【作者】 龙凯； 李涛； 左正兴； 孙宇娟；

【Author】 LONG Kai LI Tao ZUO Zheng-xing,SUN Yu-juan (Beijing Institute of Technology,Beijing 100081,China)

【机构】 北京理工大学机械与车辆工程学院；

【摘要】 提出基于独立节点变量的连续体动态拓扑优化方法。该方法吸取独立连续映射(independent continuous mapping,ICM)法设计变量独立性特点,基于不同的插值函数建立弹性模量、密度模型,并采用相同数值惩罚参数以避免局部模态现象。与ICM法不同的是,设计变量表征节点有无状态,单元内任意一点的拓扑变量值由单元形函数插值得到,从而保证拓扑变量场的连续性,在连续体拓扑模型描述上抑制棋盘格现象。分别以结构最低特征值和关心自由度振幅平方和最小为目标,体积比约束建立动态拓扑优化模型,采用单元变密度法中的优化准则法优化求解。通过数值算例对优化结果进行分析讨论,结果表明,独立节点变量法在连续体动态拓扑优化中具有可行性和有效性。更多还原

【Abstract】 A new topological optimization method of continuum structure for dynamic problems is presented based on independent node-based design variables.Due to the independence of design variables as in independent continuous mapping(ICM) method,young’s modulus and density are modeled by different filter functions and phenomenon of localized mode are avoided by the same penalty parameters。Different with ICM method,conditions of existence or null are defined by node-based design variables which ensures C0 continuity of design variables by interpolation of shape functions in a element.The new method is immune to checkerboards instabilities that are a concern in most topological optimization methods.Topological optimization models are developed where volume is taken as objective and the first order eigenvalue and the sum of displacement amplitude square in concerned domain are referred to as constraint conditions.The optimization models are solved by optimality criteria method which is the same as in element-based variable density method.Some numerical examples are presented and discussed.The results demonstrate the feasibility for the proposed method.更多还原