Abstract: To satisfy the multiple performance requirements,a methodology for topology optimization of continuum structures considering static strength and fatigue constraints was proposed.The structural static strength was calculated by the sum of absolute values for the alternating stress and the mean stress of the signed von Mises stress,and the structural fatigue strength was evaluated by modified Goodman fatigue criteria.The static strength and fatigue constraints were transformed into different stress constraints respectively.Thus,the P-norm approach was adopted to approximate the maximum value of the element stresses.The local stress constraints for all elements were transformed into the global stress constraints.The model for topology optimization of continuum structures with static strength and fatigue constraints was established.The method of moving asymptotes was applied to solve the topology optimization problem with multiple performance constraints.The numerical examples showed that the optimal layouts obtained by the proposed method could satisfy simultaneously both the static strength and the fatigue performance.

Key words: continuum structures, topology optimization, static strength constraints, fatigue performance constraints, modified Goodman criteria

摘要： 为了满足多性能指标要求,提出一种考虑静强度和疲劳约束的连续体结构拓扑优化设计方法。以带符号的von Mises应力的幅值和均值绝对值之和评定结构静强度,采用修正的Goodman疲劳准则评价结构疲劳强度,将结构静强度和疲劳约束分别转化为不同的应力约束,再采用P范数对单元应力进行近似最大处理,将局部约束转化全局约束。采用材料属性有理近似模型,以结构体积最小化作为优化目标,建立考虑静强度和疲劳约束的结构拓扑优化模型;采用移动渐近线算法求解基于多性能约束的拓扑优化问题。数值算例结果表明,所提设计方法获得的拓扑结构能够同时满足静强度和疲劳性能要求。

关键词: 连续体结构, 拓扑优化, 静强度约束, 疲劳性能约束, 修正的Goodman准则