Variable-height stiffener design using topology optimization with anisotropic filter-based casting constraints

In this paper, a novel implementation of the casting constraint in topology optimization is proposed based on the Helmholtz-type anisotropic filter approach. The basic idea is to set a far larger radius along the casting direction to ensure that the pseudo-density variables are approximately equal after filtering, which can replace the role of the variable mapping (VM). Then, an explicit parameterized height projection function is used to implement the casting constraint. Additionally, an approach using Laplace equation to approximatively calculate the casting coordinate system is introduced, which is convenient for the preprocess of complex curved shell structures. Based on the proposed method, the layout of variable-height stiffeners can be designed by the 3D continuous topology optimization method. Some illustrative examples, including the 2D MBB beam, the 3D cantilever, the special-shaped cylinders, and the special-shaped cabin, are carried out to verify the effectiveness and robustness of the proposed method. Optimization results indicate that the proposed method is able to handle the topology optimization problem with the casting constraint. Compared with the VM method, the proposed method needs less manual setup in the preprocessing course, and it still works well for the stiffener design of curved structures such as the special-shaped cabin in which the VM method is incompetent.