient flow which drives the floating image deforming to the equilibrium condition. We compared our approach to three other models: 1) the conventional linear elastic finite element model (FEM); 2) the dynamic elastic FEM; 3) the robust block matching (RBM) method. The registration accuracy was measured using three similarities: MSD (Mean Square Difference), NC (Normalized Correlation) and NMI (Normalized Mutual Information), and was also measured using the mean and max distance between the ground seeds and corresponding ones after registration. We validated our method on 60 image pairs including 30 medical image pairs with artificial deformation and 30 clinical image pairs for both the chest chemotherapy treatment in different periods and brain MRI normalization. Our method achieved a distance error of 0.320±0.138 mm in x direction and 0.326±0.111 mm in y direction, MSD of 41.96±13.74, NC of 0.9958±0.0019, NMI of 1.2962±0.0114 for images with large artificial deformations; and average NC of 0.9622±0.008 and NMI of 1.2764±0.0089 for the real clinical cases. Student’s t-test demonstrated that our model statistically outperformed the other methods in comparison (p
Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P
2011-04-01
Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
The present paper describes the development of a new hybrid computational approach for applicability for nonlinear/linear thermal structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements in conjunction with transform methods and the classical Bubnov-Galerkin schemes. Applicability of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capablities of the proposed hybrid transfinite element methodology.
Tsui, C P; Tang, C Y; Leung, C P; Cheng, K W; Ng, Y F; Chow, D H K; Li, C K
2004-01-01
An active finite element model was developed to predict the mechanical behaviors of skeletal muscle-tendon complex during isometric, shortening and lengthening contraction. The active finite element was created through incorporation of a user-defined material property into ABAQUS finite element code. The active finite element is controlled by a motor element that is activated by a mathematical function. The nonlinear passive behavior of the muscle was defined by the viscoelastic elements and can be easily altered to other properties by using other elements in the material library without the need of re-defining the constitutive relation of the muscle. The isometric force-length relationship, force-strain relations of the muscle-tendon complex during both shortening and lengthening contraction and muscle relaxation response were predicted using the proposed finite element model. The predicted results were found to be in good agreement with available experimental data. In addition, the stress distribution in the muscle-tendon complex during isometric, shortening and lengthening contractions was simulated. The location of the maximum stress may provide useful information for studying muscle damage and fatigue in the future.
Lower extremity finite element model for crash simulation
Schauer, D.A.; Perfect, S.A.
1996-03-01
A lower extremity model has been developed to study occupant injury mechanisms of the major bones and ligamentous soft tissues resulting from vehicle collisions. The model is based on anatomically correct digitized bone surfaces of the pelvis, femur, patella and the tibia. Many muscles, tendons and ligaments were incrementally added to the basic bone model. We have simulated two types of occupant loading that occur in a crash environment using a non-linear large deformation finite element code. The modeling approach assumed that the leg was passive during its response to the excitation, that is, no active muscular contraction and therefore no active change in limb stiffness. The approach recognized that the most important contributions of the muscles to the lower extremity response are their ability to define and modify the impedance of the limb. When nonlinear material behavior in a component of the leg model was deemed important to response, a nonlinear constitutive model was incorporated. The accuracy of these assumptions can be verified only through a review of analysis results and careful comparison with test data. As currently defined, the model meets the objective for which it was created. Much work remains to be done, both from modeling and analysis perspectives, before the model can be considered complete. The model implements a modeling philosophy that can accurately capture both kinematic and kinetic response of the lower limb. We have demonstrated that the lower extremity model is a valuable tool for understanding the injury processes and mechanisms. We are now in a position to extend the computer simulation to investigate the clinical fracture patterns observed in actual crashes. Additional experience with this model will enable us to make a statement on what measures are needed to significantly reduce lower extremity injuries in vehicle crashes. 6 refs.
Finite Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
1994-03-01
property for Schr ~ dinger Hanxiltonians, Helvetica Physiea Acta, 52 (1979), pp. 655-670. [13) V. GIRAULT AND P. RAVIART, Finite Element Methods for Navier...involves the von Kirma.n plate equations of nonlinear elasticity, the second the Ginzburg-Landau equations of superconductivity, and the third the...Navier-Stokes equations for incompressible, viscous flows. ’This research was supported by the National Aeronautics and Space Administration under NASA
NASA Astrophysics Data System (ADS)
Nilsson, Karl-Fredrik; Giannakopoulos, Antonios E.
1995-12-01
A theoretical study of a budding-driven, initially circular, delaminated thin film loaded in equal bi-axial compression is presented. The main objective of this investigation is to study the configurational instability phenomena frequently observed for thin debonded coatings loaded in compression. The analyses are done with the aid of a kinematically non-linear finite element formulation of the plate problem to model the film, supplemented with a method to account automatically for the redistribution of the stress field as the shape of the advancing delamination is changing. By this procedure, not only the shape of the delaminated film but also the stability properties of the growth follow automatically. The configurational stability properties of the initially circular delamination are assessed by slightly perturbing the delamination front. The configurational instability is strongly related to the fracture mode dependence in the crack growth law. Finite growth of the buckling-driven thin film was also investigated. A load perturbation was employed as well as a front perturbation. It was found that the two perturbation methods can result in quite different shapes of the advancing buckled thin film. A few examples of extensive growth are also presented, and in some cases it was observed that a part of the delamination front may start tunnelling in the interface.
Neck incision planning for total laryngectomy: A finite element analysis.
Feng, Allen L; Clark, James H; Agrawal, Nishant; Moussa, Walied; Richmon, Jeremy D
2015-11-26
Post-operative complications can be attributed to technical aspects of surgery, yet no studies have investigated the mechanics behind commonly used incisions for total laryngopharyngectomies (TLP). This procedure, seen in head and neck cancer patients, necessitates free tissue transfer to construct a neo-pharynx, creating an inherently greater risk of complications. We sought to investigate the impact of neck incision location on these post-operative complications for TLP using finite element analysis (FEA). A nonlinear hyperelastic 2-D finite element model was used to evaluate the stress and strain along the incision line of two separate neck incision models commonly used for TLP: low-neck apron (LNA) incisions that incorporate the patient׳s tracheostoma and mid-neck apron (MNA) incisions that do not communicate with the tracheostoma. A constant displacement was applied to the incision to simulate normal neck extension experienced during the post-operative phase. Each neck incision was also modeled at varying strain energy densities to simulate various stages of wound healing. For a constant displacement of 40mm, the principal von Mises stress of the LNA incision varied between 5.87 and 6.41MPa, depending on the hyperelastic properties of the healing incision. This stress was concentrated at the junction of the incision and the fixed tracheostomal edge. The MNA model demonstrated a principal von Mises stress that varied between 0.558 and 0.711MPa and was concentrated along the midline of the neck incision. MNA incisions for TL patients result in principal von Mises stresses which are up to 11 times lower than those seen in LNA incisions. These results coincided with clinical observations from a concurrent study that showed a decrease in rate of wound dehiscence for patients undergoing TLP with an MNA incision.
