We present an augmented Lagrangian-based approach for stress-constrained topology optimization of structures subjected to general dynamic loading. The approach renders structures that satisfy the stress constraints locally at every time step. To solve problems with a large number of stress constraints, we normalize the penalty term of the augmented Lagrangian function with respect to the total number of constraints (i.e., the number of elements in the mesh times the number of time steps). Moreover, we solve the stress-constrained problem effectively by penalizing constraints associated with high stress values more severely than those associated with low stress values. We integrate the equations of motion using the HHT-α method and conduct the sensitivity analysis consistently with this method via the “discretize-then-differentiate” approach. We present several numerical examples that elucidate the effectiveness of the approach to solve dynamic, stress-constrained problems under several loading scenarios including loads that change in magnitude and/or direction and loads that change in position as a function of time.

我们提出了一种基于增强拉格朗日的方法，用于对承受一般动态载荷的结构进行应力约束拓扑优化。该方法渲染在每个时间步局部满足应力约束的结构。为了解决具有大量应力约束的问题，我们将增广拉格朗日函数的惩罚项相对于约束的总数（即，网格中的元素数乘以时间步数）归一化。此外，我们通过惩罚与高应力值相关的约束比与低应力值相关的约束更严重，从而有效地解决了应力约束问题。我们使用 HHT- α对运动方程进行积分方法并通过“离散然后区分”的方法与该方法一致地进行敏感性分析。我们提供了几个数值例子，阐明了该方法在几种载荷情况下解决动态应力约束问题的有效性，包括大小和/或方向变化的载荷以及位置随时间变化的载荷。