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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 735063, 18 pages
Research Article

Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

1Gengdan Institute of Beijing University of Technology, Beijing 101301, China
2College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China

Received 8 July 2013; Accepted 29 August 2013

Academic Editor: Song Cen

Copyright © 2013 Tie Jun and Sui Yun-kang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditional -relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.