NAFEMS Finite Element Benchmarks for MDG Code Verification
Greer, R; Ferencz, R M
2004-02-24
NAFEMS was originally founded at the United Kingdom's National Engineering Laboratory as the National Agency for Finite Element Methods and Standards. It was subsequently privatized as the not-for-profit organization NAFEMS, Ltd., but retains its mission ''To promote the safe and reliable use of finite element and related technology''. That mission has been pursued in part by sponsoring a series of studies that published benchmarked deemed suitable to assess the basic accuracy of engineering simulation tools. The early studies focused on FEA for linear solid and structural mechanics and then extended to nonlinear solid mechanics, eventually including contact. These benchmarks are complemented by educational materials concerning analysis technologies and approaches. More recently NAFEMS is expanding to consider thermal-fluid problems. Further information is available at www.nafems.org. Essentially all major commercial firms selling FEA for solid mechanics are members of NAFEMS and it seemed clear that Methods Development Group should leverage from this information resource, too. In 2002, W Program ASCI funding purchased a three-year membership in NAFEMS. In the summer of 2003 the first author hosted a summer graduate student to begin modeling some of the benchmark problems. We concentrated on NIKE3D, as the benchmarks are most typically problems most naturally run with implicit FEA. Also, this was viewed as a natural path to generate verification problems that could be subsequently incorporated into the Diablo code's test suite. This report documents and archives our initial efforts. The intent is that this will be a ''living document'' that can be expanded as further benchmarks are generated, run, interpreted and documented. To this end each benchmark, or related grouping, is localized in its own section with its own pagination. Authorship (test engineers) will be listed section by section.
TACO3D. 3-D Finite Element Heat Transfer Code
Mason, W.E.
1992-03-04
TACO3D is a three-dimensional, finite-element program for heat transfer analysis. An extension of the two-dimensional TACO program, it can perform linear and nonlinear analyses and can be used to solve either transient or steady-state problems. The program accepts time-dependent or temperature-dependent material properties, and materials may be isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions and loadings are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additional specialized features treat enclosure radiation, bulk nodes, and master/slave internal surface conditions (e.g., contact resistance). Data input via a free-field format is provided. A user subprogram feature allows for any type of functional representation of any independent variable. A profile (bandwidth) minimization option is available. The code is limited to implicit time integration for transient solutions. TACO3D has no general mesh generation capability. Rows of evenly-spaced nodes and rows of sequential elements may be generated, but the program relies on separate mesh generators for complex zoning. TACO3D does not have the ability to calculate view factors internally. Graphical representation of data in the form of time history and spatial plots is provided through links to the POSTACO and GRAPE postprocessor codes.
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.
Finite element methods of studying mechanical factors in blood flow.
Davids, N
1981-01-01
This paper reviews some biomechanical analyses of blood flow in large arteries based on a general computer modeling using the finite element method. We study the following question: What is the role played by the interrelated factors of mechanical stress, flow irregularities, and diffusion through the endothelium on the etiology of atherosclerosis or the aggravation of vascular injury. It presents the computational features of the method and stresses the physiological significance of the results, such as the effect of geometric complexities, material nonlinearities, and non-Newtonian rheology of the blood. The specific mechanical and fluid dynamic factors analyzed are wall shear stress, flow profiles, and pressure variations. After simulating tubes of circular cross section, we apply the analysis to a number of physiological situations of significance, including blood flow in the entrance region, at bifurcations, in the annular region between an inserted catheter of varying diameter and the vessel. A model study of pulsatile flow in a 60 degree bifurcated channel of velocity profiles provided corroborative measurements of these processes with special emphasis on reversed or distributed flow conditions. The corresponding analysis was extended to the situation in which flow separates and reverses in the neighborhood of stagnation points. This required developing the nonlinear expression for the convective velocity change in the medium. A computer algorithm was developed to handle simultaneous effects of pressure and viscous forces on velocity change across the element and applied to the canine prebranch arterial segment. For mean physiological flow conditions, low shear stresses (0-10 dynes/cm2) are predicted near the wall in the diverging plane, higher values (50 dynes/cm2) along the converging sides of the wall. Backflow is predicted along the outer wall, pressure recovery prior to and into the branches, and a peak shear at the divider lip.
P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems
NASA Technical Reports Server (NTRS)
Kang, Kab S.
2002-01-01
The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning
Nonlinear gyrokinetic theory for finite-BETA plasmas
Hahm, T.S.; Lee, W.W.; Brizard, A.
1988-02-01
A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.
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.
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.
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
Finite Element Anlaysis of Laminated Composite Plates
1988-09-01
4.2, results depicting maximum displacement obtained using 2 x 2 integration points, 3 x 3 integration points and ’ heterosis ’ [Ref. 4] elements are...thick and thin plates. This element gives better predictions for thick plates than heterosis ele- ment, however, for thin plates, heterosis element...results showing the normalized maximum displacements are shown in Figure 4.8. The heterosis element results in about ten percent error while the
Finite-element modeling of soft tissue rolling indentation.
Sangpradit, Kiattisak; Liu, Hongbin; Dasgupta, Prokar; Althoefer, Kaspar; Seneviratne, Lakmal D
2011-12-01
We describe a finite-element (FE) model for simulating wheel-rolling tissue deformations using a rolling FE model (RFEM). A wheeled probe performing rolling tissue indentation has proven to be a promising approach for compensating for the loss of haptic and tactile feedback experienced during robotic-assisted minimally invasive surgery (H. Liu, D. P. Noonan, B. J. Challacombe, P. Dasgupta, L. D. Seneviratne, and K. Althoefer, "Rolling mechanical imaging for tissue abnormality localization during minimally invasive surgery, " IEEE Trans. Biomed. Eng., vol. 57, no. 2, pp. 404-414, Feb. 2010; K. Sangpradit, H. Liu, L. Seneviratne, and K. Althoefer, "Tissue identification using inverse finite element analysis of rolling indentation," in Proc. IEEE Int. Conf. Robot. Autom. , Kobe, Japan, 2009, pp. 1250-1255; H. Liu, D. Noonan, K. Althoefer, and L. Seneviratne, "The rolling approach for soft tissue modeling and mechanical imaging during robot-assisted minimally invasive surgery," in Proc. IEEE Int. Conf. Robot. Autom., May 2008, pp. 845-850; H. Liu, P. Puangmali, D. Zbyszewski, O. Elhage, P. Dasgupta, J. S. Dai, L. Seneviratne, and K. Althoefer, "An indentation depth-force sensing wheeled probe for abnormality identification during minimally invasive surgery," Proc. Inst. Mech. Eng., H, vol. 224, no. 6, pp. 751-63, 2010; D. Noonan, H. Liu, Y. Zweiri, K. Althoefer, and L. Seneviratne, "A dual-function wheeled probe for tissue viscoelastic property identification during minimally invasive surgery," in Proc. IEEE Int. Conf. Robot. Autom. , 2008, pp. 2629-2634; H. Liu, J. Li, Q. I. Poon, L. D. Seneviratne, and K. Althoefer, "Miniaturized force indentation-depth sensor for tissue abnormality identification," IEEE Int. Conf. Robot. Autom., May 2010, pp. 3654-3659). A sound understanding of wheel-tissue rolling interaction dynamics will facilitate the evaluation of signals from rolling indentation. In this paper, we model the dynamic interactions between a wheeled probe and a
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
Superconvergence in the Generalized Finite Element Method
2005-01-01
Galerkin method for elliptic equations based on tensor products of piecewise polynomials. RAIRO Anal. Numer., 8:61– 66, 1974. [19] M. Kř́ıžek...London, 1986. [22] P. Lesaint and M. Zlámal. Superconvergence of the gradient of finite ele- ment solutions. RAIRO Anal. Numer., 13:139–166, 1979. [23] Q
NASA Astrophysics Data System (ADS)
Kanber, Bahattin; Bozkurt, O. Yavuz
2006-08-01
In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.
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.
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.
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.
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.
Finite element analysis to evaluate optical mirror deformations
NASA Astrophysics Data System (ADS)
Izazaga-Pérez, R.; Aguirre-Aguirre, D.; Villalobos-Mendoza, B.
