Study on parameters for topological variables field interpolated by moving least square approximation
This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition, or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses, not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field, but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points, scaling parameter, weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.
Key wordstopological optimization continuum structure meshless method moving least square approximation checkerboard pattern mesh-dependence
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- Eschenauer, H.A., Kobelev, H.A. and Schumacher, A., A bubble for topology and shape optimization of structures. Structural Optimization, 1994, 8(2): 142–151.Google Scholar
- Sui, Y.K., Modelling, Transformation an Optimization: New Developments of Structural Synthesis Method. China: Dalian University of Technology Press, 1996.Google Scholar
- Sui, Y.K., Ye, H.L., Du, J.Z., Development of structural topological optimization and imminency of its model transformation into independent level. Engineering Mechanics, 2005, 22 (sup): 107–118.Google Scholar
- Sui, Y.K., Peng, X.R., The improvement for the ICM method of structural topology optimization. Acta Mechanica Sinica. 2005, 37(2): 190–198.Google Scholar
- Yuan, Z., Wu, C.C., Zhuang, S.B., Topology optimization of continuum structure using hybrid elements and artificial material model. Journal of China University of Science and Technology, 2001, 31(6): 694–699.Google Scholar
- Guo, X., Zhao, K., A new topology description function based approach for structural topology optimization. Acta Mechanica Sinica, 2004, 36(5): 520–526.Google Scholar