A staggered approach to shape and topology optimization using the traction method and an evolutionary-type advancing front algorithm

We investigate a novel approach for structural shape optimization on the basis of complementary shape and topological sensitivity analysis. As in early approaches to shape optimization, the domain variation is specified by modification of boundary nodal points, hence leading to an updated Lagrangian description for the course of optimization. To overcome the formation of oscillating boundaries in the optimal design trials, we employ the traction method to establish smooth descent directions for shape variation. Therein, an auxiliary elastic problem is solved in which the shape sensitivity constitutes the external loading and the deformation of the auxiliary elastic body is used as a descent direction for shape variation rather than the shape sensitivity itself. We complement this method through an evolutionary-type element removal procedure that is based on the topological sensitivity such that an advancing front algorithm is gradually removing elements from the design boundary of the domain. Once the minimum topological sensitivity is no longer encountered at the design boundary, we create a hole in the domain, again using the topological sensitivity to specify its exact location, and resume the element removal procedure for the newly established design boundary. Since this approach yields only a vague estimate of the true optimal shape of newly established holes, the traction method is again used for shape variation of the extended design boundary.