2015-10-01
In this work we describe the use of Finite Element Analysis software to simulate the deformations of an optical mirror. We use Finite Element Method software as a tool to simulate the mirror deformations assuming that it is a thin plate that can be mechanically tensed or compressed; the Finite Element Analysis give us information about the displacements of the mirror from an initial position and the tensions that remains in the surface. The information obtained by means of Finite Element Analysis can be easily exported to a coordinate system and processed in a simulation environment. Finally, a ray-tracing subroutine is used in the obtained data giving us information in terms of aberration coefficients. We present some results of the simulations describing the followed procedure.
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.
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.
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.
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
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.
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.
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.
Simple bounds on limit loads by elastic finite element analysis
Mackenzie, D.; Nadarajah, C.; Shi, J.; Boyle, J.T. . Dept. of Mechanical Engineering)
1993-02-01
A method for bounding limit loads by an iterative elastic continuum finite element analysis procedure, referred to as the elastic compensation method, is proposed. A number of sample problems are considered, based on both exact solutions and finite element analysis, and it is concluded that the method may be used to obtain limit-load bounds for pressure vessel design by analysis applications with useful accuracy.
Finite element analysis to model complex mitral valve repair.
Labrosse, Michel; Mesana, Thierry; Baxter, Ian; Chan, Vincent
2016-01-01
Although finite element analysis has been used to model simple mitral repair, it has not been used to model complex repair. A virtual mitral valve model was successful in simulating normal and abnormal valve function. Models were then developed to simulate an edge-to-edge repair and repair employing quadrangular resection. Stress contour plots demonstrated increased stresses along the mitral annulus, corresponding to the annuloplasty. The role of finite element analysis in guiding clinical practice remains undetermined.
NASA Astrophysics Data System (ADS)
Vohar, B.; Kegl, M.; Ren, Z.
2008-12-01
Theoretical and practical aspects of an absolute nodal coordinate formulation (ANCF) beam finite element implementation are considered in the context of dynamic transient response optimization of elastic manipulators. The proposed implementation is based on the introduction of new nodal degrees of freedom, which is achieved by an adequate nonlinear mapping between the original and new degrees of freedom. This approach preserves the mechanical properties of the ANCF beam, but converts it into a conventional finite element so that its nodal degrees of freedom are initially always equal to zero and never depend explicitly on the design variables. Consequently, the sensitivity analysis formulas can be derived in the usual manner, except that the introduced nonlinear mapping has to be taken into account. Moreover, the adjusted element can also be incorporated into general finite element analysis and optimization software in the conventional way. The introduced design variables are related to the cross-section of the beam, to the shape of the (possibly) skeletal structure of the manipulator and to the drive functions. The layered cross-section approach and the design element technique are utilized to parameterize the shape of individual elements and the whole structure. A family of implicit time integration methods is adopted for the response and sensitivity analysis. Based on this assumption, the corresponding sensitivity formulas are derived. Two numerical examples illustrate the performance of the proposed element implementation.
Wang, Wansheng; Chen, Long; Zhou, Jie
2016-05-01
A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures.
POD-Galerkin reduced-order modeling with adaptive finite element snapshots
NASA Astrophysics Data System (ADS)
Ullmann, Sebastian; Rotkvic, Marko; Lang, Jens
2016-11-01
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical issues arising from the fact that the snapshots are members of different finite element spaces. We propose a method to create a POD-Galerkin model without interpolating the snapshots onto their common finite element mesh. The error of the reduced-order solution is not necessarily Galerkin orthogonal to the reduced space created from space-adapted snapshot. We analyze how this influences the error assessment for POD-Galerkin models of linear elliptic boundary value problems. As a numerical example we consider a two-dimensional convection-diffusion equation with a parametrized convective direction. To illustrate the applicability of our techniques to non-linear time-dependent problems, we present a test case of a two-dimensional viscous Burgers equation with parametrized initial data.
Nonlinearly Coupled Superconducting Lumped Element Resonators
NASA Astrophysics Data System (ADS)
Collodo, Michele C.; Potočnik, Anton; Rubio Abadal, Antonio; Mondal, Mintu; Oppliger, Markus; Wallraff, Andreas
We study SQUID-mediated tunable coupling between two superconducting on-chip resonators in the microwave frequency range. In this circuit QED implementation, we employ lumped-element type resonators, which consist of Nb thin film structured into interdigitated finger shunt capacitors and meander inductors. A SQUID, functioning as flux dependent and intrinsically nonlinear inductor, is placed as a coupling element together with an interdigitated capacitor between the two resonators (cf. A. Baust et al., Phys Rev. B 91 014515 (2015)). We perform a spectroscopic measurement in a dilution refrigerator and find the linear photon hopping rate between the resonators to be widely tunable as well as suppressible for an appropriate choice of parameters, which is made possible due to the interplay of inductively and capacitively mediated coupling. Vanishing linear coupling promotes nonlinear effects ranging from onsite- to cross-Kerr interaction. A dominating cross-Kerr interaction related to this configuration is notable, as it induces a unique quantum state. In the course of analog quantum simulations, such elementary building blocks can serve as a precursor for more complex geometries and thus pave the way to a number of novel quantum phases of light
Least-squares finite element methods for compressible Euler equations
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Carey, G. F.
1990-01-01
A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.
FEMA: a Finite Element Model of Material Transport through Aquifers
Yeh, G.T.; Huff, D.D.
1985-01-01
This report documents the construction, verification, and demonstration of a Finite Element Model of Material Transport through Aquifers (FEMA). The particular features of FEMA are its versatility and flexibility to deal with as many real-world problems as possible. Mechanisms included in FEMA are: carrier fluid advection, hydrodynamic dispersion and molecular diffusion, radioactive decay, sorption, source/sinks, and degradation due to biological, chemical as well as physical processes. Three optional sorption models are embodied in FEMA. These are linear isotherm and Freundlich and Langmuir nonlinear isotherms. Point as well as distributed source/sinks are included to represent artificial injection/withdrawals and natural infiltration of precipitation. All source/sinks can be transient or steady state. Prescribed concentration on the Dirichlet boundary, given gradient on the Neumann boundary segment, and flux at each Cauchy boundary segment can vary independently of each other. The aquifer may consist of as many formations as desired. Either completely confined or completely unconfined or partially confined and partially unconfined aquifers can be dealt with effectively. FEMA also includes transient leakage to or from the aquifer of interest through confining beds from or to aquifers lying below and/or above.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-03-22
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
Finite element algorithm reproducing hip squeak measured in experiment
NASA Astrophysics Data System (ADS)
Kang, Jaeyoung
2017-04-01
In this study, the frequency spectrum of squeak noise in hip joint system is measured in experiment. The numerical reproduction of hip squeak signal involves the formulation of the finite element geometry, the analytical contact kinematics such as Hertz theory and Coulomb's law and the mode-discretization. For general approach, the contact kinematics are analytically modeled to easily adjust the contact location, the contact area, the rotation direction, the pressure distribution, the friction law, and so on. Furthermore the friction stress vectors act on the 3-dimensional spherical contact surfaces where they can be divided into the steady-sliding and its transverse slip directions. Numerical calculations for the various contact parameters are conducted to investigate the possibility of hip squeak occurrence and the nonlinear oscillations after the onset of squeak are also solved. In the transient analysis, the periodic limit cycle of hip squeaking is shown to be the stick-slip type oscillation. Then the numerical frequency spectrum is qualitatively compared with hip squeak signal measured in experiment. The stick-slip oscillation during hip squeaking and its contact behavior will be also discussed over the contact area within one period.
Stress concentration around an atelectatic region: a finite element model.
