基于改进水平集结构拓扑优化方法的理论研究

Theoretical research of structure topology optimization based on the level set method

通过水平集拓扑优化方法建立了以结构的刚度最大化为目标函数、以结构的体积为约束条件的优化问题数学模型;通过反应扩散方程来更新水平集函数,同时实现了结构的形状和拓扑优化。针对水平集拓扑优化方法在求解优化模型时出现的体积约束不收敛的问题,分析了问题产生的原因,提出了拉格朗日乘子的直接与间接控制方式来控制体积约束收敛的方法,并通过相关算例验证了两种方法的有效性。

Based on the level set topological optimization method,a mathematical model for the optimization problem is established to maximize the stiffness of the structure as the objective function,and the structure volume is used as the constraint conditions.The level set function is updated by the reaction diffusion equation,and the shape and topology of the structure are optimized together.To the problem of volume constraint non-convergence when solving the optimization model by level set topological optimization method,the reasons are analyzed and a method to control the volume constraint convergence is proposed by the direct and indirect control of Lagrange multipliers.The validity of the two methods is verified by the relevant examples.