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At least 1,189 records · Page 66

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NASA NTRS1989

On the accuracy of shape sensitivity derivatives

Six methods for calculating shape sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the finite-element mesh is refined, displacement sensitivity derivatives converge more slowly than the displacement themselves. Five of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer, rather than reduced accuracy.

Haftka, Raphael T.↗

NASA NTRS1992

Vibration attenuation of the NASA Langley evolutionary structure experiment using H(sub infinity) and structured singular value (micron) robust multivariable control techniques

The use is studied of active control to attenuate structural vibrations of the NASA Langley Phase Zero Evolutionary Structure due to external disturbance excitations. H sub infinity and structured singular value (mu) based control techniques are used to analyze and synthesize control laws for the NASA Langley Controls Structures Interaction (CSI) Evolutionary Model (CEM). The CEM structure experiment provides an excellent test bed to address control design issues for large space structures. Specifically, control design for structures with numerous lightly damped, coupled flexible modes, collocated and noncollocated sensors and actuators and stringent performance specifications. The performance objectives are to attenuate the vibration of the structure due to external disturbances, and minimize the actuator control force. The control design problem formulation for the CEM Structure uses a mathematical model developed with finite element techniques. A reduced order state space model for the control design is formulated from the finite element model. It is noted that there are significant variations between the design model and the experimentally derived transfer function data.

Balas, Gary J.↗

NASA NTRS1992

A general explicit or semi-explicit algorithm for compressible and incompressible flows

A unified finite element algorithm is developed which is applicable to a wide range of problems of fluid mechanics without recourse to artificial, empirically determined factors. In its explicit form, the algorithm is similar to the Taylor-Galerkin scheme and is easily adopted to standard codes. The scheme proposed here possesses sufficient natural balancing diffusion and thus reduces and sometimes eliminates the need for special 'shock capturing' diffusion. The efficiency of the algorithm is demonstrated using several examples ranging from incompressible through transonic regions to supersonic flows.

Zienkiewicz, O. C.↗

NASA NTRS2002

Gust Acoustics Computation with a Space-Time CE/SE Parallel 3D Solver

The benchmark Problem 2 in Category 3 of the Third Computational Aero-Acoustics (CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem concerns the unsteady response of an isolated finite-span swept flat-plate airfoil bounded by two parallel walls to an incident gust. The acoustic field generated by the interaction of the gust with the flat-plate airfoil is computed by solving the 3D (three-dimensional) Euler equations in the time domain using a parallel version of a 3D CE/SE solver. The effect of the gust orientation on the far-field directivity is studied. Numerical solutions are presented and compared with analytical solutions, showing a reasonable agreement.

Wang, X. Y.↗

DOE OSTI2022

Transient MOC with frequency transform and DSA on unstructured mesh

We present an implementation of the transient method of characteristics (MOC) with isotropic time derivatives, accelerated by diffusion synthetic acceleration (DSA). The fully implicit frequency transform method is used to solve the transient problem with analytic precursor integration. The code works on meshes composed of almost any of the commonly used non-curvilinear finite element types, and can handle the deformation of geometry in time-dependent transport calculations. We present results of a continuous Fourier analysis for the transient multigroup DSA problem, and representative benchmarking results are presented for the C5G7-TD benchmark in 2D showing reasonable performance and agreement compared to other codes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

A stable potential-based time-domain method for wideband elec- tromagnetic analysis

In previous research, the frequency-domain A-ϕ formulation has been validated using the finite element method for electromagnetic simulations of low-frequency and multi- scale problems, demonstrating excellent numerical accuracy, good matrix condition, and high computational efficiency. Time- domain simulations provide significant advantages for modeling wideband problems and are crucial for multiphysics applications. In this paper, the frequency-domain A-ϕ formulation is extended to the time domain. The central difference scheme is employed for temporal discretization to ensure both accuracy and stability. A numerical example is presented to demonstrate the capability of the proposed time-domain method in wideband electromagnetic analysis.

Mekonnen, Minyichil↗

NASA NTRS1989

Advanced development of the boundary element method for steady-state heat conduction

Considerable progress has been made in recent years toward advancing the state-of-the-art in solid mechanics boundary element technology. In the present work, much of this new technology is applied in the development of a general-purpose boundary element method (BEM) for steady-state heat conduction. In particular, the BEM implementation involves the use of higher-order conforming elements, self-adaptive integration and multi-region capability. Two- and three-dimensional, as well as axisymmetric analysis, are incorporated within a unified framework. In addition, techniques are introduced for the calculation of boundary flux, and for the inclusion of thermal resistance across interfaces. As a final extension, an efficient formulation is developed for the analysis of solid three-dimensional bodies with embedded holes. For this last class of problems, the new BEM formulation is particularly attractive, since use of the alternatives (i.e. finite element or finite difference methods) is not practical. A number of detailed examples illustrate the suitability and robustness of the present approach for steady-state heat conduction.

Dargush, G. F.↗

DOE OSTI2015

A stochastic approach to uncertainty in the equations of MHD kinematics

The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertainty in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Verification Problems for Parameterized Load Curves in DYNA3D

Two verification problems are presented which test a set of newly implemented load curve features in the explicit finite element program DYNA3D. Each test consists of a single element, with the velocity of each node specified via a different load curve type. The first test covers initialization and run-time execution of these new features, while the second test covers redefinition of load curves upon restart. The proposed problems may be easily extended to test additional load curve features.

