Chinese Journal of Theoretical and Applied Mechani ›› 2009, Vol. 41 ›› Issue (4): 518-529.DOI: 10.6052/0459-1879-2009-4-2007-540

• Research paper • Previous Articles     Next Articles

Structural topological optimization based on displacement and stress sensitivity analyses

Jianhua Rong Sen Ge Guo Deng Xiaojuan Xing Zhijun Zhao   

  • Received:2007-11-09 Revised:2008-03-18 Online:2009-07-25 Published:2009-07-25

Abstract: Stress constrained topology optimization problem has not been paid the same attention as the minimum compliance problem in the literatures. The traditional minimum compliance formulations offer some obvious advantages to avoid dealing with a large number of highly non-linear constraints. This could be considered crucial, if one takes into account the large number of design variables, i.e. inherent to topology optimization. However, one can also argue that this gives rise to several important drawbacks since no constraints are imposed on stresses and displacements, for example, multiple load cases cannot be considered; different solutions are obtained for different restrictions; the final design could be unfeasible in practice. This paper deals with topology optimization of continuum structures with stress and displacement constraints or with only stress constraints, based on the ICM method and the evolutionary structural optimization method. New displacement and stress constraint limits are formed and introduced into the optimization model at the beginning of each optimization iteration sub-loop, so that moving limits of design variables can be easily constructed. Instead of all stress constraints, only the most potential effective stress constraints are considered. In this way, stress sensitivity analysis is much less costly. Moreover, the element deletion and a set of structural optimization strategies are given. In order to make the structure optimized be non-singular and the proposed method be of element restorable functions, some elements with artificial material property are inserted around the cavities and boundaries of the structure optimized. Meanwhile, an equivalent topological optimization model is developed. Incorporating displacement and stress sensitivity analyses, a new continuum structural topological optimization method is also proposed. Two simulation examples demonstrate that the proposed method is of validity and effectiveness.

Key words: topological optimization, displacement constraint, stress constraint, continuum structure, ICM method