CMES-Vol. 5, No. 6, 2004

Open Access

ARTICLE

The Generalized Interpolation Material Point Method
S. G. Bardenhagen^1,2, E. M. Kober³
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 477-496, 2004, DOI:10.3970/cmes.2004.005.477
Abstract The Material Point Method (MPM) discrete solution procedure for computational solid mechanics is generalized using a variational form and a Petrov–Galerkin discretization scheme, resulting in a family of methods named the Generalized Interpolation Material Point(GIMP) methods. The generalizationpermits identification with aspects of other point or node based discrete solution techniques which do not use a body–fixed grid, i.e. the “meshless methods”. Similarities are noted and some practical advantages relative to some of these methods are identified. Examples are used to demonstrate and explain numerical artifact noise which can be expected inMPM calculations. Thisnoiseresultsin non-physical local More >

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ARTICLE

Finite Element Modeling of Thin Layers
Dan Givoli¹
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 497-514, 2004, DOI:10.3970/cmes.2004.005.497
Abstract Very thin layers with material properties which significantly differ from those of the surrounding medium appear in a variety of applications. Traditionally there are two extreme ways of handling such layers in finite element analysis: either they are fully modelled or they are totally ignored. The former option is often very expensive computationally, while the latter may lead to significant inaccuracies. Here a special technique of modeling thin layers is devised within the framework of the finite element method. This technique constitutes a prudent compromise between the two extremes mentioned above. The layer is replaced More >

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A Hybrid Atomistic–Continuum Formulation for Unsteady, Viscous, Incompressible Flows
H.S. Wijesinghe¹, N.G. Hadjiconstantinou²
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 515-526, 2004, DOI:10.3970/cmes.2004.005.515
Abstract We present an implicit hybrid atomisticcontinuum formulation for unsteady, viscous, incompressible flows. The coupling procedure is derived from a domain decomposition method known as the Schwarz alternating method. A dilute gas impulsive Couette flow test problem is used to verify the hybridscheme. Finally, a method to reduce computational costs through limited ensemble averaging is presented. The implicit formulation proposed here is expected to be significantly faster than a time explicit approach based on a compressible formulation for the simulation of low speed flows such as those found in micro- and nano–scale devices. More >

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Atomistic Simulations of Dislocation-Void Interactions using Green’s Function Boundary Relaxation
Xiangli Liu¹, S. I. Golubov¹, C. H. Woo^1,2, Hanchen Huang³
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 527-540, 2004, DOI:10.3970/cmes.2004.005.527
Abstract A Green’s function technique is developed for the relaxation of simulation cell boundaries in the modelling of dislocation interactions using molecular dynamics. This method allows the replacement of fixed or periodical boundary conditions with flexible boundary conditions, thus minimizing the artificial effects due to images forces introduced by the fixed boundary condition, or the periodic repetition of simulation cells. The effectiveness of the Green’s function in the removal of the fixed boundary image forces is first checked in the atomistic simulation involving the glide of the a/2<110> dislocation in bcc tungsten. This method is then applied More >

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Directly Derived Non-Hyper-Singular Boundary Integral Equations for Acoustic Problems, and Their Solution through Petrov-Galerkin Schemes
Z.Y. Qian¹, Z.D. Han¹, S.N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 541-562, 2004, DOI:10.3970/cmes.2004.005.541
Abstract Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r⁻²) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity potential, are used in this derivation. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived. Using these basic identities, the strongly singular integral equations for the potential and its gradients [denoted here as φ-BIE, and… More >

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Weight-Minimization of Sandwich Structures by a Heuristic Topology Optimization Algorithm
C. Tapp¹, W. Hansel, C. Mittelstedt, W. Becker²
CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 563-574, 2004, DOI:10.3970/cmes.2004.005.563
Abstract A heuristic algorithm for the weight minimization of sandwich plates is presented. The method is based on a preexisting algorithm for the layerwise topology optimization of symmetric laminates under in-plane loads. The presented algorithm uses structural analyses based on finite elements and explicitly accounts for the special sandwich situation. During the optimization procedure the algorithm adds or subtracts material from the layers of the face sheets and the core of the sandwich plate in regions of high or low stresses respectively. The orientation angles of the layers of the sandwich facings are not varied inorder More >

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