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At least 271 records · Page 15

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NASA NTRS1990

A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Collins, Jeffery D.↗

NASA NTRSDate not supplied

High-Order Shock Fitting with Finite Element Methods

A moving-grid, shock-tracking, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. Three different methods for specifying the shock motion have been tested,and the order of accuracy of the resulting solutions was verified. It was found that one of the methods is applicable only for problems with a constant upstream flow state, whereas the other two methods converge to the expected solution for general shock problems. When using a finite element method with polynomial degree p, the two general shock motion methods converged with the expected order of accuracy of (p+1). Finally, accurate solutions are obtained for supersonic nozzle and blunt body bow shock problems. Based on the results, it is concluded that the shock tracking method can preserve high-order solution accuracy in the vicinity of a shock wave.

Luke D'Aquila↗

NASA NTRS1992

On development of a finite dynamic element and solution of associated eigenproblem by a block Lanczos procedure

The paper first presents the details of the development of a new six-noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.

Gupta, K. K.↗

NASA NTRS1993

Development of an hp-version finite element method for computational optimal control

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.

Hodges, Dewey H.↗

NASA NTRS1975

Development and applications of two computational procedures for determining the vibration modes of structural systems

Two computational procedures for analyzing complex structural systems for their natural modes and frequencies of vibration are presented. Both procedures are based on a substructures methodology and both employ the finite-element stiffness method to model the constituent substructures. The first procedure is a direct method based on solving the eigenvalue problem associated with a finite-element representation of the complete structure. The second procedure is a component-mode synthesis scheme in which the vibration modes of the complete structure are synthesized from modes of substructures into which the structure is divided. The analytical basis of the methods contains a combination of features which enhance the generality of the procedures. The computational procedures exhibit a unique utilitarian character with respect to the versatility, computational convenience, and ease of computer implementation. The computational procedures were implemented in two special-purpose computer programs. The results of the application of these programs to several structural configurations are shown and comparisons are made with experiment.

Kvaternik, R. G.↗

NASA NTRS1989

A combined finite element and boundary integral formulation for solution via CGFFT of 2-dimensional scattering problems

A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principle advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

Collins, Jeffery D.↗

NASA NTRS1990

Periodic trim solutions with hp-version finite elements in time

Finite elements in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-finite elements for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time finite elements in which one element is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that finite elements in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.

Peters, David A.↗

NASA NTRS1991

Periodic trim solutions with hp-version finite elements in time

Hou, Lin-Jun↗

NASA NTRS1982

Reliability of the finite element method for calculating free edge stresses in composite laminates

The interlaminar normal stress distributions along the interface between the +45 deg and -45 deg plies of a graphite/epoxy laminate, obtained by various investigators, were found to disagree in both magnitude and sign. The reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated. The history of the edge-stress problem is reviewed, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed. The finite element analysis in these problems yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a + or -45 deg ply laminate near the singularity were similar to those of the two elasticity problems, demonstrating the methods, accuracy for calculating interlaminar stresses in composite laminates. The disagreement between the numerical methods was attributed to the unsymmetric stress tensor at singularity.

Whitcomb, J. D.↗

NASA NTRS1993

Development of an hp-version finite element method for computational optimal control

The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. 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.

Hodges, Dewey H.↗

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 NTRS1982

A wave envelope finite element scheme for acoustical radiation

The aeroacoustic problem associated with the radiation of fan noise from the inlet of a turbofan aircraft engine, the dimensions of which are generally many times larger than the acoustical wavelengths of the major energy-carrying frequencies, is considered. In the present approach, a conventional finite element solution in the inner region is compatibly matched to a 'wave envelope' finite element solution in a large but finite outer region. The inclusion of a wavelike variation with the correct asymptotic decay in the shape functions for the outer region preserves the correct behavior of the solution at large distances. The method is initially presented for a simple one-dimensional model based on the solution of Webster's horn equation. Results are presented for the specific case of a uniform cylindrical section joined to a conical expansion, and also for a simple axisymmetric test case of the calculation of acoustical pressure generated by a vibrating circular piston located at the center of an infinite rigid baffle.

Astley, R. J.↗

NASA NTRS1993

Application of symbolic and algebraic manipulation software in solving applied mechanics problems

As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.

Tsai, Wen-Lang↗

NASA NTRS1983

Numerical simulation of transient finite deformations of thin beams

The formulation of the problem of finite elastic-viscoplastic deformation of thin beams is described. The finite element analysis of a representative problem is presented and various solution methods are surveyed.

Rodal, J. J. A.↗

NASA NTRS1983

Two-dimensional Finite Element Modeling for Modeling Tectonic Stress and Strain

Techniques of finite element analysis in two dimensional plane strain were applied to problems of geophysics and tectonics. More specifically, the flexibility of the finite element method was employed to address problems involving geological complexity and fault interactions. The modeling of effective anisotropy in material elastic properties proved useful in describing the deformation of faulted crustal blocks. The applications of this modeling work to problems of actual tectonics in southern California was explored. Preliminary models show encouraging agreement with measured tectonic strain in this region, and modeling work was done to gain an understanding of the stress state in a locked fault region with future seismic potential.

Lyzenga, G. A.↗

NASA NTRS2002

A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems

A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.

Ransom, Jonathan B.↗

NASA NTRS1992

Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Gupta, Viney K.↗

NASA NTRS1992

Modal test/analysis correlation of Space Station structures using nonlinear sensitivity

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Gupta, Viney K.↗