Makiyama, A M; Gibson, L J; Harris, R S; Venegas, J G
2014-09-15
Lung parenchyma surrounding an atelectatic region is thought to be subjected to increased stress compared with the rest of the lung. Using 37 hexagonal cells made of linear springs, Mead et al. (1970) measured a stress concentration greater than 30% in the springs surrounding a stiffer central cell. We re-examine the problem using a 2D finite element model of 500 cells made of thin filaments with a non-linear stress-strain relationship. We study the consequences of increasing the central stiff region from one to nine contiguous cells in regular hexagonal honeycombs and random Voronoi honeycombs. The honeycomb structures were uniformly expanded with strains of 15%, 30%, 45% and 55% above their resting, non-deformed geometry. The curve of biaxial stress vs. fractional area change has a similar shape to that of the pressure-volume curve of the lung, showing an initial regime with relatively flat slope and a final regime with decreasing slope, tending toward an asymptote. Regular honeycombs had little variability in the maximum stress in radially oriented filaments adjacent to the central stiff region. In contrast, some filaments in random Voronoi honeycombs were subjected to stress concentration approximately 16 times the average stress concentration in the radially oriented filaments adjacent to the stiff region. These results may have implications in selecting the appropriate strategy for mechanical ventilation in ARDS and defining a "safe" level of alveolar pressure for ventilating atelectatic lungs.
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.
Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods
NASA Astrophysics Data System (ADS)
Bause, M.; Knabner, P.
2004-06-01
We present adaptive mixed hybrid finite element discretizations of the Richards equation, a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated porous medium. The approach simultaneously constructs approximations of the flux and the pressure head in Raviart-Thomas spaces. The resulting nonlinear systems of equations are solved by a Newton method. For the linear problems of the Newton iteration a multigrid algorithm is used. We consider two different kinds of error indicators for space adaptive grid refinement: superconvergence and residual based indicators. They can be calculated easily by means of the available finite element approximations. This seems attractive for computations since no additional (sub-)problems have to be solved. Computational experiments conducted for realistic water table recharge problems illustrate the effectiveness and robustness of the approach.
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.
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.
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.
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.
Time domain finite element analysis of multimode microwave applicators
Dibben, D.C.; Metaxas, R.
1996-05-01
Analysis of multimode applicators in the frequency domain via the finite element technique produces a set of very ill-conditioned equations. This paper outlines a time domain finite element method (TDFE) for analyzing three dimensional microwave applicators where this ill-conditioning is avoided. Edge elements are used in order to handle sharp metal edges and to avoid spurious solutions. Analysis in the time domain allows field distributions at a range of different frequencies to be obtained with a single calculation. Lumping is investigated as a means of reducing the time taken for the calculation. The reflection coefficient is also obtained.
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.
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.
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.
Footbridge between finite volumes and finite elements with applications to CFD
NASA Astrophysics Data System (ADS)
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
Mohammadi, Hadi; Bahramian, Fereshteh; Wan, Wankei
2009-11-01
Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering. To date, many models have been developed to describe heart valve leaflet tissue mechanics, which are accurate to some extent. Nevertheless, there is no comprehensive method to modeling soft tissue mechanics, This is because (1) the degree of anisotropy in the heart valve leaflet changes layer by layer due to a variety of collagen fiber densities and orientations that cannot be taken into account in the model and also (2) a constitutive material model fully describing the mechanical properties of the leaflet structure is not available in the literature. In this framework, we develop a new high-order element using p-type finite element formulation to create anisotropic material properties similar to those of the heart valve leaflet tissue in only one single element. This element also takes the nonlinearity of the leaflet tissue into consideration using a bilinear material model. This new element is composed a two-dimensional finite element in the principal directions of leaflet tissue and a p-type finite element in the direction of thickness. The proposed element is easy to implement, much more efficient than standard elements available in commercial finite element packages. This study is one step towards the modeling of soft tissue mechanics using a meshless finite element approach to be applied in real-time haptic feedback of soft-tissue models in virtual reality simulation.
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.
Effective Finite Elements for Shell Analysis.
1984-02-20
important mode of deformation , and when an element is not capable of representing inextensional bending, parasitic membrane energy is generated in many modes...of deformation . In the same manner that parasitic shear causes shear locking, this spurious membrane energy causes membrane locking. Membrane locking...dominant mode of deformation . (cont.) 20. OISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION UNCLASSIFIEO/UNLIMITEO X SAME AS
The Mathematics of Finite Elements and Applications
1993-04-30
suitable geometrical mapping between the parametric u,v-plane and the physical xy- plane. In the u,v-plane the geometry of the elements is linear. In...the plate. For thin plates there may be a boundary layer, the existence and structure of which depends on the boundary conditions, the plate geometry ...exhibits a boundary layer except for very special data or plate geometry . The bending moment tensor and shear force vector have more pronounced boundary
Characteristics Analysis on Various Kinds of Hybrid Stepping Motors Using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Enomoto, Yuji; Maki, Kohji; Miyata, Kenji; Oonishi, Kazuo; Sakamoto, Masafumi; Abukawa, Toshimi
We have presented a powerful scheme of investigating hybrid stepping motor characteristics by using 3D finite element method. A linear magnetic field analysis is effectively applicable to predict relative performance of several motors in an extremely short computing time. The waveforms of cogging torque by linear and nonlinear analysis resemble each other, while the wave amplitude in the linear analysis is about 2 times larger than one in the nonlinear analysis in the presented example. The overestimation factor of cogging torque is approximately constant for the same material composition.
Stabilized plane and axisymmetric Lobatto finite element models
NASA Astrophysics Data System (ADS)
Hu, Y. C.; Sze, K. Y.; Zhou, Y. X.
2015-11-01
High order elements are renowned for their high accuracy and convergence. Among them, Lobatto spectral finite elements are commonly used in explicit dynamic analyses as their mass matrices when evaluated by the Lobatto integration rule are diagonal. While there are numerous advanced first and second order elements, advanced high order elements are rarely seen. In this paper, generic stabilization schemes are devised for the reduced integrated plane and axisymmetric elements. Static and explicit dynamic tests are considered for evaluating the relatively merits of the stabilized and conventional elements. The displacement errors of the stabilized elements are less than those of the conventional Lobatto elements. When the material is nearly incompressible, the stabilized elements are also more accurate in terms of the energy error norm. This advantage is of practical importance for bio-tissue and hydrated soil analyses.
NASA Technical Reports Server (NTRS)
Reaves, Mercedes C.; Belvin, W. Keith; Bailey, James P.
1992-01-01
Results of two different nonlinear finite element analyses and preliminary test results for the final design of the Controls-Structures Interaction Evolutionary Model are presented. Load-deflection data bases are generalized from analysis and testing of the 16-foot diameter, dish shaped reflector. Natural frequencies and mode shapes are obtained from vibrational analysis. Experimental and analytical results show similar trends; however, future test hardware modifications and finite element model refinement would be necessary to obtain better correlation. The two nonlinear analysis procedures are both adequate techniques for the analysis of prestressed structures with complex geometries.
NASA Astrophysics Data System (ADS)
Kim, D.-J.; Duarte, C. A.; Proenca, S. P.
2012-11-01
The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J 2 plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.
NASA Astrophysics Data System (ADS)
Blanloeuil, P.; Meziane, A.
