CMES-Vol. 10, No. 1, 2005

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Meshless Local Petrov-Galerkin (MLPG) Approaches for Solving Nonlinear Problems with Large Deformations and Rotations
Z. D. Han¹, A. M. Rajendran², S.N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 1-12, 2005, DOI:10.3970/cmes.2005.010.001
Abstract A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of velocity gradients are expressed in terms of the independently interpolated nodal values of displacements (or velocities), by enforcing the compatibility conditions directly at the nodal points. For validating the present large deformation MLPG formulation, two example problems are considered: 1) large deformations and rotations of… More >

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A Group Preserving Scheme for Inverse Heat Conduction Problems
C.-W. Chang¹, C.-S. Liu², J.-R. Chang^1,3
CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 13-38, 2005, DOI:10.3970/cmes.2005.010.013
Abstract In this paper, the inverse heat conduction problem governed by sideways heat equation is investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes. Then the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group preserving scheme, and the stable range of the index r = 1/2ν Δt is investigated. When the numerical results are compared with exact solutions, it is found that they are… More >

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Facet-facet barriers on Cu{111} surfaces for Cu dimers
Alberto M. Coronado¹, Hanchen Huang²
CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 39-44, 2005, DOI:10.3970/cmes.2005.010.039
Abstract Nanostructure fabrication or surface processing in general is predominantly kinetics-limited. One of the kinetics factors is surface diffusion, which involves intricate interplay between the diffusing atoms and substrate atoms. On Cu{111} surfaces, both adatoms and dimers diffuse very fast. Recent studies have shown that adatoms encounter a large facet-facet barrier, even though their conventional Ehrlich-Schwoebel barriers are small. This work examines the facet-facet diffusion barriers of dimers. Our results show that a dimer prefers diffusion through atom-by-atom mechanism, having a barrier of 0.52 eV from {111} to {111} facet and a barrier of 0.55 eV from {111} to {100} facet.… More >

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BIE Method for 3D Problems of Rigid Disk-Inclusion and Crack Interaction in Elastic Matrix
V.V. Mykhas’kiv¹, O.I. Stepanyuk²
CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 45-64, 2005, DOI:10.3970/cmes.2005.010.045
Abstract The 3D elastostatic problem for an infinite remotely loaded matrix containing a finite number of arbitrarily located rigid disk-inclusions and plane cracks is solved by the boundary integral equation (BIE) method. Its boundary integral formulation is achieved by the superposition principle with the subsequent integral representations of superposition terms through surface integrals, which should satisfy the displacement linearity conditions in the inclusion domains and load-free conditions in the crack domains. The subtraction technique in the conjunction with mapping technique under taking into account the structure of the solution at the edges of inhomogeneities is applied for the regularization of BIE… More >

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Extension of the Variational Self-Regular Approach for the Flux Boundary Element Method Formulation
P. A. C. Porto¹, A. B. Jorge¹, G. O. Ribeiro²
CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 65-78, 2005, DOI:10.3970/cmes.2005.010.065
Abstract This work deals with a numerical solution technique for the self-regular gradient form of Green's identity, the flux boundary integral equation (flux-BIE). The required C^1,α inter-element continuity conditions for the potential derivatives are imposed in the boundary element method (BEM) code through a non-symmetric variational formulation. In spite of using Lagrangian C⁰ elements, accurate numerical results were obtained when applied to heat transfer problems with singular or quasi-singular conditions, like boundary points and interior points which may be arbitrarily close to the boundary. The numerical examples proposed show that the developed algorithm based on the self-regular flux-BIE are highly efficient,… More >

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Non-uniform Hardening Constitutive Model for Compressible Orthotropic Materials with Application to Sandwich Plate Cores
Zhenyu Xue¹, Ashkan Vaziri¹, John W. Hutchinson¹
CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 79-96, 2005, DOI:10.3970/cmes.2005.010.079
Abstract A constitutive model for the elastic-plastic behavior of plastically compressible orthotropic materials is proposed based on an ellipsoidal yield surface with evolving ellipticity to accommodate non-uniform hardening or softening associated with stressing in different directions. The model incorporates rate-dependence arising from material rate-dependence and micro-inertial effects. The basic inputs are the stress-strain responses under the six fundamental stress histories in the orthotropic axes. Special limits of the model include classical isotropic hardening theory, the Hill model for incompressible orthotropic solids, and the Deshpande-Fleck model for highly porous isotropic foam metals. A primary motivation is application to metal core structure in… More >

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