Topology optimization of structures subject to self-weight loading has received considerable attention in the last decades. However, by using standard formulations based on compliance minimization under volume constraint, several difficulties arise once the self-weight of the structure becomes dominant, including non-monotonic behavior of the compliance, possible unconstrained character of the optimum, and parasitic effects for low densities when using density-based methods. In order to overcome such difficulties, a regularized formulation that allows for imposing any feasible volume constraint is proposed. The standard formulation based on compliance minimization under volume constraint is recovered when the regularizing parameter vanishes. The resulting topology optimization problem is solved with the help of the topological derivative method leading to a 0-1 topology design algorithm, which seems to be crucial when the self-weight loading is dominant. Finally, several numerical experiments are presented, showing the effectiveness of the proposed approach in solving a structural topology optimization problem under self-weight loading.

在过去的几十年中，承受自重载荷的结构的拓扑优化受到了极大的关注。但是，通过在体积约束下使用基于最小顺应性的标准配方，一旦结构的自重成为主导，就会出现一些困难，包括顺应性的非单调行为，最佳的可能不受约束的特性以及低密度的寄生效应。当使用基于密度的方法时。为了克服这些困难，提出了允许施加任何可行的体积约束的正则化公式。当正则化参数消失时，将恢复基于体积约束下的合规性最小化的标准公式。由此产生的拓扑优化问题借助拓扑导数方法得以解决，从而得出了0-1拓扑设计算法，这在自重负载占主导地位时显得至关重要。最后，给出了几个数值实验，表明了该方法在自重载荷作用下解决结构拓扑优化问题的有效性。