2015-10-01
The non-collinear mixing technique is applied for detection and characterization of closed cracks. The method is based on the nonlinear interaction of two shear waves generated with an oblique incidence. This interaction leads to the scattering of a longitudinal wave. A Finite Element model is used to demonstrate its application to a closed crack. Contact acoustic nonlinearity is the nonlinear effect considered here and is modeled using unilateral contact law with Coulomb's friction. Directivity patterns are computed using a two-step procedure. The Finite Element (FE) model provides the near-field solution on a circular boundary surrounding the closed crack. The solution in the far-field is then determined assuming that the material has a linear behavior. Directivity patterns will be used to analyze the direction of propagation of longitudinal wave(s) scattered from the closed crack. Numerical results show that the method is effective and promising when applied to a closed crack. Scattering of the longitudinal wave also enables us to image the crack, giving position and size indications. Finally, the method offers the possibility to distinguish classical nonlinearity from contact acoustic nonlinearity.
The Constraint Method for Solid Finite Elements.
1982-11-30
Sciences 13 . NUMBER S Bolling Air Force Base, DC 20332 - -Jfi’ 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) IS. SECURITY CVASS...1- 4)Q2 (n) (’+C) Higher degree elements add edge modes, face modes and internal modes. More details are given in [12, 13 ]. triangular prism A...23) N2 (L2 , L3)(l-z) edge u (31) N2 (L3 ’ L)(1-z) nodes s u s (45). N2 (L1, L2 )z uso (56) N2 (L2, L3 )z K - 13 - nodal variable shape function u
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.
NASA Technical Reports Server (NTRS)
Barut, A.; Madenci, Erdogan; Tessler, A.
1997-01-01
This study presents a transient nonlinear finite element analysis within the realm of a multi-body dynamics formulation for determining the dynamic response of a moderately thick laminated shell undergoing a rapid and large rotational motion and nonlinear elastic deformations. Nonlinear strain measure and rotation, as well as 'the transverse shear deformation, are explicitly included in the formulation in order to capture the proper motion-induced stiffness of the laminate. The equations of motion are derived from the virtual work principle. The analysis utilizes a shear deformable shallow shell element along with the co-rotational form of the updated Lagrangian formulation. The shallow shell element formulation is based on the Reissner-Mindlin and Marguerre theory.
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, Joseph M.
2004-03-01
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.
Finite element methods on supercomputers - The scatter-problem
NASA Technical Reports Server (NTRS)
Loehner, R.; Morgan, K.
1985-01-01
Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.
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 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.
Derivation of a Tappered p-Version Beam Finite Element
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1989-01-01
A tapered p-version beam finite element suitable for dynamic applications is derived. The taper in the element is represented by allowing the area moments of inertia to vary as quartic polynomials along the length of the beam, and the cross-sectional area to vary as a quadratic polynomial. The p-version finite-element characteristics are implemented through a set of polynomial shape functions. The lower-order shape functions are identical to the classical cubic and linear shape functions normally associated with a beam element. The higher-order shape functions are a hierarchical set of polynomials that are integrals of orthogonal polynomials. Explicit expressions for the mass and stiffness matrices are presented for an arbitrary value of p. The element has been verified to be numerically stable using shape functions through 22nd order.
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.
Kooijman, Gerben; Ouweltjes, Okke
2009-04-01
A lumped element electroacoustic model for a synthetic jet actuator is presented. The model includes the nonlinear flow resistance associated with flow separation and employs a finite difference scheme in the time domain. As opposed to more common analytical frequency domain electroacoustic models, in which the nonlinear resistance can only be considered as a constant, it allows the calculation of higher harmonics, i.e., distortion components, generated as a result of this nonlinear resistance. Model calculations for the time-averaged momentum flux of the synthetic jet as well as the radiated sound power spectrum are compared to experimental results for various configurations. It is shown that a significantly improved prediction of the momentum flux-and thus flow velocity-of the jet is obtained when including the nonlinear resistance. Here, the current model performs slightly better than an analytical model. For the power spectrum of radiated sound, a reasonable agreement is obtained when assuming a plausible slight asymmetry in the nonlinear resistance. However, results suggest that loudspeaker nonlinearities play a significant role as well in the generation of the first few higher harmonics.
Finite dimensional approximation of a class of constrained nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Gunzburger, Max D.; Hou, L. S.
1994-01-01
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.
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.
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.
Convergence of finite element approximations of large eddy motion.
Iliescu, T.; John, V.; Layton, W. J.; Mathematics and Computer Science; Otto-von-Guericke Univ.; Univ. of Pittsburgh
2002-11-01
This report considers 'numerical errors' in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. Keywords: Navier Stokes equations, large eddy simulation, finite element method I. INTRODUCTION Consider the (turbulent) flow of an incompressible fluid. One promising and common approach to the simulation of the motion of the large fluid structures is Large Eddy Simulation (LES). Various models are used in LES; a common one is to find (w, q), where w : {Omega}
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.
Analysis of the Performance of Mixed Finite Element Methods.
1986-10-01
October 1986 SUMMARY The initial goal of this project is to analyze various mixed methods based on the p- and h-p versions of the finite element methods...The convergence of mixed methods depends on two factors: (1) Approximability of polynomial spaces used (2) Stability. In the past year, the question...significant portion of the research is geared towards the investigation of mixed methods based on the ’p’ and ’h-p’ versions of the finite element method
Predicting Rediated Noise With Power Flow Finite Element Analysis
2007-02-01
Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow Finite Element Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW FINITE ELEMENT ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated
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.
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.
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element...SM4), 1,435-1,457. Fernando Dams During the Earthquakes of February Davis, E. H., and Poulos, H. G. (1972). “Rate of Report EERC-73-2, Berkeley, CA
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.
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.
Correlation of composite material test results with finite element analysis
NASA Astrophysics Data System (ADS)
Guƫu, M.
2016-08-01
In this paper are presented some aspects regarding the method of simulation of composite materials testing with finite element analysis software. There were simulated tensile and shear tests of specimens manufactured from glass fiber reinforced polyester. For specimens manufacturing two types of fabrics were used: unidirectional and bidirectional. Experimentally determined elastic properties of composite material were used as input data. Modeling of composite architecture of the specimens was performed with ANSYS Composite PrepPost software. Finite element analysis stresses and strains on strain gauges bonding area were considered and compared with the real values in a diagram. After results comparison, potential causes of deviations were identified.
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.
Using Finite-Element Analysis In Estimating Reliability
NASA Technical Reports Server (NTRS)
Zaretsky, Erwin V.; August, Richard
1994-01-01
Method of estimating design survivability of structural component incorporates finite-element and probabilistic properties of materials. Involves evaluation of design parameters through direct comparisons of survivability of component expressed in terms of percentages of like components that survive at various lifetimes. Probabilistic properties of materials, given in terms of Weibull parameters, coupled with stress field computed by finite-element analysis to determine fatigue life based on initiation of cracks. Method applied to rotating disk containing bolt holes, representative of disks used in aerospace propulsion turbines. Also used in early stages of design process to optimize life-based designs, reducing testing of full-sized components needed to validate designs.
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.
NASA Technical Reports Server (NTRS)
Dame, L. T.; Stouffer, D. C.
1986-01-01
A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.
Nonlinear harmonic generation in finite amplitude black hole oscillations
NASA Astrophysics Data System (ADS)
Papadopoulos, Philippos
2002-04-01
The nonlinear generation of harmonics in gravitational perturbations of black holes is explored using numerical relativity based on an ingoing light-cone framework. Localized, finite, perturbations of an isolated black hole are parametrized by amplitude and angular harmonic form. The response of the black hole spacetime is monitored and its harmonic content analyzed to identify the strength of the nonlinear generation of harmonics as a function of the initial data amplitude. It is found that overwhelmingly the black hole responds at the harmonic mode perturbed, even for spacetimes with 10% of the black hole mass radiated. The coefficients for down and up scattering in harmonic space are computed for a range of couplings. Down scattering, leading to smoothing out of angular structure, is found to be equally as or more efficient than the up scatterings that would lead to increased rippling. The details of this nonlinear balance may form the quantitative mechanism by which black holes avoid fission even for arbitrary strong distortions.
