Stiffness design of plate/shell structures by evolutionary topology optimization

This work aims at developing a simple and viable evolutionary design approach to optimally orient stiffeners for plate and shell structures so as to maximize stiffness while satisfying volume requirements. The evolutionary algorithm is transformed into a mathematical model, where stiffeners are treated as being alive, and the optimization is perceived as an adaptive growth procedure that starts from the constraint points and extends along the gradient directions of plate and shell stiffness. To eliminate the expensive re-meshing upon design changes, a special numerical treatment called “stiffness transformation approach” is developed. In this approach, the stiffness matrix of growing stiffeners is interpolated within their surrounding regions, and the stiffness of neighboring finite elements is modified to simulate the presence of stiffeners. Such a transformation allows the growing stiffeners to be mathematically separated from the underlying finite element method mesh; thus, stiffeners can extend toward arbitrary directions to form an optimized layout solution. An easy-to-use implementation of the evolutionary algorithm is demonstrated in detail through a machine tool design example. Compared to the original design, both numerical and experimental tests confirm that the stiffness in the proposed design is improved; as a result, new possibilities emerge for the design of large-scale plate and shell structures in engineering.