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.

本文提出了一种自适应的分层优化方法，以优化具有截断的分层B样条的可变刚度层压板的层压参数分布。传统方法使用统一的网格来设计分布，尽管其变化率可能随点而变化。结果，密集的网格导致较高的计算成本，而粗糙的网格失去了设计自由度。这项研究的主要动机是通过对分层参数的非均匀表示分别在分层B样条的不同级别网格上执行优化的分层来解决此问题。在每个级别优化的最后，选择多级网格中的某些元素以根据细化规则进一步细化。由新生成的元素和未精炼的元素组成的分层网格用于表示解决方案，并使用新的优化步骤更新其对应的分层B样条表达式。基于针对自适应优化问题提出的敏感性分析方法，针对各个级别的优化实现了顺序二次规划算法。最后，选择了三个合规性最小的示例来验证所提出方法的效率和准确性。顺序二次编程算法是针对各个级别的优化实现的。最后，选择了三个合规性最小的示例来验证所提出方法的效率和准确性。顺序二次编程算法是针对各个级别的优化实现的。最后，选择了最小化合规性的三个示例来验证所提出方法的效率和准确性。