A novel topology optimization approach for the robust design of structures is presented. The method considers both deterministic and random loadings, and minimizes the compliance subject to a constraint on the volume, as well as a constraint on the failure probability. Handling the failure probability is often challenging in numerical terms, potentially leading to an intractable model as the problem scales. It is addressed by employing the Bernstein approximation, resulting in a model that has the remarkable property of being a linear conic programming problem, therefore, solvable in polynomial time with respect to the input size by using interior point methods. Furthermore, a more efficient reformulation of the problem, involving small semidefinite constraints is derived. To demonstrate the practicality of the proposed method, solutions to several examples of truss topology optimization are provided.

提出了一种用于结构稳健设计的新颖拓扑优化方法。该方法考虑了确定性载荷和随机载荷，并在体积约束和失效概率约束下最小化合规性。从数值角度来说，处理故障概率通常具有挑战性，随着问题规模的扩大，可能会导致模型变得棘手。它通过采用伯恩斯坦近似来解决，产生的模型具有线性二次曲线规划问题的显着特性，因此可以使用内点方法多项式时间此外，还导出了涉及小的半定约束的更有效的问题重新表述。为了证明该方法的实用性，提供了几个桁架拓扑优化示例的解决方案。