Structural shape and topology optimization based on level-set modelling and the element-propagating method

Abstract

This article introduces the element-propagating method to structural shape and topology optimization. Structural optimization based on the conventional level-set method needs to solve several partial differential equations. By the insertion and deletion of basic material elements around the geometric boundary, the element-propagating method can avoid solving the partial differential equations and realize the dynamic updating of the material region. This approach also places no restrictions on the signed distance function and the Courant–Friedrichs–Lewy condition for numerical stability. At the same time, in order to suppress the dependence on the design initialization for the 2D structural optimization problem, the strain energy density is taken as a criterion to generate new holes in the material region. The coupled algorithm of the element-propagating method and the method for generating new holes makes the structural optimization more robust. Numerical examples demonstrate that the proposed approach greatly improves numerical efficiency, compared with the conventional level-set method for structural topology optimization.

Keywords:

• shape optimization
• topology optimization
• level-set method
• sensitivity analysis
• element propagating

Acknowledgements

This research work is supported in part by National Natural Science Foundation of China under grant No. 50775146, 50805093 and National Basic Research Program of China under grant No. 2005CB724103.