塔式起重机臂架腹杆布局及尺寸优化设计

摘要 为实现塔式起重机臂架布局和尺寸的优化，提出了桁架结构拓扑及尺寸两阶段优化设计方法.第一阶段先建立臂架的周期性板梁拓扑优化模型，使用周期性SKO方法对腹板进行连续体拓扑优化，得到优化的腹板拓扑构型，并通过提取主应力路径将优化的腹板拓扑结构转化为离散的腹杆布局;第二阶段以臂架腹杆截面半径为设计变量，臂架柔度为目标函数，材料体积为约束条件建立优化模型，基于Lagrange乘子法和库恩塔克条件推导腹杆截面尺寸优化迭代准则，基于欧拉公式推导了腹杆稳定性约束条件以保证尺寸优化过程中臂架稳定性.数值分析结果表明，该优化方法能有效地减轻臂架结构质量，提高臂架的刚度，减少变形并降低结构应力水平.
Abstract：For the layout and size optimization of tower crane booms， a two-stage topology and size optimization method was proposed. In the first stage， a periodic plate-beam topology optimization model of the boom was established， and the continuum topology optimization of the web plate was performed by using the periodic SKO method. After getting the optimized topology of web plate， the optimized web topology was transformed into a discrete web layout through the extraction of the principal stress path. In the second stage， the size optimization mathematical model was established with the web radius taken as the design variable， the boom compliance as the objective function and the material volume of the boom as the constraint. The size optimization criterion was deduced by the Lagrange multiplier method and Kuhn-Tucker condition. In addition， the stability constraints of the webs were proposed to ensure the boom stability during the size optimization process based on the Euler formula. By comparing the original boom with the optimal booms， the optimization method can effectively reduce the mass of the boom， increase the rigidity of the boom， and reduce the deformation and structural stress level.