Topology optimization of thin-walled structures with directional straight stiffeners

Continuum topology optimization is a powerful method to find the optimal design of structures. However, it usually leads to complex nonregular configurations of stiffeners for thin-walled structures, which are difficult to manufacture using traditional production techniques. Therefore, this study proposes a novel topology representation and optimization method for thin-walled structures with directional straight stiffeners using the material-field series expansion and multifield superposition. The material field function with an anisotropic correlation is introduced to describe the straight stiffeners in a given direction, and the entire stiffeners’ topology is represented by the superposition of multiple material fields. Moreover, the stiffener's direction can be designed because of the inherent merit of separating the material field and the finite element mesh. The proposed method connects the characteristics of regular shape and topology of directional straight stiffeners into the optimization model without introducing additional manufacturing constraints. The optimization model is effectively solved using a gradient-based optimization algorithm incorporating the design sensitivity information. Several numerical examples are presented to demonstrate that the proposed method can successfully obtain the optimized topology while being easy to manufacture in stiffened structures design problems.