Open Access
ARTICLE
D. H. Pahr1, H.J. Böhm1
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 117-136, 2008, DOI:10.3970/cmes.2008.034.117
Abstract The combination of heterogeneous volume elements and numerical analysis schemes such as the Finite Element method provides a powerful and well proven tool for studying the mechanical behavior of composite materials. Periodicity boundary conditions (PBC), homogeneous displacement boundary conditions (KUBC) and homogeneous traction boundary conditions (SUBC) have been widely used in such studies. Recently Pahr and Zysset (2008) proposed a special set of mixed uniform boundary conditions (MUBC) for evaluating the macroscopic elasticity tensor of human trabecular bone. These boundary conditions are not restricted to periodic phase geometries, but were found to give the same predictions as PBC for the… More >
Open Access
ARTICLE
Zheng Juan1,2,3, Long Shuyao1,2, Xiong Yuanbo1,2, Li Guangyao1
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 137-154, 2008, DOI:10.3970/cmes.2008.034.137
Abstract In this paper, the meshless radial point interpolation method (RPIM) is applied to carry out a topology optimization design for the continuum structure. Considering the relative density of nodes as a design variable, and the minimization of compliance as an objective function, the mathematical formulation of the topology optimization design is developed using the SIMP (solid isotropic microstructures with penalization) interpolation scheme. The topology optimization problem is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design for the continuum structure, and can effectively overcome the checkerboard phenomenon. More >
Open Access
ARTICLE
Chein-Shan Liu1, Satya N. Atluri2
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 155-178, 2008, DOI:10.3970/cmes.2008.034.155
Abstract In this paper we propose a novel method for solving a nonlinear optimization problem (NOP) under multiple equality and inequality constraints. The Kuhn-Tucker optimality conditions are used to transform the NOP into a mixed complementarity problem (MCP). With the aid of (nonlinear complementarity problem) NCP-functions a set of nonlinear algebraic equations is obtained. Then we develop a fictitious time integration method to solve these nonlinear equations. Several numerical examples of optimization problems, the inverse Cauchy problems and plasticity equations are used to demonstrate that the FTIM is highly efficient to calculate the NOPs and MCPs. The present method has some… More >
Open Access
ARTICLE
Y.C. Cai1 and H.H. Zhu1
CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 179-204, 2008, DOI:10.3970/cmes.2008.034.179
Abstract The popular Shepard PU approximations are easy to construct and have many advantages, but they have several limitations, such as the difficulties in handling essential boundary conditions and the known problem of linear dependence regarding PU-based methods, and they are not the good choice for MLPG method. With the objective of alleviating the drawbacks of Shepared PU approximations, a new meshless PU-based Shepard and Least Square (SLS) interpolation is employed here to develop a new type of MLPG method, which is named as Local Meshless Shepard and Least Square (LMSLS) method. The SLS interpolation possesses the much desired Kronecker-delta property,… More >
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