结构周期性布局优化理论与方法研究

Periodic structure has attracted extensive attention because of its unique configurations, good machinability and excellent mechanical properties. So it has important research significance and application value in the field of civil and national defense industry. At present, optimization method of periodic structure is inadequate. From the point of topology optimization, theoretical model of periodic layout optimization is constructed. Periodic layout optimization method is put forward based on guide-weight method and variable density method. The periodic distribution rule of stiffener and the influence rule on substructure's size effect to configuration transformation and structural performance are the key points of this project research. By compared experiments, the influence rule on periodic layout scheme of plate and shell structure to structural performance is revealed on the experimental study platform. The project will lay a theoretical foundation for plate and shell structure in the application of civil and national defense industry.

周期性结构以其独特的构型、良好的加工性和优异的力学性能而备受关注，在民用及国防工业等领域具有重要研究意义和应用价值。针对目前周期性结构的优化方法研究不充分的现状，本课题从结构拓扑优化的角度出发，构建结构周期性布局优化的理论模型，提出基于导重理论和变密度法的结构周期性布局优化方法。重点研究板壳加强筋的周期性分布规律，加强筋拓扑子结构的尺寸效应对子结构构型变化和板壳结构性能的影响规律。搭建试验研究平台，通过对比试验揭示加强筋周期性布局方案对板壳结构性能的影响。为周期性板壳结构在民用及国防工业中的应用奠定理论基础。

为了解决周期性结构的材料最优分配问题，引入周期性约束条件，构建结构周期性布局优化理论的数学模型。以单元应变能密度为基础，提出一种改进的过滤方案以解决结构周期性布局优化中单元体积依赖性问题。利用导重法推导结构周期性布局优化的迭代准则，提出一种基于导重法的结构周期性布局优化方法。把本文所提方法应用到典型板壳结构-单立柱巷道堆垛机的轻量化中。通过仿真试验，综合考虑《钢结构设计规范》对立柱强度和静刚度的要求，确定了本单立柱堆垛机立柱结构周期性布局优化的最优拓扑形式，并以此提出了具有周期性拓扑形式的立柱轻量化设计方案。同时把本方法拓展到了塔式起重机臂架结构优化设计中，提出了桁架结构拓扑及尺寸两阶段优化设计方法，实现了臂架桁架结构布局优化和尺寸优化。