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Toward perfectly absorbing boundary conditions for Euler equations

AIAA JOURNAL 1999年第8期37卷 912-918页

作者： Hayder, ME Hu, FQ Hussaini, MY Rice Univ Ctr Res Parallel Computat Houston TX 77005 USA Old Dominion Univ Dept Math & Stat Norfolk VA 23529 USA Florida State Univ Program Computat Sci & Engn Tallahassee FL 32306 USA

We examine the effectiveness of absorbing layers as nonreflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems-shock-vortex interactions, a plane free shear how, and an axisymmetric jet-with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

关键词： Euler Equations Maxwell Equation Vortices Shear Layers numerical Modeling Kelvin Helmholtz Instability Navier Stokes Equations Shock Wave Interaction numerical algorithms MacCormack Method

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A variational formulation for nonlocal damage models

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INTERNATIONAL JOURNAL OF PLASTICITY 1999年第2期15卷 119-138页

作者： Lorentz, E Andrieux, S Elect France Direct Etud & Rech F-92141 Clamart France Lab Mecan & Technol Cachan F-94235 Cachan France

To control localization phenomena exhibited by strain softening constitutive relations, several issues have been proposed by various authors, based on spatial regularization. In this paper, we define a variational framework, thought to encompass some of these issues: the constitutive relations are written at the structural scale and become minimization problems. Such a framework is not only well-suited to the mathematical study of the boundary value problem, but also leads in a natural way to an efficient numerical algorithm. The formulation is first presented, then applied to several classes of models existing in the literature : a homogenization-based constitutive relation, a porosity model and gradient plasticity. Besides the higher degree of generality confered by the formulation, it will be shown that several proper ties can be obtained for these models. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： fracture constitutive behaviour energy methods numerical algorithms

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Fatigue crack-growth behavior of materials in viscous fluid environments

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第9期47卷 1843-1871页

作者： Yi, KS Cox, BN Dauskardt, RH Stanford Univ Dept Mat Sci & Engn Stanford CA 94305 USA Rockwell Int Sci Ctr Thousand Oaks CA 91360 USA

The potent effect of the hydrodynamic pressure developed in the wake of a crack growing under cyclic loads in a viscous fluid environment is considered. While existing semi-analytical solutions provide an estimate of the hydrodynamic pressure effect, they are inherently restricted by the assumption of specific crack opening profiles. To correct this limitation and to extend the study to a complete range of materials and fluid environments, a fully consistent numerical approach was developed. A self-consistent fracture mechanics solution procedure is derived initially for atomistically sharp cracks in brittle materials, and then extended to include the effect of crack tip blunting in more ductile materials. Three important dimensionless parameters are identified through which effects of various physical properties on crack-growth behavior can be examined. These include specimen geometry, material properties, fluid viscosity and cyclic loading conditions. General plots are constructed spanning wide ranges of these dimensionless parameters so that the hydrodynamic pressure contribution to crack-growth rates can easily be estimated for a complete range of materials, fluid environments and loading parameters. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： fracture fluid crack mechanics cyclic loading numerical algorithms

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A return-map algorithm for general associative isotropic elasto-plastic materials in large deformation regimes

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INTERNATIONAL JOURNAL OF PLASTICITY 1999年第12期15卷 1359-1378页

作者： Auricchio, F Taylor, RL Univ Pavia Dipartimento Meccan Strutturale I-27100 Pavia Italy Univ Calif Berkeley Dept Civil Engn Berkeley CA 94720 USA

The present paper addresses a flexible solution algorithm for associative isotropic elasto-plastic materials, i.e. for materials whose elastic and plastic behaviors are described through an isotropic free-energy function, an isotropic yield function and an associative flow rule. The discussion is relative to a large deformation regime, while no hardening mechanisms are included. The algorithm is based on a combination of the operator split method and a return map scheme. Both the algorithm linearization and the requirements for the yield criterion convexity are discussed in detail. Finally, to show the algorithm flexibility and performance, the discussion is specialized to three yield criteria and some test problems are studied. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： elastic-plastic finite strain finite elements numerical algorithms return map

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The role of texture in tension-compression asymmetry in polycrystalline NiTi

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INTERNATIONAL JOURNAL OF PLASTICITY 1999年第1期15卷 69-92页

作者： Gall, K Sehitoglu, H Univ Illinois Dept Mech & Ind Engn Urbana IL 61801 USA

The purpose of the present study is to thoroughly understand the stress-strain behavior of polycrystalline NiTi deformed under tension versus compression, To do this, a micromechanical model is used which incorporates single crystal constitutive relationships and experimentally measured polycrystalline texture into the self-consistent formulation. For the first time it is quantitatively demonstrated that texture measurements coupled with a micromechanical model can accurately predict tension/compression asymmetry in NiTi shape memory alloys. The predicted critical transformation stress levels and transformation stressstrain slopes under both tensile and compressive loading are consistent with experimental results, For textured polycrystalline NiTi deformed under tension it is demonstrated that the martensite evolution is very abrupt, consistent with the Luders type deformation experimentally observed. The abrupt transformation under tension is attributed to the fact that the majority of the grains are oriented along the [111] crystallographic direction, which is soft under tensile loading. Since single crystals of the [111] orientation are hard under compression it is also demonstrated that under compression the martensite in textured polycrystalline NiTi evolves relatively slower. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： phase transformation constitutive behavior polycrystalline material numerical algorithms textured shape memory alloy

