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Topology optimization using the improved element-free Galerkin method for elasticity |
| Yi Wu(吴意)1, Yong-Qi Ma(马永其)1,2, Wei Feng(冯伟)1, Yu-Min Cheng(程玉民)1 |
1 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
2 Department of Mechanics, Shanghai University, Shanghai 200444, China |
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Abstract The improved element-free Galerkin (IEFG) method of elasticity is used to solve the topology optimization problems. In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin (EFG) method. The central processing unit (CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown.
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Received: 19 December 2016
Revised: 05 April 2017
Accepted manuscript online:
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PACS:
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02.60.Cb
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(Numerical simulation; solution of equations)
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02.60.-x
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(Numerical approximation and analysis)
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45.10.Db
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(Variational and optimization methods)
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46.15.-x
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(Computational methods in continuum mechanics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11571223 and U1433104). |
Corresponding Authors:
Yu-Min Cheng
E-mail: ymcheng@shu.edu.cn
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| About author: 0.1088/1674-1056/26/8/ |
Cite this article:
Yi Wu(吴意), Yong-Qi Ma(马永其), Wei Feng(冯伟), Yu-Min Cheng(程玉民) Topology optimization using the improved element-free Galerkin method for elasticity 2017 Chin. Phys. B 26 080203
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