Stress-based topological shape optimization for thick shells using the level set method and trimmed non-conforming multi-patch isogeometric analysis

This paper introduces a novel method for optimal shape design of thick shells. We consider shells based on the Reissner-Mindlin theory, with the assumption of linear elastic material behavior. The goal is to find the optimal material distribution within the shell's mid-surface. This is achieved using a cost function that minimizes the volume while considering stress-based constraints, with the material distribution represented by a level set function. The evolution of the shape is driven by the gradient of the cost function within the framework of a Hamilton-Jacobi equation. Both the level set and the displacement fields are described using computer aided design compatible tools, within the framework of isogeometric analysis. This allows for precise definition of the optimal shape and straightforward export of the resulting design to commercial software for manufacturing. Furthermore, the proposed method handles complex, non-conforming multi-patch geometries thanks to an augmented Lagrangian formulation. The latter guarantees strong compatibility with real-world engineering applications. The effectiveness of the method is demonstrated through its application to various three-dimensional multi-patch geometries under different loading conditions.