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ASTM Special Technical Publication 2000年第1387期 126-135页

作者： Arzt, Markus Brocks, Wolfgang Mohr, Tainer GKSS Forschungszentrum Geesthacht G. Institut für Werkstofforschung Max-Planck-Straße 21502 Geesthacth Germany

A Newton algorithm is discussed. This algorithm allows for studying nonlinear material behavior, such as plasticity and viscoplasticity. The material behavior is described by so-called internal variables. The model applied in this paper was developed by Lemaitre and Chaboche. The Newton algorithm is implemented as a user-subroutine in the commercial finite-element method package ABAQUS. The results of a numerical analysis of the rotation of an aircraft turbine disk are presented. Cyclic loading conditions are studied, and the results are compared with numerical results in the literature.

关键词： Constitutive equations Cyclic loading Elasto-viscoplastic material Finite elements numerical algorithms

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Filter bank methods for hyperbolic PDEs

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SIAM JOURNAL ON numerical ANALYSIS 1999年第4期36卷 1183-1233页

作者： Waldén, J Uppsala Univ Dept Comp Sci SE-75104 Uppsala Sweden

We use biorthogonal filter banks to solve hyperbolic PDEs adaptively with a sparse multilevel representation of the solution. The methods described are of finite difference type, and the filter banks are used to give a sparse representation of signals and to transform between grids on different scales. We derive bounds for the error and number of coefficients in the sparse representation. These bounds also apply for filter banks that are not associated with any wavelets. We develop algorithms for fast differentiation and multiplication in detail. The strength of the method is shown in various test problems.

关键词： wavelets adaptive PDE methods hyperbolic equations numerical algorithms

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Uniqueness of a class of nonlinear electrostatic field problems

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IEE PROCEEDINGS-SCIENCE MEASUREMENT AND TECHNOLOGY 1999年第4期146卷 175-181页

作者： de Hoop, AT Lager, IE Delft Univ Technol Fac Informat Technol & Syst Lab Electromagnet Res NL-2628 CD Delft Netherlands Delft Univ Technol Fac Informat Technol & Syst Int Res Ctr Telecommun Transmiss & Radar NL-2628 CD Delft Netherlands

The uniqueness properties of a class of nonlinear electrostatic field problems are investigated. The study was motivated by the development of numerical algorithms to analyse the performance of nonlinear semiconducting electron devices. Here, existence and uniqueness of the solution are prerequisites for the numerical results to have any meaning at all.

关键词： Mathematical analysis Function theory, analysis 3D Euclidean space nonlinear semiconducting electron device nonlinear electrostatic field problems Electrostatics, magnetostatics semiconductor device models constitutive operators classical field theory electric fields uniqueness properties numerical algorithms electric potential performance analysis interface boundary conditions Classical field theory Semiconductor device modelling, equivalent circuits, design and testing partial differential equations Electrostatics

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Integration algorithm for modeling the elasto-viscoplastic response of polycrystalline materials

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第6期47卷 1219-1238页

作者： Sarma, G Zacharia, T Oak Ridge Natl Lab Oak Ridge TN 37831 USA

An integration scheme is presented for modeling the texture evolution and stress-strain response of elasto-viscoplastic polycrystalline materials. Single crystal kinematics based on a multiplicative decomposition of the deformation gradient is used to obtain an evolution equation for the crystal elastic deformation gradient. An implicit scheme to integrate this equation is presented which is stable and efficient. The reorientation of the crystal as well as the elastic strain can then be obtained from a polar decomposition of the elastic deformation gradient. numerical studies are presented using material parameters for aluminum (FCC crystals) and zircaloy (HCP crystals) to demonstrate the general nature of the model. Predictions of the model are also compared with those obtained using a rigid-viscoplastic polycrystal model which neglects the elastic response. Retaining the elastic response makes the model useful for large deformation analyses where both anisotropy due to texture as well as elastic effects such as springback and residual stresses are important. (C) 1999 Elsevier Science Ltd, All rights reserved.

关键词： constitutive behavior crystal plasticity elastic-viscoplastic material polycrystalline material numerical algorithms

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Accuracy of shock capturing in two spatial dimensions

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AIAA JOURNAL 1999年第9期37卷 1072-1079页

作者： Carpenter, MH Casper, JH NASA Langley Res Ctr Aerodynam & Acoust Methods Branch Hampton VA 23681 USA Old Dominion Univ Norfolk VA 23529 USA

An assessment of the accuracy of shock-capturing schemes is made for two-dimensional steady flow around a cylindrical projectile. Both a linear fourth-order method and a nonlinear third-order method are used in this study. This study shows, contrary to conventional wisdom, that captured two-dimensional shocks are asymptotically first order, regardless of the design accuracy of the numerical method. The practical implications of this finding are discussed in the context of the efficacy of high-order numerical methods for discontinuous flows.

