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At least 343 records · Page 19

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NASA NTRS1972

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Wu, R. W.↗

NASA NTRS1984

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

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

Putcha, N. S.↗

DOE OSTI2021

Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

Here, we present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to resolve. Finite element analysis methods, which rely on Gauss quadrature integration schemes, must solve two sets of coupled differential equations: one at the global level and the other at the local, i.e. Gauss point level. In contrast to the conventional return mapping algorithm, which solves these two sets of coupled differential equations separately using a nested Newton procedure, we propose a scheme to solve the local and global differential equations simultaneously. In the process we also derive closed-form expressions used to update the internal/constitutive state variables, and unify the popular closest-point and cutting plane methods with our formulas. Numerical testing indicates that our method allows for larger thermomechanical loading steps and provides increased computational efficiency, over the standard return mapping algorithm.

42 ENGINEERING↗

NASA NTRS1990

COMGEN: A computer program for generating finite element models of composite materials at the micro level

COMGEN (Composite Model Generator) is an interactive FORTRAN program which can be used to create a wide variety of finite element models of continuous fiber composite materials at the micro level. It quickly generates batch or session files to be submitted to the finite element pre- and postprocessor PATRAN based on a few simple user inputs such as fiber diameter and percent fiber volume fraction of the composite to be analyzed. In addition, various mesh densities, boundary conditions, and loads can be assigned easily to the models within COMGEN. PATRAN uses a session file to generate finite element models and their associated loads which can then be translated to virtually any finite element analysis code such as NASTRAN or MARC.

Melis, Matthew E.↗

NASA NTRS1999

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

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.

Kurdila, Andrew J.↗

NASA NTRS1975

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗

NASA NTRS1995

Large Scale Finite Element Modeling Using Scalable Parallel Processing

An iterative solver for use with finite element codes was developed for the Cray T3D massively parallel processor at the Jet Propulsion Laboratory. Finite element modeling is useful for simulating scattered or radiated electromagnetic fields from complex three-dimensional objects with geometry variations smaller than an electrical wavelength.

finite element modeling parallel processing iterat↗

NASA NTRS1993

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

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.

Arya, Vinod K.↗

NASA NTRS1987

Finite element modeling of electromagnetic propagation in composite structures

A finite element Galerkin formulation has been developed to study electromagnetic propagation in complex two-dimensional absorbing ducts. The reflection and transmission at entrance and exit boundaries are determined by coupling the finite element solutions at the entrance and exit to the eigenfunctions of an infinite uniform perfect conducting duct. Example solutions are presented for electromagnetic propagation with absorbing duct walls and propagating through dielectric-metallic matrix materials.

Baumeister, K. J.↗

DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Large-amplitude finite element flutter analysis of composite panels in hypersonic flow

Consideration is given to a finite-element approach for determining the nonlinear flutter characteristics of 3D thin laminated composite panels using the full third-order-piston transverse-loading aerodynamic theory. The unsteady hypersonic aerodynamic theory and the von Karman large-deflection-plate theory are used to formulate the aeroelasticity problem. Nonlinear flutter analyses are performed to assess the influence of the higher-order aerodynamic theory on the structure's limit-cycle amplitude and the dynamic pressure of the flow velocity. A solution procedure is presented to solve the nonlinear panel flutter and large-amplitude free-vibration finite-element equations. Nonlinear flutter analyses are performed for different boundary support-conditions and for various system parameters. Linear finite-element flutter for isotropic and composite panels and large-amplitude isotropic panel flutter results are compared with existing classical solutions. The large-amplitude panel flutter results using the full third-order piston aerodynamic theory are presented to assess the influence of the nonlinear aerodynamic theory.

Gray, Carl E., Jr.↗

NASA NTRS1987

Adaptive finite element methods for high-speed compressible flows

An adaptive finite element algorithm for solving the unsteady Euler equations is described. The finite element algorithm is based on a Taylor/Galerkin formulation and uses a very fast and efficient data structure to refine and unrefine the grid in order to optimize the approximation. A general version of the method which can be applied to moving grids with sliding interfaces is given, and results for a transient supersonic calculation of rotor-stator interaction are presented.

Oden, J. T.↗

NASA NTRS1990

Least-squares finite element methods for compressible Euler equations

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.

Jiang, Bo-Nan↗

NASA NTRS1978

A multi-microprocessor system for finite element structural analysis

During the last few years, advances in microprocessor technology have spurred a renewed interest in special-purpose computers. The microprocessor has become small, inexpensive, and powerful enough to be considered as a building block for special-purpose hardware. A description is presented of the architecture of a prototype 'finite element machine' currently being built. Attention is given to details regarding the finite element analysis problem, the arrangement of the processors as finite element nodes in the structural model, the influence of the architecture on the solution algorithm, interprocessor communication primitives, and the performance of the finite element machine.

Jordan, H. F.↗

NASA NTRS1984

Parameter studies of gear cooling using an automatic finites element mesh generator

The range of accuracies achieved in the gear tooth temperature using an automatic finite element mesh generator were investigated. Gear web contribution to the gear cooling process was studied by introducing a varying size hole at the center of the gear because of the versatility of program TARG in allowing different heat transfer coefficients in different areas of the gear tooth. A study was carried out to evaluate the contribution of the loaded and unloaded faces as well as the top and bottom lands. A general purpose two-dimensional finite element preprocessor ATOGEN has been developed for automatic generation of a finite element mesh over a pie-shaped sector of a gear. The program was used for facilitating the input to an upgraded version of a previously developed program for the thermal analysis of running gears (TARG). The latter program determined the steady state temperature distribution throughout the specified gear. The automatic mesh generator program includes a band width minimization routine for reducing computer cost.

El-Bayoumy, L. E.↗

NASA NTRS1993

A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS

Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).

Chatterjee, A.↗

NASA NTRS1990

Finite element two-dimensional panel flutter at high supersonic speeds and elevated temperature

A consistent finite element formulation for flutter of two-dimensional panels including effects of temperature variation along panel length is presented. The von Karman nonlinear strain-displacement relation is used to account for the large-deflections, and the quasi-steady first-order piston theory is employed for aerodynamic loading in the finite-element formulation. The panel flutter under combined thermal/aerodynamic loading can be separated into solving two problems in sequence. They are: (1) postbuckling deflection, stresses and buckling stability boundary, and (2) critical dynamic pressure and linear flutter boundary. The solution procedures in solving these problems are presented in detail. Finite element results of two-dimensional panels with uniform temperature change are compared with classic analytical solutions. Influence of nonuniform temperature distributions on critical buckling temperature, flutter deflection and stresses, and flutter boundary is also given.

Xue, David Y.↗

NASA NTRS1986

Mathematical aspects of finite element methods for incompressible viscous flows

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Gunzburger, M. D.↗