Finite Element Model Development and Validation for Aircraft Fuselage Structures
NASA Technical Reports Server (NTRS)
Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.
2000-01-01
The ability to extend the valid frequency range for finite element based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid element models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The finite element models are validated using experimental modal analysis results. The increased frequency range results in a corresponding increase in the number of modes, modal density and spatial resolution requirements. In this study, conventional modal tests using accelerometers are complemented with Scanning Laser Doppler Velocimetry and Electro-Optic Holography measurements to further resolve the spatial response characteristics. Whenever possible, component and subassembly modal tests are used to validate the finite element models at lower levels of assembly. Normal mode predictions for different finite element representations of components and assemblies are compared with experimental results to assess the most accurate techniques for modeling aircraft fuselage type structures.
Finite element analyses for seismic shear wall international standard problem
Park, Y.J.; Hofmayer, C.H.
1998-04-01
Two identical reinforced concrete (RC) shear walls, which consist of web, flanges and massive top and bottom slabs, were tested up to ultimate failure under earthquake motions at the Nuclear Power Engineering Corporation`s (NUPEC) Tadotsu Engineering Laboratory, Japan. NUPEC provided the dynamic test results to the OECD (Organization for Economic Cooperation and Development), Nuclear Energy Agency (NEA) for use as an International Standard Problem (ISP). The shear walls were intended to be part of a typical reactor building. One of the major objectives of the Seismic Shear Wall ISP (SSWISP) was to evaluate various seismic analysis methods for concrete structures used for design and seismic margin assessment. It also offered a unique opportunity to assess the state-of-the-art in nonlinear dynamic analysis of reinforced concrete shear wall structures under severe earthquake loadings. As a participant of the SSWISP workshops, Brookhaven National Laboratory (BNL) performed finite element analyses under the sponsorship of the U.S. Nuclear Regulatory Commission (USNRC). Three types of analysis were performed, i.e., monotonic static (push-over), cyclic static and dynamic analyses. Additional monotonic static analyses were performed by two consultants, F. Vecchio of the University of Toronto (UT) and F. Filippou of the University of California at Berkeley (UCB). The analysis results by BNL and the consultants were presented during the second workshop in Yokohama, Japan in 1996. A total of 55 analyses were presented during the workshop by 30 participants from 11 different countries. The major findings on the presented analysis methods, as well as engineering insights regarding the applicability and reliability of the FEM codes are described in detail in this report. 16 refs., 60 figs., 16 tabs.
Development of an hp-version finite element method for computational optimal control
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Warner, Michael S.
1993-01-01
The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.
A new formulation of hybrid/mixed finite element
NASA Technical Reports Server (NTRS)
Pian, T. H. H.; Kang, D.; Chen, D.-P.
1983-01-01
A new formulation of finite element method is accomplished by the Hellinger-Reissner principle for which the stress equilibrium conditions are not introduced initially but are brought-in through the use of additional internal displacement parameters. The method can lead to the same result as the assumed stress hybrid model. However, it is more general and more flexible. The use of natural coordinates for stress assumptions leads to elements which are less sensitive to the choice of reference coordinates. Numerical solutions by 3-D solid element indicate that more efficient elements can be constructed by assumed stresses which only partially satisfy the equilibrium conditions.
Finite element approach for transient analysis of multibody systems
NASA Technical Reports Server (NTRS)
Wu, Shih-Chin; Chang, Che-Wei; Housner, Jerrold M.
1992-01-01
A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.
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.
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.
Crack modeling of rotating blades with cracked hexahedral finite element method
NASA Astrophysics Data System (ADS)
Liu, Chao; Jiang, Dongxiang
2014-06-01
Dynamic analysis is the basis in investigating vibration features of cracked blades, where the features can be applied to monitor health state of blades, detect cracks in an early stage and prevent failures. This work presents a cracked hexahedral finite element method for dynamic analysis of cracked blades, with the purpose of addressing the contradiction between accuracy and efficiency in crack modeling of blades in rotor system. The cracked hexahedral element is first derived with strain energy release rate method, where correction of stress intensity factors of crack front and formulation of load distribution of crack surface are carried out to improve the modeling accuracy. To consider nonlinear characteristics of time-varying opening and closure effects caused by alternating loads, breathing function is proposed for the cracked hexahedral element. Second, finite element method with contact element is analyzed and used for comparison. Finally, validation of the cracked hexahedral element is carried out in terms of breathing effects of cracked blades and natural frequency in different crack depths. Good consistency is acquired between the results with developed cracked hexahedral element and contact element, while the computation time is significantly reduced in the previous one. Therefore, the developed cracked hexahedral element achieves good accuracy and high efficiency in crack modeling of rotating blades.
Finite element modeling of the deformation of magnetoelastic film
Barham, Matthew I.; White, Daniel A.; Steigmann, David J.
2010-09-01
Recently a new class of biocompatible elastic polymers loaded with small ferrous particles, a magnetoelastic polymer, has been developed. This engineered material is formed into a thin film using spin casting. An applied magnetic field will deform the film. The magnetic deformation of this film has many possible applications, particularly in microfluidic pumps and pressure regulators. In this paper a finite element method suitable for the transient simulation of arbitrarily shaped three-dimensional magnetoelastic polymers subjected to time-varying magnetic fields is developed. The approach is similar to that employed in finite elment magnetohydrodynamic simulations, the key difference is a more complex hyperelastic material model. In order to confirm the validity of the approach, finite element solutions for an axially symmetric thin film are compared to an analytical solution based on the membrane (infinitely thin) approximation. For this particular problem the two approaches give qualitatively similar results and converge as the film thickness approaches zero.
Miller, K; Horton, A; Joldes, G R; Wittek, A
2012-10-11
To be useful in clinical (surgical) simulations, a method must use fully nonlinear (both geometric and material) formulations to deal with large (finite) deformations of tissues. The method must produce meaningful results in a short time on consumer hardware and not require significant manual work while discretizing the problem domain. In this paper, we showcase the Meshless Total Lagrangian Explicit Dynamics Method (MTLED) which meets these requirements, and use it for computing brain deformations during surgery. The problem geometry is based on patient-specific MRI data and includes the parenchyma, tumor, ventricles and skull. Nodes are distributed automatically through the domain rendering the normally difficult problem of creating a patient-specific computational grid a trivial exercise. Integration is performed over a simple, regular background grid which does not need to conform to the geometry boundaries. Appropriate nonlinear material formulation is used. Loading is performed by displacing the parenchyma surface nodes near the craniotomy and a finite frictionless sliding contact is enforced between the skull (rigid) and parenchyma. The meshless simulation results are compared to both intraoperative MRIs and Finite Element Analysis results for multiple 2D sections. We also calculate Hausdorff distances between the computed deformed surfaces of the ventricles and those observed intraoperatively. The difference between previously validated Finite Element results and the meshless results presented here is less than 0.2mm. The results are within the limits of neurosurgical and imaging equipment accuracy (~1 mm) and demonstrate the method's ability to fulfill all of the important requirements for surgical simulation.
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.
Finite-element analysis of end-notch flexure specimens
NASA Technical Reports Server (NTRS)
Mall, S.; Kochhar, N. K.
1986-01-01
A finite-element analysis of the end-notch flexure specimen for Mode II interlaminar fracture toughness measurement was conducted. The effects of friction between the crack faces and large deflection on the evaluation of G(IIc) from this specimen were investigated. Results of this study are presented in this paper.
