Meshfree Method for the Topological Design of Microstructural Composites
Y. Wang, E. Lü, J. Zhao and J. Guo

doi:10.3970/cmes.2015.109.035
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 109, No. 1, pp. 35-53, 2015
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Keywords Topology optimization, meshfree, RPIM, composite materials.
Abstract

Meshfree methods have found good applications in many new researches, which show very good potential to be powerful numerical tools. As an alternative to the mesh based methods, meshfree methods have the advantage of not using a predefined mesh for the domain discretization. In this study, a mesh free scheme based on the radial point interpolation method was used to solve the topological design of microstructures for composite materials. The explicit form of the radial point interpolation method (RPIM) interpolation augmented with polynomials is presented, which satisfies range-restricted properties and is applicable to integrate a physically meaningful density interpolation. Meanwhile gauss quadrature scheme was applied in order to calculate the physical meaningful properties of microstructure, while the homogenization method is applied to evaluate the effective macroscopic properties of a periodic microstructure. Typical numerical examples are used to demonstrate the effectiveness of the proposed method for designing composite materials with expected effective elasticity tensor.

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