导重法求解柔性机构多目标拓扑优化问题
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摘要
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.
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.
引文
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[4]张宪民.柔性机构拓扑优化设计[J].机械工程学报,2003,39(11):47-51.
[5]陈树勋,韦齐峰,黄锦成.结构优化导重准则及其意义与合理性[J].固体力学学报,2013,34(6):628-638.
[6]陈树勋.精密复杂结构的几种现代设计方法[M].北京:北京航空航天大学出版社,1992.
[7]李枝东,刘辛军.导重法求解单工况的拓扑优化问题[J].机械工程学报,2011,47(15):107-114.
[8]LIU X J,LI Z D,CHEN X.A new solution for topology optimization problems with multiple loads:the guide-weight method[J].Sci China Tech Sci,2011,54(6):1505-1514.
[9]许华旸,关立文,王立平,等.惯性载荷下飞行模拟器大臂结构的拓扑优化[J].机械工程学报,2014,50(9):14-23.
[10]左孔天,赵雨东,钟毅芳,等.微型柔性机构的多目标计算机辅助拓扑优化设计[J].计算机辅助设计与图形学学报,2006,18(6):855-859.
[11]马成业,黎锁平,杨胜良.模糊多目标可靠性优化设计的遗传算法[J].兰州理工大学学报,2009,35(1):156-158.
[12]叶尚辉,陈树勋.天线结构优化设计的最佳准则[J].西北电讯工程学院学报,1982,9(1):11-28.
[2]崔明涛,陈建军,陈永琴,等.整体式柔性机构的多目标可靠性拓扑优化设计[J].中国机械工程,2007,34(5):784-788.
[3]谢先海.柔顺机构的设计与分析方法研究[D].武汉:华中科技大学,2002.
[4]张宪民.柔性机构拓扑优化设计[J].机械工程学报,2003,39(11):47-51.
[5]陈树勋,韦齐峰,黄锦成.结构优化导重准则及其意义与合理性[J].固体力学学报,2013,34(6):628-638.
[6]陈树勋.精密复杂结构的几种现代设计方法[M].北京:北京航空航天大学出版社,1992.
[7]李枝东,刘辛军.导重法求解单工况的拓扑优化问题[J].机械工程学报,2011,47(15):107-114.
[8]LIU X J,LI Z D,CHEN X.A new solution for topology optimization problems with multiple loads:the guide-weight method[J].Sci China Tech Sci,2011,54(6):1505-1514.
[9]许华旸,关立文,王立平,等.惯性载荷下飞行模拟器大臂结构的拓扑优化[J].机械工程学报,2014,50(9):14-23.
[10]左孔天,赵雨东,钟毅芳,等.微型柔性机构的多目标计算机辅助拓扑优化设计[J].计算机辅助设计与图形学学报,2006,18(6):855-859.
[11]马成业,黎锁平,杨胜良.模糊多目标可靠性优化设计的遗传算法[J].兰州理工大学学报,2009,35(1):156-158.
[12]叶尚辉,陈树勋.天线结构优化设计的最佳准则[J].西北电讯工程学院学报,1982,9(1):11-28.