关键词： Projectiles Freestream Conditions Rankine Hugoniot Relation Bow Shock Roe Approximate Riemann Solver Stagnation Point numerical algorithms Shock Capturing Method Cartesian Coordinate System Spectral Algorithm

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Arnold tongue predictions of secondary buckling in thin elastic plates

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第10期47卷 2187-2206页

作者： Everall, PR Hunt, GW Univ Bath Dept Mech Engn Bath BA2 7AY Avon England

The stability of post-buckled states for simply-supported flat elastic plates under compression is investigated for a range of in-plane boundary conditions. The von Karman plate equations are reduced to a series of ODEs which are solved numerically under parametric variation of both load and length. Results are checked against full numerical solutions of the PDEs, and comparison with a modal analysis highlights the dominant passive contaminations. The nondimensional amplitude at secondary bifurcation, for any combination of modes and all plate lengths, is presented in a concise form using the parameter space of Arnold tongues. This demonstrates that compound bifurcation represents a worst case for post-buckling reserve, and that long plates have inherently more such reserve than short plates. It is also shown that stiffening the boundaries against inplane movement is destabilizing, in that it induces mode jumping at secondary bifurcation to occur at an earlier stage in the post-buckling regime. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： structures energy methods numerical algorithms mode jumping

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Modelling high-velocity impact phenomena using unstructured dynamically-adaptive Eulerian meshes

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第4期47卷 731-762页

作者： Kelmanson, MA Maunder, SB Univ Leeds Dept Appl Math Leeds LS2 9JT W Yorkshire England

Presented herein is an adaptive-mesh computational method for the efficient solution of the continuum equations of compressible flow for high-velocity impact dynamics. The integral forms of the governing equations are used to derive a stable form of energy equation, using internal rather than total energy, after which the corresponding differential forms are solved approximately in two dimensions via a three-stage-pressure, stress and advection-finite-difference scheme. The finite-difference equations are applied on a fully-unstructured adaptive mesh which. as time proceeds, both coarsens or refines locally and automatically in response to a prescribed adaption criterion. The truncation errors of the scheme are studied, and the scheme is first verified on a test problem of a collapsing hollow spherical shell, for which an analytical solution is known, before being applied to more general configurations motivated by the study of penetration mechanics. Results indicate that, for both CPU and memory requirements, the adaptive scheme is considerably cheaper than the corresponding comparable-resolution regular-mesh scheme, both schemes calculating results to a similar degree of accuracy. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： dynamics elastic-plastic material finite differences numerical algorithms plate impact

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A new leapfrog integrator of rotational motion. The revised angular-momentum approach

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MOLECULAR SIMULATION 1999年第3期22卷 213-236页

作者： Omelyan, IP Natl Acad Sci Ukraine Inst Condensed Matter Phys UA-290011 Lviv Ukraine

A new algorithm is introduced to integrate the equations of rotational motion. The algorithm is derived within a leapfrog framework and the quantities involved into the integration are mid-step angular momenta and on-step orientational positions. Contrary to the standard implicit method by Fincham [Mol. Sim., 8, 165 (1992)], the revised angular momentum approach presented corresponds completely to the leapfrog idea on interpolation of dynamical variables without using any extrapolations. The proposed scheme intrinsically preserves rigid molecular structures and considerably improves stability properties and energy conservation. As is demonstrated on the basis of simulations for water, it reproduces correct results even with extra large step sizes of order 5 fs and 10 fs in the cases of energy- and temperature-conserving dynamics, respectively. We show also that iterative solutions can be avoided within our implicit scheme shifting from quaternions to the entire rotation-matrix representation.

关键词： numerical algorithms long-term integration motion of rigid bodies polyatomic molecules

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Development and validation of Navier-Stokes procedure for turbomachinery unsteady flow

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AIAA JOURNAL 1999年第5期37卷 557-563页

作者： Chernobrovkin, A Lakshminarayana, B Penn State Univ Ctr Gas Turbines & Power University Pk PA 16802 USA

An unsteady viscous how solver based on the Runge-Kutta scheme has been developed. Three low-Reynolds-number k-epsilon turbulence models have been assessed for their ability to predict unsteady transitional how The k-epsilon model has been modified to incorporate leading-edge effects. A pseudo time approach has been used to accelerate the numerical algorithm for unsteady flows. A sensitivity study has been carried out, including the effects of the artificial dissipation, the grid density, and the physical and pseudo time steps. The numerical simulation of the unsteady transitional flow in a compressor cascade has been carried out successfully. Good agreement with the measured data as well as the previous Euler/boundary-layer predictions has been achieved. The numerical solver has been able to predict major features, associated with the wake-induced transition on a compressor blade (wake-induced transitional strip, wake-induced turbulent strip, etc.). An analysis and an interpretation of the results from the unsteady flow simulation have been carried out to understand additional how physics associated with the transitional flow.

关键词： Turbomachinery Transitional Flow Turbulent Boundary Layer Courant Friedrichs Lewy Leading Edges Turbulence Models Compressor Cascade numerical algorithms Rotor Stator Interactions Flow Visualization

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The distributed dislocation method applied to the analysis of elastoplastic strain concentrations

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1999年第5期47卷 1007-1026页

作者： Blomerus, PM Hills, DA Kelly, PA Univ Oxford Dept Engn Sci Oxford OX1 3PJ England

Conventionally, the use of continuous distributions of dislocations to model plasticity has been confined to the analysis of crack tip plasticity using linear arrays of dislocations, within the framework of plane analysis. By expanding this technique into a distribution of dislocation over an area, a method is developed to model the plasticity at stress raising feat;res such as notches or holes under plane strain conditions. The method explicitly takes account of the boundary conditions by using a dislocation solution which accounts for the presence of the stress-raise itself. Other free boundaries may be modelled more approximately using boundary elements which also correctly include the presence of the stress raiser. The dislocations are distributed over finite sized cells, and the solutions found for the strain fields compare favourably with both finite element and bounding Neuber and Glinka results. (C) 1999 Elsevier Science Ltd. All rights reserved.

关键词： dislocations stress concentrations elastic-plastic material numerical algorithms

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