Finite element analysis of end notch flexure specimen
NASA Technical Reports Server (NTRS)
Mall, S.; Kochhar, N. K.
1986-01-01
A finite element analysis of the end notch flexure specimen for mode II interlaminar fracture toughness measurement was conducted. The effect of friction between the crack faces and large deflection on the evaluation of G sub IIc from this specimen were investigated. Results of this study are presented in this paper.
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.
2-D Finite Element Cable and Box IEMP Analysis
Scivner, G.J.; Turner, C.D.
1998-12-17
A 2-D finite element code has been developed for the solution of arbitrary geometry cable SGEMP and box IEMP problems. The quasi- static electric field equations with radiation- induced charge deposition and radiation-induced conductivity y are numerically solved on a triangular mesh. Multiple regions of different dielectric materials and multiple conductors are permitted.
Finite-element analysis of an epoxy-curing process
Gartling, D K; Hickox, C E; Nunziato, J W
1983-01-01
A finite element numerical procedure is used to study the curing of an epoxy compound. The problem involves the gelation of an incompressible liquid due to an exothermic chemical reaction. Nonuniform temperature fields produce buoyancy-driven fluid motions that interact with the solidifying material. The numerical simulations provide temperature histories and the progression of the gel front that are compared with experimental data.
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.
Coupling finite element and spectral methods: First results
NASA Technical Reports Server (NTRS)
Bernardi, Christine; Debit, Naima; Maday, Yvon
1987-01-01
A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.
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.
Finite-Element Fracture Analysis of Pins and Bolts
NASA Technical Reports Server (NTRS)
Nord, K. J.
1986-01-01
Stress intensities calculated in bending and tension. Finite-element stress-analysis method gives stress-intensity estimates for surface flaws on smooth and threaded round bars. Calculations done for purely tensile and purely bending loads. Results, presented in dimensionless form, useful for determining fatigue lives of bolts and pins.
Coupling of Peridynamics and Finite Element Formulation for Multiscale Simulations
2012-10-16
state-based peridynamic method, Warren et al. [46] studied the elastic deformation and fracture of a bar. Littlewood [47] presented fragmentation of an...Journal of Solids and Structures 46 (2009) 1186-1195. [47] D. J. Littlewood , Simulation of dynamic fracture using peridynamics, finite element modeling
DYCAST: A finite element program for the crash analysis of structures
NASA Technical Reports Server (NTRS)
Pifko, A. B.; Winter, R.; Ogilvie, P.
1987-01-01
DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.
Prediction of Colles' fracture load in human radius using cohesive finite element modeling.
Ural, Ani
2009-01-05
Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles' fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731-6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4-5% per decade based only on material level changes and by 6-20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r(2)=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.
Finite element modeling of hyper-viscoelasticity of peripheral nerve ultrastructures.
Chang, Cheng-Tao; Chen, Yu-Hsing; Lin, Chou-Ching K; Ju, Ming-Shaung
2015-07-16
The mechanical characteristics of ultrastructures of rat sciatic nerves were investigated through animal experiments and finite element analyses. A custom-designed dynamic testing apparatus was used to conduct in vitro transverse compression experiments on the nerves. The optical coherence tomography (OCT) was utilized to record the cross-sectional images of nerve during the dynamic testing. Two-dimensional finite element models of the nerves were built based on their OCT images. A hyper-viscoelastic model was employed to describe the elastic and stress relaxation response of each ultrastructure of the nerve, namely the endoneurium, the perineurium and the epineurium. The first-order Ogden model was employed to describe the elasticity of each ultrastructure and a generalized Maxwell model for the relaxation. The inverse finite element analysis was used to estimate the material parameters of the ultrastructures. The results show the instantaneous shear modulus of the ultrastructures in decreasing order is perineurium, endoneurium, and epineurium. The FE model combined with the first-order Ogden model and the second-order Prony series is good enough for describing the compress-and-hold response of the nerve ultrastructures. The integration of OCT and the nonlinear finite element modeling may be applicable to study the viscoelasticity of peripheral nerve down to the ultrastructural level.
An extended finite element method for dislocations in arbitrary three-dimensional entities
NASA Astrophysics Data System (ADS)
Oswald, Jay
A finite element method is developed for dislocations in arbitrary, three-dimensional bodies, including micro-/nano-devices, and layered materials, such as thin films. The method is also compatible with anisotropic materials, and can readily be applied to non-linear media. In this method, dislocation are modeled by adding discontinuities to extend the conventional finite element basis. Two approaches for adding discontinuities to the conventional finite element basis are proposed. In the first, a simple discontinuous enrichment imposes a constant jump in displacement across dislocation glide planes. In the second approach, the enrichments more accurately approximate the dislocations by capture the singular asymptotic behavior near the dislocation core. A basis of singular enrichments are formed from the analytical solutions to straight dislocation lines, but are applicable for more general, curved dislocation configurations. Methods for computing the configurational forces on dislocation lines within the XFEM framework have also been developed. For jump enrichments, an approach based on an energy release rate or J-integral is proposed. When singular enrichments are available, it is shown that the Peach-Koehler equation can be used to compute forces directly. This new approach differs from many existing methods for studying dislocations because it does not rely on superposition of solutions derived analytically or through Green's functions. This extended finite element approach is suitable to study dislocations in micro- and nano-devices, and in specific material micro-structures, where complicated boundaries and material interfaces are pervasive.
2016-01-01
Purpose This study investigated the effects of bone density and crestal cortical bone thickness at the implant-placement site on micromotion (relative displacement between the implant and bone) and the peri-implant bone strain distribution under immediate-loading conditions. Methods A three-dimensional finite element model of the posterior mandible with an implant was constructed. Various bone parameters were simulated, including low or high cancellous bone density, low or high crestal cortical bone density, and crestal cortical bone thicknesses ranging from 0.5 to 2.5 mm. Delayed- and immediate-loading conditions were simulated. A buccolingual oblique load of 200 N was applied to the top of the abutment. Results The maximum extent of micromotion was approximately 100 μm in the low-density cancellous bone models, whereas it was under 30 μm in the high-density cancellous bone models. Crestal cortical bone thickness significantly affected the maximum micromotion in the low-density cancellous bone models. The minimum principal strain in the peri-implant cortical bone was affected by the density of the crestal cortical bone and cancellous bone to the same degree for both delayed and immediate loading. In the low-density cancellous bone models under immediate loading, the minimum principal strain in the peri-implant cortical bone decreased with an increase in crestal cortical bone thickness. Conclusions Cancellous bone density may be a critical factor for avoiding excessive micromotion in immediately loaded implants. Crestal cortical bone thickness significantly affected the maximum extent of micromotion and peri-implant bone strain in simulations of low-density cancellous bone under immediate loading. PMID:27382504
1993-11-01
methou, mn: A.K. Aziz (ed.), The mathematical foundations of tile finite element, method with applicai.4ons to partial differential equations , Academic...nonlinear differential equations and problems in linear and nonlinear algebra. "* To help bridge gaps between computational directions in engineering, physics...Life of Contract Equation with High Wave Number Part 1: The h-Version of the FEM 7. Au TNO R(a)COTATO ATgUSAs Frank Ihlenburgi - Ivo Babuska 2 2ONR
Modelling of orbital deformation using finite-element analysis
Al-Sukhun, Jehad; Lindqvist, Christian; Kontio, Risto
2005-01-01
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury. This study investigated the hypothesis that such deformation could be modelled using finite-element techniques. One patient who had CT-scan examination to the maxillofacial skeleton including the orbits, as part of her treatment, was selected for this study. A FEM of one of the orbits containing the globe was constructed, based on CT-scan images. Simulations were performed with a computer using the finite-element software NISA (EMRC, Troy, USA). The orbit was subjected to a blunt injury of a 0.5 kg missile with 30 m s−1 velocity. The FEM was then used to predict principal and shear stresses or strains at each node position. Two types of orbital deformation were predicted during different impact simulations: (i) horizontal distortion and (ii) rotational distortion. Stress values ranged from 213.4 to 363.3 MPa for the maximum principal stress, from −327.8 to −653.1 MPa for the minimum principal stress, and from 212.3 to 444.3 MPa for the maximum shear stress. This is the first finite-element study, which demonstrates different and concurrent patterns of orbital deformation in a subject following a blunt injury. Finite element modelling is a powerful and invaluable tool to study the multifaceted phenomenon of orbital deformation. PMID:16849235
Valentín, A; Humphrey, J D; Holzapfel, G A
2013-08-01
We implemented a constrained mixture model of arterial growth and remodeling in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and nonhomogenous degradation of elastin or loss of smooth muscle function. The nonlinear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons with prior results for two special cases: uniform transmural changes in mass and differential growth and remodeling within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement.
