This paper proposes a methodology for the topology optimization of continuum structures subject to dynamic stress response constraints under stochastic loads. The topology optimization model is built, where the objective function is the structural weight, and the dynamic stress constraints are applied. In order to greatly reduce the computational cost of dynamic stress responses and prevent stress concentration phenomenon, the P-norm aggregation function is adopted to replace the dynamic stress response constraints. To solve the defined topology optimization problem, a method with varying dynamic stress response limit is presented, and the sensitivities of the equivalent dynamic stress response constraints with respect to the reciprocal design variables is derived so as to form the explicit approximate functions for structural equivalent dynamic stress response constraints. Then, based on dual theory, an algorithm by using nonlinear programming method with simple trust regions is introduced to solve the optimization problem. Finally, the results of several numerical examples are given to demonstrate the validity and effectiveness of the proposed approach.

本文提出了一种在随机载荷下承受动态应力响应约束的连续体结构拓扑优化的方法。建立了拓扑优化模型，其中目标函数为结构权重，并应用了动态应力约束。为了大大降低动态应力响应的计算成本，防止应力集中现象，采用P-范数聚合函数代替动态应力响应约束。为了解决定义的拓扑优化问题，提出了一种具有变化的动态应力响应极限的方法，推导了等效动应力响应约束条件对倒易设计变量的敏感性，从而形成了结构等效动应力响应约束条件的显式近似函数。然后，基于对偶理论，提出了一种采用简单信赖域的非线性规划方法求解算法。最后，给出了几个数值例子的结果，以证明所提方法的有效性和有效性。