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Topology optimization of finite similar periodic continuum structures based on a density exponent interpolation model

Jian Hua Rong1,2,3, Zhi Jun Zhao4, Yi Min Xie5, Ji Jun Yi1,2
School of Automotive and Mechanical Engineering, Changsha University of Science and Technology, Changsha, Hunan Province 410004, P. R. China
Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, The Education Department of Hunan Province, Changsha, 410004, China
Corresponding author, Email address
Department of Civil Engineering, Changsha Institute, Changsha, Hunan Province 410076, P. R.China
Centre for Innovative Structures and Materials, School of Civil, Environmental and Chemical Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Australia

Computer Modeling in Engineering & Sciences 2013, 90(3), 211-231.


Similar periodic structures have been widely used in engineering. In order to obtaining the optimal similar periodic structures, a topology optimization method of similar periodic structures with multiple displacement constraints is proposed in this paper. Firstly, in the proposed method, the design domain is divided into sub-domains. Secondly, a penalty term considering discrete conditions of density variables is introduced into the objective function, and the reciprocal density exponents of structural elements are taken as design variables. A topological optimization model of a similar periodic continuum structure with the objective function being the structural mass and the constraint functions being structural displacements is constructed in the proposed method. The optimization dual method is introduced and a set of iteration formula for Lagrange multipliers is built. Then, virtual sub-domain design variables are introduced to establish the relation of corresponding variables between all the sub-domains of the similar periodic continuum structure in order to enforce structurally similar periodic requirement. Three examples are provided to demonstrate that the proposed method is feasible and effective for obtaining optimal similar periodic structures.


similar periodic structure, topological optimization, displacement constraint, quadratic programming, Lagrange multiplier

Cite This Article

Rong, J. H., Zhao, Z. J., Xie, Y. M., Yi, J. J. (2013). Topology optimization of finite similar periodic continuum structures based on a density exponent interpolation model. CMES-Computer Modeling in Engineering & Sciences, 90(3), 211–231.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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