Stiffness design of plate/shell structures by evolutionary topology optimization

• Published in: Thin-walled structures Vol. 141; pp. 232 - 250
• Main Authors: Li, Baotong, Liu, Honglei, Yang, Zihui, Zhang, Jinhua
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2019
• Subjects: Evolutionary algorithm; Plate/shell structures; Stiffness; Topology optimization; Topology optimization; Plate/shell structures; Stiffness; Evolutionary algorithm
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2019.04.012

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. •An explicit topology optimization approach is proposed based on the adaptive growth simulation.•The growth rule is transformed into a mathematical model and written as an evolutionary algorithm.•Propose a numerical method (STA) to make stiffeners being able to grow freely in the design domain.•The re-design of an actual boring-milling machine bed validates the method's effectiveness.