Search NASA⌕ Search

SEARCH · Search NASA

Results for “Finite element method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Nonlinear transient responses of structures by the spatial finite-element method.

Based upon the Principle of Virtual Work and D'Alembert's Principle, the assumed-displacement version of the spatial finite-element method is developed to predict the large deflection transient responses of structures including elastic-plastic, strain hardening, and strain-rate material behavior. The formulations are developed in detail for curved beamlike structures undergoing planar (1) Bernouilli-Euler-type or (2) Timoshenko-type deformation behavior. The resulting equations of motion are solved timewise by a finite-difference numerical procedure. The present predictions are evaluated via several beam and ring examples for which experimental measurements and independent finite-difference predictions in both space and time are available; very good agreement is noted. The consequences of employing several types of timewise finite-difference operators are examined. Also, some comparisons between finite-element predictions and finite-difference predictions are shown to illustrate 'typical comparisons' of efficiency for a given prediction accuracy.

Wu, R. W.-H.↗
NASA NTRS1998

Development of Least-Squares Finite Element Method

The main purpose of this final report is to study the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications.

Jiang, Bo-Nan↗
NASA NTRS2002

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

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

Kang, Kab S.↗
NASA NTRS2001

Finite Element Methods for real-time Haptic Feedback of Soft-Tissue Models in Virtual Reality Simulators

We have applied the linear elastic finite element method to compute haptic force feedback and domain deformations of soft tissue models for use in virtual reality simulators. Our results show that, for virtual object models of high-resolution 3D data (>10,000 nodes), haptic real time computations (>500 Hz) are not currently possible using traditional methods. Current research efforts are focused in the following areas: 1) efficient implementation of fully adaptive multi-resolution methods and 2) multi-resolution methods with specialized basis functions to capture the singularity at the haptic interface (point loading). To achieve real time computations, we propose parallel processing of a Jacobi preconditioned conjugate gradient method applied to a reduced system of equations resulting from surface domain decomposition. This can effectively be achieved using reconfigurable computing systems such as field programmable gate arrays (FPGA), thereby providing a flexible solution that allows for new FPGA implementations as improved algorithms become available. The resulting soft tissue simulation system would meet NASA Virtual Glovebox requirements and, at the same time, provide a generalized simulation engine for any immersive environment application, such as biomedical/surgical procedures or interactive scientific applications.

Frank, Andreas O.↗
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↗
DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Users manual for AUTOMESH-2D: A program of automatic mesh generation for two-dimensional scattering analysis by the finite element method

AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

Hua, Chongyu↗
NASA NTRS1996

Three-Dimensional Simulations of Marangoni-Benard Convection in Small Containers by the Least-Squares Finite Element Method

This paper reports a numerical study of the Marangoni-Benard (MB) convection in a planar fluid layer. The least-squares finite element method (LSFEM) is employed to solve the three-dimensional Stokes equations and the energy equation. First, the governing equations are reduced to be first-order by introducing variables such as vorticity and heat fluxes. The resultant first-order system is then cast into a div-curl-grad formulation, and its ellipticity and permissible boundary conditions are readily proved. This numerical approach provides an equal-order discretization for velocity, pressure, vorticity, temperature, and heat conduction fluxes, and therefore can provide high fidelity solutions for the complex flow physics of the MB convection. Numerical results reported include the critical Marangoni numbers (M(sub ac)) for the onset of the convection in containers with various aspect ratios, and the planforms of supercritical MB flows. The numerical solutions compared favorably with the experimental results reported by Koschmieder et al..

Yu, Sheng-Tao↗
NASA NTRS1975

A general algorithm using finite element method for aerodynamic configurations at low speeds

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Balasubramanian, R.↗
NASA NTRS2007

Simulating Space Capsule Water Landing with Explicit Finite Element Method

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.

Wang, John T.↗
NASA NTRS1972

Application of finite-element method in the computation of temperature with emphasis on radiative exchanges.

Analyses pertaining to the solution of heat transfer problems in combined modes based on the finite-element method are presented. Two elements - a triangular element employing two spatial variables and a multi-faceted bar element employing one spatial variable - with nonlinear radiation on the boundaries are detailed. The radiative effects considered on the diffuse-gray surface elements include: (1) directional radiant fluxes from distant sources, (2) radiative exchanges including surfaces of prescribed temperatures, and (3) radiative exchanges including elements whose temperatures are not known a priori. The nonlinear part of the boundary condition is treated in two different ways: (1) a consistent linearization method, and (2) a direct energy distribution method. Applications of these elements together with solution algorithms to three sample problems exhibit solution capability and obtainable accuracy.

Lee, H.-P.↗
NASA NTRS1988

A proposed method for enhanced eigen-pair extraction using finite element methods: Theory and application

The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Jara-Almonte, J.↗
NASA NTRS1987

Finite element methods for compressible flows

The problems of mesh generation and developing effective algorithms for the solution of the equations of compressible flow on unstructured meshes are discussed. Adaptive mesh refinement methods can be implemented in a straightforward manner. Possible adaptive strategies are examined. A finite element method adapted to problems involving high speed compressible flow is described. The adaptive mesh regeneration procedure appears to offer the possibility of large computational savings in three dimensional flow computation.

Morgan, K.↗
NASA NTRS1979

Application of a finite element method for computing grazing incidence wave structure in an impedance tube - Comparison with experiment

The acoustic performance of a liner specimen, in a grazing incidence impedance tube, is analyzed using a finite element method. The liner specimen was designed to be a locally reacting, two-degree-of-freedom type with the resistance and reactance provided by perforated facesheets and compartmented cavities. Measured and calculated wave structures are compared for both normal and grazing incidence from 0.3 to 1.2 kHz. A finite element algorithm was incorporated into an optimization loop in order to predict liner grazing incidence impedance from measured SWR and null position data. Results suggest that extended reaction effects may have been responsible for differences between normal and grazing incidence impedance estimates.

Lester, H. C.↗
NASA NTRS1979

The application of the least squares finite element method to Abel's integral equation

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

Balasubramanian, R.↗
DOE OSTI2026

Full-wave modeling of RF waves in fusion plasmas with finite element method: Progress in past decades and its future role

This paper reviews the progress in computing radio frequency (RF) wave fields in fusion plasmas, specifically focusing on simulations utilizing the finite element method (FEM) over the past few decades. Computing RF wave fields in fusion plasmas presents unique challenges due to large simulation domains, complex antenna structures, non-local dielectric properties, and wide ranges of spatial scales. It highlights key developments and outlines future directions, primarily addressing waves in the ion cyclotron (IC) to lower hybrid (LH) frequency range. We begin with briefly revisiting earlier developments before the widespread availability of modern computer-aided engineering (CAE) software based on FEM. This historical perspective illuminates early progress and the physics difficulties that motivated ongoing work within the community. Modern wave simulations for RF antennas based on FEM are characterized by the use of detailed 3D antenna model geometry generated from engineering CAD software and localized wave dielectric model. Significant advancements have also been made in improving physics models to include phenomena such as RF sheath rectification and wave scattering. FEM-based RF simulations have also been applied to compute wave propagation in the core region, where the inclusion of non-local dielectric response is crucial. This is a challenging goal, and several promising approaches have been proposed in this area. Additionally, RF simulation development initiatives based on open-source libraries have gained popularity, demonstrating scalability and flexibility in extending physics models. This paper will discuss the advantages and disadvantages of using such a publicly available FEM library.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