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

Juan Zheng1,2,3, Shuyao Long1,2, Yuanbo Xiong1,2, Guangyao Li1

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, China
College of Mechanics and Aerospace Engineering, Hunan University, Changsha, China
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.

## Keywords

APA Style
Zheng, J., Long, S., Xiong, Y., Li, G. (2009). A finite volume meshless local petrov-galerkin method for topology optimization design of the continuum structures. Computer Modeling in Engineering & Sciences, 42(1), 19-34. https://doi.org/10.3970/cmes.2009.042.019
Vancouver Style
Zheng J, Long S, Xiong Y, Li G. A finite volume meshless local petrov-galerkin method for topology optimization design of the continuum structures. Comput Model Eng Sci. 2009;42(1):19-34 https://doi.org/10.3970/cmes.2009.042.019
IEEE Style
J. Zheng, S. Long, Y. Xiong, and G. Li "A Finite Volume Meshless Local Petrov-Galerkin Method for Topology Optimization Design of the Continuum Structures," Comput. Model. Eng. Sci., vol. 42, no. 1, pp. 19-34. 2009. https://doi.org/10.3970/cmes.2009.042.019

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