仿叶脉分布的板壳结构加强筋声辐射拓扑优化方法

The problem of layout optimization of stiffeners in plates/shells aimed at optimal vibration and acoustic characteristics is significant for ship structures to improve the dynamic characteristics subjected to the light weight requirement. The reinforced palte/shell structure by introduction of beams is featured with the branched configuration, for which the layout optimization of stiffeners is not suitable to be resolved by homogenization method, artificial density method, level set method and volutionary structure optimization method. The inherent connection of the mechanics induced venation growth mechanism to the reinforcement layout design is investigated in detail. Subsequently the bionic optimization model of stiffeners layout is established characterized with the hierarchical structure including the principal veins, secondary veins and three level veins. Consequently the bionic design method is presented for the stiffeners layout optimization in plates/shells. A novel bionic adaptive growth method of stiffeners based on optimization criterion is presented integrating with globally convergent method of moving asymptotes. It can address the layout optimization of stiffeners under the complicated design constraints with the vibration and acoustic characteristics as the objective function. In view of acoustic optimization of plates/shells in high frequency vibration, the layout optimization of stiffeners based on power flow analysis is constructed to control and optimize the energy flow propagation in plates/shells. Accordingly this layout optimization method of stiffeners in plates/shells provides the significant theoretical and technical support to the light weight design on the basis of vibration and acoustic characteristics.

面向板壳结构声振特性的加强筋布局优化设计，对于提高船舶结构的动态特性要求和轻量化设计具有重要的现实意义。目前常用的均匀化方法、变密度法、水平集法和渐进结构优化法，不适于求解具有分枝构型特征的板梁复合结构的布局优化问题。本项目探究植物脉序生长机理的力学规律和加强筋布局设计的内在联系，建立以主脉、次脉和支脉等三级脉序为特点的加强筋仿生优化模型，提出板壳结构加强筋仿脉序布局的仿生设计方法。针对复杂约束下板壳结构声振特性的拓扑优化问题，将优化准则法(KKT条件)与移动渐进线法(MMA法)相融合，提出基于最优准则法的加强筋仿脉序自适应生长方法。针对高频振动板壳结构的声辐射优化问题，构建基于功率流分析的加强筋布局优化方法，实现对抗振板壳结构能量流传播过程的控制和优化。综上，本项目提出的板壳结构加强筋布局设优化计方法，将为面向声振特性的结构轻量化设计奠定重要的理论基础和技术支撑。

面向板壳结构声振特性的加强筋布局优化设计，对于提高船舶结构的动态特性要求和轻量化设计具有重要的现实意义。目前常用的均匀化方法、变密度法、水平集法和渐进结构优化法，不适于求解具有分枝构型特征的板梁复合结构的布局优化问题。本项目探究了叶脉脉序形态的形成机理及构型规律，提取叶脉脉序生长的结构力学准则。以最小弹性应变能与抑制最大剪应力为主及次脉生长准则、以矢量平衡方程为脉序分歧准则建立具有叶脉分枝结构特征的板壳加强结构仿生设计模型。以降低谐振结构声辐射为目标，利用相似原理提出适合板壳结构加强筋布局设计的仿生脉序生长算法。针对复杂约束下板壳结构声振特性的拓扑优化问题，将优化准则法(KKT条件)与移动渐进线法(MMA法)相融合，提出了基于导重法的加强筋仿脉序自适应生长方法。针对高频振动板壳结构的声辐射优化问题，考虑结构弯曲波在结构-结构耦合截面的功率流耦合关系，构建基于功率流分析的加强筋布局优化方法，实现对抗振板壳结构能量流传播过程的控制和优化。针对典型薄板结构进行加强筋分布设计，构建板壳加筋结构振动和声辐射性能测试系统，开展抗振板壳结构加强筋仿生布局优化方法的实验研究。对比典型约束条件下仿生结构、正交加筋结构与基板结构的频率响应及辐射声功率，分析加强筋布局与板梁复合结构振动和噪声之间的关系，研究仿生布局加强筋板壳结构的振动与声学特性，验证板壳结构加强筋仿脉序分布自适应生长方法的合理性与有效性。综上，本项目提出的板壳结构加强筋布局设优化计方法，将为面向声振特性的结构轻量化设计奠定重要的理论基础和技术支撑。