导重法求解柔性机构多目标拓扑优化问题

Solution of problem of multi-objective topology optimization of compliant mechanism with guide-weight method

柔性机构中为同时考虑结构的刚性和机构的柔性,研究结构整体柔度最小化和结构输出位移最大化的多目标拓扑优化设计方法.建立基于RAMP插值模型的多目标拓扑优化设计模型,采用伴随敏度分析法进行目标函数敏度分析.将导重法引入到柔性机构拓扑优化问题的求解中,推导出柔性机构多目标拓扑优化问题的迭代表达式.对柔性机构的典型算例进行拓扑优化计算,算例结果表明,基于RAMP插值模型结合导重法求解柔性机构多目标拓扑优化问题具有设计变量少、收敛速度快、优化效率高的特点,上述方法的结合为求解柔性机构多目标拓扑优化问题提供了一条新途径.

In order to take into account simultaneously the stiffness and compliance of the structure,a design method was studied for multi-objective topology optimization with minimization of structural overall compliance and maximization of structural output displacement,an optimization model was established based on RAMP interpolation model,and sensitivity analysis of objective function was conducted with adjoint sensitivity analysis method.The guide-weight method was introduced into the solution of topology optimization of compliant mechanism and the iterative expression of the topology optimization was derived.The topology optimization of a typical compliant mechanism was conducted and its result showed that RAMP interpolation model combined with guide-weight method would have the such advantage as less design variables,fast convergence,and high optimization efficiency.Above-mentioned method would provide a new way for solving compliant mechanism with multi-objective topology optimization.