Concurrent topology optimization design of stiffener layout and cross-section for thin-walled structures

Stiffened plates or shells are widely used in engineering structures as primary or secondary load-bearing components. How to design the layout and sizes of the stiffeners is of great significance for structural lightweight. In this work, a new topology optimization method for simultaneously optimizing the layout and cross-section topology of the stiffeners is developed to solve this issue. The stiffeners and base plates are modeled by the beam and shell elements, respectively, significantly reducing the computational cost. The Giavotto beam theory, instead of the widely employed Euler or Timoshenko beam theory, is applied to model the stiffeners for considering the warping deformation in evaluating the section stiffness of the beam. A multi-scale topology optimization model is established by simultaneously optimizing the layout of the beam and the topology of the cross-section. The design space is significantly expanded by optimizing these two types of design variables. Several numerical examples are applied to illustrate the validity and effectiveness of the proposed method. The results show that the proposed two-scale optimization approach can generate better designs than the single-scale method.