复杂结构拓扑/尺寸一体化与混合变量优化问题研究

A great lot of structural analyses are always needed in topology optimizations of discrete structures and post-processing skills are required for continuum topology problems, which are quite unsuitable to dealing with topology designs for complex engineering structures that can contain bars, beams, shells and their combinations. Aiming to solve these problems, the present research is to propose and study and an optimization method for integrated sizing and topology optimizations of complex structures. This method is also expected to be effective in handling other problems that involve mixed variables, and its core idea is that a kind of branched explicit functions is constructed to approximate the implicit functions which are difficult to be approximated with common techniques like Taylor expansions when considering both discrete and continuous variables. Correspondingly, a series of explicit approximate problems can be established for the original implicit problem involving mixed variables. Genetic algorithm and dual method are introduced to optimize the discrete variables and continuous variables, respectively, in the approximate problem, and the original problem is to be solved after multiple iterations. This method can be expected to significantly improve the efficiency when solving structural optimization problems with mixed variables. Actually, the preliminary work in truss topology/size optimization problems proves that this approach makes the required structural analyses stay the same order of magnitude as the pure sizing optimization. The proposed method will be verified in the integrated sizing and topology optimization of trusses, frames, shells or a combination of them, as well as other design problems with mixed variables like optimal actuator placement in adaptive trusses and stacking sequence optimization designs. By applying this method in aerospace vehicle structure designs that involve mixed variables, its applicability in practical engineering problems can be demonstrated.

针对目前离散结构或连续体拓扑优化方法所需结构分析次数高或结果需再处理、难于适用于复杂工程结构拓扑优化等问题，本项目旨在提出和研究一种可包含杆、梁、板壳等及其组合的复杂结构拓扑-尺寸一体化优化方法。该方法也适用于其它混合变量结构优化问题求解。其核心思想就是通过对难于用Taylor展开等手段逼近的混合变量函数构造特殊的分叉近似，建立混合变量结构优化问题的序列近似问题，并引入遗传算法和对偶算法分别确定近似问题中离散和连续变量的最优值；通过逐步迭代最终求解原问题。该方法可望使此类优化问题的求解效率得以大幅提升（桁架拓扑优化等初步研究已证实该方法可使此类问题求解的结构分析次数与尺寸优化处同一量级）。项目将通过桁架、刚架、板壳及其组合结构的拓扑-尺寸一体化优化算例以及自适应结构主动元件配置、层合板铺层顺序优化等算例验证其有效性，最后应用于空间飞行器结构的混合变量优化问题，以说明方法的工程实用性。

针对目前桁架结构或连续体拓扑优化方法所需结构分析次数高或结果需再处理、难于适用于复杂工程结构拓扑优化等问题，本项目提出并研究了一种可包含杆、梁、板壳等及其组合的复杂结构拓扑-尺寸一体化优化方法。该方法也可为其它含离散变量工程优化问题求解参考。其核心思想就是通过对难于用Taylor展开等手段逼近的含离散变量的混合变量函数构造特殊的分叉近似，由此建立结构拓扑-尺寸一体化的混合变量优化问题的序列近似问题，并引入分层优化策略，用遗传算法和对偶算法分别确定近似问题中离散拓扑变量和连续尺寸变量的最优值；通过迭代最终求解原结构优化问题。通过桁架、刚架、板壳及其组合结构的拓扑-尺寸一体化优化，以及自适应结构主动元件配置、层合板铺层顺序优化等各种算例表明，该方法使复杂结构拓扑优化和含离散变量优化问题的求解效率大幅提升，使此类问题求解所需的结构分析次数与尺寸优化处同一量级（结构分析次数稍多，一般不超过10倍）。项目最后应用于某无人飞行器的结构布局与尺寸优化设计，取得了很好的效果，由此说明了方法的工程实用性。方法进一步在航空航天飞行器结构设计中的工程应用还在洽谈之中。