Considering stress constraints in multi-material topology optimization is of great importance from both theoretical and application perspectives. In this article, the stress-constrained multi-material topology optimization problem is considered under the framework of an alternating active-phase algorithm. A nodal variable strategy is employed. In addition, a material distribution-based cluster method is employed instead of a global stress constraint to improve control of the local stress level. The von Mises stresses of the elements are aggregated into several clusters using a p-norm function to represent the stress constraints. Numerical examples are presented, and the influences of key parameters are discussed. The effectiveness of the proposed approach is demonstrated through numerical results.

从理论和应用的角度来看，在多材料拓扑优化中考虑应力约束都非常重要。在本文中，应力约束的多材料拓扑优化问题是在交替活跃相算法的框架下考虑的。采用节点变量策略。此外，采用基于材料分布的聚类方法代替全局应力约束，以改善对局部应力水平的控制。单元的 von Mises 应力使用p范数函数聚合成几个簇来表示应力约束。给出了数值例子，并讨论了关键参数的影响。通过数值结果证明了所提出方法的有效性。