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ARTICLE

A Finite Volume Meshless Local Petrov-Galerkin Method for Topology Optimization Design of the Continuum Structures

Juan Zheng^1,2,3, Shuyao Long^1,2, Yuanbo Xiong^1,2, Guangyao Li¹

1 State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, China
2 College of Mechanics and Aerospace Engineering, Hunan University, Changsha, China
3 Corresponding author. Tel.: +86-0731-8824724. E-mail: dingdang8209@163.com

Computer Modeling in Engineering & Sciences 2009, 42(1), 19-34. https://doi.org/10.3970/cmes.2009.042.019

Abstract

In this paper, the finite volume meshless local Petrov-Galerkin method (FVMLPG) is applied to carry out a topology optimization design for the continuum structures. In FVMLPG method, the finite volume method is combined with the meshless local Petrov-Galekin method, and both strains as well as displacements are independently interpolated, at randomly distributed points in a local domain, using the moving least squares (MLS) approximation. The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simple enforcing the strain-displacement relationships directly. Considering the relative density of nodes as design variable, and the minimization of compliance as objective function, the mathematical formulation of the topology optimization design is developed using the solid isotropic microstructures with penalization (SIMP) 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 of the continuum structures.

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Keywords

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