Optimal layout of internal stiffeners for three-dimensional box structures based on natural branching phenomena

Thin-wall box structures combine an outer wall and internal stiffeners. These stiffeners can improve the stiffness of box structures. The adaptive growth method based on natural branching phenomena is applied to solve this layout optimization problem, in which techniques of ground structure construction, stiffener growth direction control, ‘seeding-line’ selection and sensitivity filtering are studied. First, the ground structure with solid and shell elements is established. Then, an iteration formula based on Karush–Kuhn–Tucker optimum conditions is derived. Stiffeners start at the seeding line and grow gradually according to the design sensitivities. Finally, an optimum stiffener layout is obtained. Draft manufacturing constraints are also included in the design procedure. The validity of the method is verified by several design examples. An actual machine tool bed is redesigned, and the performance comparison between the original and optimized beds shows the superiority of the suggested method.