Topology optimization of thin-walled structures

Thin-walled structures find applications in various disciplines, including aerospace, civil, and mechanical engineering, thanks to their high stiffness-to-mass ratio. Recent advancements in manufacturing processes, which enable the production of structural elements with complex geometries, have made topology optimization an integral part of the design process.

The intricate cross-sections of thin-walled beams result in complex deformation modes that are not adequately captured by traditional beam theories, especially when torsional behavior is expected. In addition, these elements are prone to buckling due to their slenderness.

In this presentation, we will discuss a recently developed efficient topology optimization method for designing these elements. The method relies on a density-based approach that is solved iteratively using an efficient gradient-based optimization framework, allowing for a large number of design variables. The optimization problem is formulated considering linearized buckling, stiffness, and stress constraints.

The solution procedure of the optimization problem involves a large number of analyses of different designs, making traditional 3D FEM formulations impractical for such a problem. Therefore, we have developed a novel method for the analysis of these elements consisting of a 3D finite element mesh enhanced with global enrichment functions, utilizing the XFEM method. These global enrichment functions incorporate physical knowledge about the expected behavior of the beam, allowing for a substantial reduction in the computational burden.

The results demonstrate that the proposed approach allows designing these elements while considering various performance constraints.