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Infinite eigenvalue assignment for singular systems

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LINEAR ALGEBRA AND ITS APPLICATIONS 1999年第1-3期298卷 21-37页

作者： Chu, DL Ho, DWC Natl Univ Singapore Dept Math Singapore 119260 Singapore City Univ Hong Kong Dept Math Hong Kong Peoples R China

In this paper the infinite eigenvalue assignment problem for singular systems is studied. Necessary and sufficient conditions are presented under which there exists a state feedback such that the closed-loop system is regular and has only infinite eigenvalues. The main result is proved constructively based on some simple numerical algorithms. These numerical algorithms consist of an orthogonal reduction to an upper (block) Hessenberg form and a simple linear recursion deduced from 2 x 2 Givens transformations. (C) 1999 Elsevier Science Inc. All rights reserved.

关键词： infinite eigenvalue singular systems numerical algorithms orthogonal transformations

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Feasible direction algorithm for optimal control problems with state and control constraints: Implementation

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第3期101卷 623-649页

作者： Pytlak, R Vinter, RB Mil Univ Technol Fac Cybernet Warsaw Poland Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London England

In this paper, we describe the implementation aspects of an optimization algorithm for optimal control problems with control, state, and terminal constraints presented in our earlier paper. The important aspect of the implementation is that, in the direction-finding subproblems, it is necessary only to impose the state constraint at relatively few points in the time involved. This contributes significantly to the algorithmic efficiency. The algorithm is applied to solve several optimal control problems, including the problem of the abort landing of an aircraft in the presence of windshear.

关键词： optimal control state-constrained problems numerical algorithms

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Solid-solid phase transition modelling: relaxation procedures, configurational energies and thermomechanical behaviours

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INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 1999年第14期37卷 1821-1840页

作者： Pagano, S Alart, P Univ Montpellier 2 Mech & Civil Engn Lab F-34095 Montpellier 5 France

The behaviour of materials involving Solid-solid phase transitions may be modelled by more or less smooth laws. The corresponding physical basis and microscopic mechanisms are still in most cases controversial and out of our purpose. In a previous paper, we studied (from mathematical and numerical point of view) relaxation procedures of non-convex bulk potentials issued from the Fremond modelling. For example, the quasiconvexification is obtained by considering specific microstructures. By accepting local minima of the total energy as possible equilibrium state, we can find, numerically, hysteretic behaviours and fronts of phase transition. However, some thermomechanical modellings of solid-solid phase transitions involve interaction energies between the phases which account at the macroscopic scale for the incompatibilities between deformations at the microscopic scale. We define a class of models which contains the Fremond model as the simplest one. An interaction term is introduced and is discussed in the context of the generalized standard materials. This term may lead, according to a parameter noted G, to the instability of the equilibrium. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： shape memory alloys relaxation procedures configurational energies thermomechanical models numerical algorithms

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Solution of the state-dependent noise optimal control problem in terms of Lyapunov iterations

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AUTOMATICA 1999年第5期35卷 951-954页

作者： Gajic, Z Losada, R Rutgers State Univ Dept Elect & Comp Engn Piscataway NJ 08855 USA

In this paper we present the solution to the algebraic Riccati-type equation of the state-dependent noise linear-quadratic optimal control problem in terms of algebraic Lyapunov iterations. By properly initializing the sequence of algebraic Lyapunov iterations we got monotonic convergence from above to the positive-definite stabilizing solution of the algebraic Riccati-type equation (the solution that represents the optimal solution to the corresponding optimal control problem). The proposed algorithm requires much less computational efforts than those previously used to solve the same problem. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： stochastic control linear-quadratic regulators algebraic riccati equations Lyapunov methods numerical algorithms

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Optimal reduced-order compensation of time-varying discrete-time systems with deterministic and white parameters

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AUTOMATICA 1999年第1期35卷 129-138页

作者： Van Willigenburg, LG De Koning, WL Agr Univ Wageningen Syst & Control Grp NL-6703 HD Wageningen Netherlands Delft Univ Technol Fac Informat Technol & Syst NL-2628 CD Delft Netherlands

The finite-horizon optimal compensation problem is considered in the case of linear time-varying discrete-time systems with deterministic and white stochastic parameters and quadratic criteria. The dimensions of the compensator are a priori fixed and may be time varying. Also the dimensions of the system may be time varying. Strengthened discrete-time optimal projection equations (SDOPE) are developed which, within the class of minimal compensators, are equivalent to the first-order necessary optimality conditions. Based on the SDOPE and their associated boundary conditions, two numerical algorithms are presented to solve the two point boundary value problem. One is a homotopy algorithm while the second iterates the SDOPE repeatedly forward and backward in time. The latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation Riccati equations, associated with the full-order problem for systems with deterministic parameters. The algorithms are illustrated with a numerical example. The case of systems with deterministic parameters will be treated as a special case of systems with white parameters. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： reduced-order control numerical algorithms white stochastic parameters multiplicative noise finite horizon LQG control

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