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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

A finite element solution of unsteady transonic flow problems for three-dimensional wings and bodies

A computerized finite element method has been developed to solve a form of the three-dimensional inviscid, irrotational unsteady transonic equation for pointed and rectangular wings and wing-body combinations. The equation is a 'parabolized' version of the full unsteady transonic equation which includes the effect of the advancing wave and the acceleration in the steady flow field thus including a thickness effect. Automatic mesh generation using conformal mapping has the advantage of allowing relatively arbitrary cross-sections to be closely approximated while taking advantage of the body's similarity to a more simple configuration. Plunge, pitch, and roll modes are computed

Kimble, K. R.↗
NASA NTRS1980

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

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.

Atluri, S. N.↗
NASA NTRS1984

A high-accuracy optical linear algebra processor for finite element applications

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Casasent, D.↗
NASA NTRS1994

Analysis of random structure-acoustic interaction problems using coupled boundary element and finite element methods

A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.

Mei, Chuh↗
NASA NTRS1985

Finite element methods on supercomputers - The scatter-problem

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.

Loehner, R.↗
NASA NTRS1988

An adaptive finite element solver for transient problems with moving bodies

The combination of adaptive remeshing techniques, flow solvers for transient problems with moving grids, and integrators for rigid body motion is presented. The resulting scheme allows the economic simulation of fully coupled fluid-rigid body interaction problems of arbitrary geometric complexity. Several results are given to demonstrate the capabilities developed.

Lohner, Rainald↗
NASA NTRS1974

Compressible seal flow analysis using the finite element method with Galerkin solution technique

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.

Zuk, J.↗
NASA NTRS1974

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Yu, Y.-Y.↗
NASA NTRS1991

Periodic trim solutions with HP-version finite elements in time

Finite Element in Time has been proven to be a powerful alternative solving strategy for the rotor craft trim problem. Additionally, Finite Element Method in Time has been developed in various versions like time-marching framework, Galerkin framework, Rayleigh-Ritz framework, and mixed formulation. Recently, this method was applied to the rotorcraft trim problem to obtain linearized solutions. The rotorcraft trim problem consists of trying to find a period solution for period-coefficient, differential equations subject to side constraints where certain force and momentum balance equations are forced to be equal to zero. There are free (or trim) parameters that are chosen to meet these side constraints. This project aims at expanding the application, in terms of the rotorcraft trim problem, from a linearized solution to nonlinear solution.

Source record↗
NASA NTRS1981

Acoustic transmission in non-uniform ducts with mean flow. I - The method of weighted residuals. II - The finite element method

The problem of acoustic transmission through nonuniform ducts containing a high-speed subsonic flow is studied by means of the method of weighted residuals in the form of a modified Galerkin method and a Galerkin formulation of the finite element method. The method of weighted residuals is shown to employ the basis functions generated from eigenvalue calculations for the case of no flow, and is verified by comparison with exact eigenvalue calculations in the uniform duct case and numerical solutions of the one-dimensional form of the equations in the nonuniform duct case. The finite element scheme based on both the Galerkin method and the residual least squares method and employing eight-noded isoparametric elements is presented and used to investigate multimodal propagation by the coupling of the solution in the duct nonuniform section to modal expansions in uniform sections. Comparison of the results of the two methods reveals them to be in substantial agreement, and predicts the importance of multimodal interactions at high Mach numbers.

Eversman, W.↗
NASA NTRS1989

Probabilistic boundary element method

The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.

Cruse, T. A.↗
NASA NTRS1996

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

Chen, Zhangxin↗
NASA NTRS1982

A penalty finite element algorithm for parabolic flow problems

The thin-layer simplification of the two-dimensional Navier-Stokes equations for steady viscous flow are developed using an order of magnitude analysis. A space marching finite element solution algorithm is developed, wherein the first order continuity effects are enforced as a penalty function differential constraint. Numerical results are presented to document accuracy and convergence features of the numerical solution algorithm.

Baker, A. J.↗
NASA NTRS1975

ISOFINEL: Isoparametric finite element code for elastic analysis of two-dimensional bodies

A formulation is presented for the development of a finite element program for the elastic analysis of two-dimensional bodies using the eight-node isoparametric quadrilateral. The program solves for both plane stress and plane strain problems. The finite element formulation based on the isoparametric displacement functions is presented. The program structure is given in the form of flow diagrams with descriptions of the numerical procedure used to obtain the element stiffness matrix, and the solution method employed to solve for nodal displacements. Three numerical examples (a plate under uniaxial tension, a plate under pure shear, and a beam under pure bending) are presented to illustrate the capability and limitations of the element implementation. The first problem is solved exactly by the element, as predicted by the form of its displacement functions. In the other two problems the accuracy of the solution is highly dependent upon the slenderness of the element, the number of elements in the map, and the numerical integration scheme used to build the element stiffness matrix.

Marino, C.↗
NASA NTRS1980

Application of finite-element-techniques to the interaction of conduction and radiation in an absorbing, scattering and emitting medium

In this paper, the authors demonstrate that a Galerkin finite element method of analysis, utilizing isoparametric elements, offers a viable means of solving continuum thermal radiation problems with conduction in a participating medium. The participating medium was considered to be a gray radiation medium exhibiting isotropic absorption, emission, and scattering characteristics and optical properties that are independent of temperature. The medium was considered to be bounded by infinite parallel opaque, gray surfaces with diffuse emission and reflection characteristics. In solving this problem, a finite element formulation was developed to describe a system in radiative equilibrium. Then the results of this first analysis were linked with a second finite element model which incorporated conduction into the analysis. The results of this study were found to be in good agreement with existing published data. The model offers the following advantageous features: geometric generality, a computational algorithm which is 'convenient' and 'computable', and a functional basis for extension of the radiation model to higher order approximation.

Wu, S. T.↗
NASA NTRS1982

Finite element formulation of transonic flow problems

Reference is made to the study by Akay and Ecer (1982), which treated the solution of full Euler equations for transonic, rotational, inviscid flows. Attention is given here to some of the important features of a general finite element formulation for transonic flows. Both rotational and irrotational cases are treated. Transonic flow through a parallel channel with a 4.2 percent thick circular bump is analyzed for an upstream Mach number of 0.85. A figure is included showing the computational grid of 44 x 8 elements. In this case, the distance between the walls of the channel is 2.073 times the chord length of the bump. The pressure distributions over the bump for rotational assumptions are presented.

Akay, H. U.↗
NASA NTRS1981

Accuracy and stability of finite element schemes for the duct transmission problem

An investigation is conducted regarding the feasibility of approaches for improving the efficiency and stability of existing finite element method (FEM) schemes, taking into account both analytical and numerical studies. Of the four schemes considered for the 'steady' problem, the Hermitian Galerkin formulation appears to be the most efficient and therefore the most suitable scheme for futher full scale implementation. The Hermitian residual least squares (RLS) scheme although comparable in accuracy for the cases considered exhibits a slight tendency to cumulative errors. The performance of both the Lagrangian element schemes considered compares poorly with that of their Hermitian element counterparts. This is particularly true of the Lagrangian RLS scheme. The presence of internal oscillatory components is an inevitable consequence of all Galerkin schemes irrespective of element type.

Astley, R. J.↗