42 ENGINEERING↗

NASA NTRS1988

Accuracy analysis of the semi-analytical method for shape sensitivity calculation

The semianalytical method, widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements, is studied in this paper. The paper shows that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. The errors are shown to be associated with the structural model. An error index is developed to test the accuracy of the semianalytical method. It characterizes the difference in errors between a general finite-difference method and the semianalytical method. Moreover, a method for improving the accuracy of the semianalytical method (when possible) is provided. Examples are presented to demonstrate the use of the error index.

Barthelemy, Bruno↗

NASA NTRS1986

Simplified cyclic structural analyses of SSME turbine blades

Anisotropic high-temperature alloys are used to meet the safety and durability requirements of turbine blades for high-pressure turbopumps in reusable space propulsion systems. The applicability to anisotropic components of a simplified inelastic structural analysis procedure developed at the NASA Lewis Research Center is assessed. The procedure uses as input the history of the total strain at the critical crack initiation location computed from elastic finite-element analyses. Cyclic heat transfer and structural analyses are performed for the first stage high-pressure fuel turbopump blade of the space shuttle main engine. The blade alloy is directionally solidified MAR-M 246 (nickel base). The analyses are based on a typical test stand engine cycle. Stress-strain histories for the airfoil critical location are computed using both the MARC nonlinear finite-element computer code and the simplified procedure. Additional cases are analyzed in which the material yield strength is arbitrarily reduced to increase the plastic strains and, therefore, the severity of the problem. Good agreement is shown between the predicted stress-strain solutions from the two methods. The simplified analysis uses about 0.02 percent (5 percent with the required elastic finite-element analyses) of the CPU time used by the nonlinear finite element analysis.

Kaufman, A.↗

NASA NTRS1989

Inverse dynamics of a 3 degree of freedom spatial flexible manipulator

A technique is presented for solving the inverse dynamics and kinematics of 3 degree of freedom spatial flexible manipulator. The proposed method finds the joint torques necessary to produce a specified end effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested through simulation analysis. Results show the potential use of this method for the smooth motion control of space telerobots.

Bayo, Eduardo↗

NASA NTRS1993

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Farhat, Charbel↗

NASA NTRS1988

A comparison of experimental and calculated thin-shell leading-edge buckling due to thermal stresses

High-temperature thin-shell leading-edge buckling test data are analyzed using NASA structural analysis (NASTRAN) as a finite element tool for predicting thermal buckling characteristics. Buckling points are predicted for several combinations of edge boundary conditions. The problem of relating the appropriate plate area to the edge stress distribution and the stress gradient is addressed in terms of analysis assumptions. Local plasticity was found to occur on the specimen analyzed, and this tended to simplify the basic problem since it effectively equalized the stress gradient from loaded edge to loaded edge. The initial loading was found to be difficult to select for the buckling analysis because of the transient nature of thermal stress. Multiple initial model loadings are likely required for complicated thermal stress time histories before a pertinent finite element buckling analysis can be achieved. The basic mode shapes determined from experimentation were correctly identified from computation.

Jenkins, Jerald M.↗

DOE OSTI2019

The Target-Matrix Optimization Paradigm for High-Order Meshes

Here, we describe a framework for controlling and improving the quality of high-order finite element meshes based on extensions of the Target-Matrix Optimization Paradigm (TMOP) of [P. Knupp, Eng. Comput., 28 (2012), pp. 419--429]. This approach allows high-order applications to have a very precise control over local mesh quality, while still improving the mesh globally. We address the adaption of various TMOP components to the settings of general isoparametric element mappings, including the mesh quality metric in 2D and 3D, the selection of sample points and the solution of the resulting mesh optimization problem. We also investigate additional practical concerns, such as tangential relaxation and restricting the deviation from the original mesh. The benefits of the new high-order TMOP algorithms are illustrated on a number of test problems and examples from a high-order arbitrary Lagrangian--Eulerian (ALE) application [BLAST: High-order curvilinear finite elements for shock hydrodynamics, http://www.llnl.gov/CASC/blast]. Our implementation is freely available in an open-source library form [MFEM: Modular parallel finite element methods library, http://mfem.org].

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

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.

Cerro, J. A.↗

DOE OSTI2024

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of working on a weighted space by establishing operator-norm bounds for finite element and graph-based discretizations of Matérn-type priors and deconvolution forward models. For linear-Gaussian inverse problems, we develop a general theory to characterize the error in the approximation to the posterior. We also embed the computational framework into ensemble Kalman methods and MAP estimators for nonlinear inverse problems. Furthermore, our operator-norm bounds for prior discretizations guarantee the scalability and accuracy of these algorithms under mesh refinement.

Bayesian inverse problem↗

DOE OSTI2024

A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization’s superior accuracy over other discretizations of anisotropic heat flux, achieving error 1000x smaller for anisotropy ratio of 10 9 , for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

97 MATHEMATICS AND COMPUTING↗