具有多约束连续体结构仿生拓扑优化方法

通过浮动参考区间法分析具有多约束连续体结构拓扑优化问题。浮动区间法是指将结构的拓扑优化过程看作是骨骼重建过程,通过引入参考应变区间,将结构中所有各点处主应变绝对值落入参考应变区间作为重建平衡状态,当结构处于重建平衡状态时获得结构的最优材料分布。为了使得优化结果满足给定的性态约束,参考应变区间在优化迭代过程中须不断变化。讨论了几种常见性态约束对结构性能的要求。给出了结构具有多约束时优化问题的算法。数值算例表明该方法可行。

TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES WITH MULTI-CONSTRAINTS

The topology optimization problems with multi-constraints are solved by the floating-reference- interval method which simulates the structural topology optimization process with a bone remodelling process based on Wolff’s law. The optimal material distribution of structure is obtained when the structure reaches a remodelling equilibrium state. At that state, the absolute values of principal strains locate in an interval of reference strain. To satisfy the character constraints of an optimal problem, the reference interval must change during iteration process. Several types of character constraints, e.g., stress constraint, displacement constraint and volume constraint of structure, are discussed about their influence on the reference interval. The algorithm for solving the topology optimization problems with multi-constraints is given and is verified to be feasible by numerical examples.