An adaptive hierarchical optimization approach for the minimum compliance design of variable stiffness laminates using lamination parameters. (December 2020) - Zeng, Jiani; Huang, Zhengdong; Fan, Kuan; Wu, Wenbo
Abstract: This paper presents an adaptive hierarchical optimization approach to optimize the lamination parameter distribution of variable-stiffness laminated plate with truncated hierarchical B-Splines. Traditional methods use a uniform grid to design the distribution though its variation rate could change dramatically from point to point. As a consequence, the dense grid incurs a high computation cost while the rough one loses the design freedom. The main motivation of this research is to resolve this problem by performing a hierarchy of the optimizations respectively on different level grids of the hierarchical B-Spline for a non-uniform representation of lamination parameters. At the end of each level optimization, some elements in the multi-level grid are selected to be refined further according to a refinement rule. The hierarchical mesh consisting of newly generated elements and unrefined ones, is used to represent the solution, and its corresponding hierarchical B-Spline expression is updated with a new optimization step. Based on the sensitivity analysis approach proposed for the adaptive optimization problem, the sequential quadratic programming algorithm is implemented for the optimizations at individual levels. Finally, three examples of compliance minimization are chosen to validate the efficiency and accuracy of the proposed method. Highlights: A non-uniform mesh is employed to design the distribution of lamination parameters (LP). The truncated hierarchical B-splines are utilized to represent the progressively refined LP solution. The strain energy density of each element is evaluated to serve as a criterion in selecting the elements for refinement. A prestorage approach for sensitivity analysis is developed to save the computation time in each sub-optimization problem.