Valentín, A.; Humphrey, J. D.; Holzapfel, G. A.
2013-01-01
We implemented a constrained mixture model of arterial growth and remodeling (G&R) in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and non-homogenous degradation of elastin or loss of smooth muscle function. The non-linear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons to prior results for two special cases: uniform transmural changes in mass and differential G&R within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement. PMID:23713058
High-order Finite Element Analysis of Boundary Layer Flows
NASA Astrophysics Data System (ADS)
Zhang, Alvin; Sahni, Onkar
2014-11-01
Numerical analysis of boundary layer flows requires careful approximations, specifically the use of a mesh with layered and graded elements near the (viscous) walls. This is referred to as a boundary layer mesh, which for complex geometries is composed of triangular elements on the walls that are inflated or extruded into the volume along the wall-normal direction up to a desired height while the rest of the domain is filled with unstructured tetrahedral elements. Linear elements with C0 inter-element continuity are employed and in some situations higher order C0 elements are also used. However, these elements only enforce continuity whereas high-order smoothness is not attained as will be the case with C1 inter-element continuity and higher. As a result, C0 elements result in a poor approximation of the high-order boundary layer behavior. To achieve greater inter-element continuity in boundary layer region, we employ B-spline basis functions along the wall-normal direction (i.e., only in the layered portion of the mesh). In the rest of the fully unstructured mesh, linear or higher order C0 elements are used as appropriate. In this study we demonstrate the benefits of finite-element analysis based on such higher order and continuity basis functions for boundary layer flows.
Failure analysis of laminated composites by using iterative three-dimensional finite element method
NASA Astrophysics Data System (ADS)
Hwang, W. C.; Sun, C. T.
1989-05-01
A failure analysis of laminated composites is accomplished by using an iterative three-dimensional finite element method. Based on Tsai-Wu failure theory, three different modes of failure are proposed: fiber breakage, matrix cracking, and delamination. The first ply failure load is then evaluated. As the applied load exceeds the first ply failure load, localized structural failure occurs and the global structural stiffness should change. The global stiffness matrix is modified by taking nonlinearity due to partial failures within a laminate into consideration. The first ply failure load is analyzed by using a iterative mixed field method in solving the linear part of the finite element equations. The progressive failure problem is solved numerically by using Newton-Raphson iterative schemes for the solution of nonlinear finite element equations. Numerical examples include angle-ply symmetric Thornel 300 graphite/934 resin epoxy laminates under uniaxial tension. First ply failure loads as well as the final failure loads are evaluated. Good correlation between analytical results and experimental data are observed. Numerical results also include the investigation of composite specimens with a centered hole, under uniaxial tension. Excellent correlation with the experimental data is observed.
Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses
NASA Technical Reports Server (NTRS)
Rizzi, Stephen A.; Przekop, Adam
2006-01-01
A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.
Finite bandwidth, nonlinear convective flow in a mushy layer
NASA Astrophysics Data System (ADS)
Riahi, D. N.
2017-04-01
Finite amplitude convection with a continuous finite bandwidth of modes in a horizontal mushy layer during the solidification of binary alloys is investigated. We analyze the nonlinear convection for values of the Rayleigh number close to its critical value by using multiple scales and perturbation techniques. Applying a combined temporal and spatial evolution approach, we determine a set of three coupled differential equations for the amplitude functions of the convective modes. A large number of new subcritical or supercritical stable solutions to these equations in the form of steady rolls and hexagons with different horizontal length scales are detected. We find, in particular, that depending on the parameter values and on the magnitude and direction of the wave number vectors for the amplitude functions, hexagons with down-flow or up-flow at the cells’ centers or rolls can be stable. Rolls or hexagons with longer horizontal wave length can be stable at higher amplitudes, and there are cases where hexagons are unstable for any value of the Rayleigh number, while rolls are stable only for the values of the Rayleigh number beyond some value. We also detected new stable and irregular flow patterns with two different horizontal scales in the form of superposition of either two sets of hexagons or two sets of inclined rolls.
Dynamic quasistatic characterization of finite elements for shell structures.
Thomas, Jesse David
2010-11-01
Finite elements for shell structures have been investigated extensively, with numerous formulations offered in the literature. These elements are vital in modern computational solid mechanics due to their computational efficiency and accuracy for thin and moderately thick shell structures, allowing larger and more comprehensive (e.g. multi-scale and multi-physics) simulations. Problems now of interest in the research and development community are routinely pushing our computational capabilities, and thus shell finite elements are being used to deliver efficient yet high quality computations. Much work in the literature is devoted to the formulation of shell elements and their numerical accuracy, but there is little published work on the computational characterization and comparison of shell elements for modern solid mechanics problems. The present study is a comparison of three disparate shell element formulations in the Sandia National Laboratories massively parallel Sierra Solid Mechanics code. A constant membrane and bending stress shell element (Key and Hoff, 1995), a thick shell hex element (Key et al., 2004) and a 7-parameter shell element (Buechter et al., 1994) are available in Sierra Solid Mechanics for explicit transient dynamic, implicit transient dynamic and quasistatic calculations. Herein these three elements are applied to a set of canonical dynamic and quasistatic problems, and their numerical accuracy, computational efficiency and scalability are investigated. The results show the trade-off between the relative inefficiency and improved accuracy of the latter two high quality element types when compared with the highly optimized and more widely used constant membrane and bending stress shell element.
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.
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.
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).
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.
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.
Edge-based finite element scheme for the Euler equations
NASA Astrophysics Data System (ADS)
Luo, Hong; Baum, Joseph D.; Loehner, Rainald
1994-06-01
This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of the upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.
Edge-based finite element scheme for the Euler equations
NASA Astrophysics Data System (ADS)
Luo, Hong; Baum, Joseph D.; Lohner, Rainald
1994-06-01
This paper describes the development, validation, and application of a new finite element scheme for the solution of the compressible Euler equations on unstructured grids. The implementation of the numerical scheme is based on an edge-based data structure, as opposed to a more traditional element-based data structure. The use of this edge-based data structure not only improves the efficiency of the algorithm but also enables a straightforward implementation of upwind schemes in the context of finite element methods. The algorithm has been tested and validated on some well-documented configurations. A flow solution about a complete F-18 fighter is shown to demonstrate the accuracy and robustness of the proposed algorithm.
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-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.
NASA Astrophysics Data System (ADS)
Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.
2015-12-01
Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties