基于变厚度杂交元的二维连续体结构拓扑优化

Topology Optimization of 2D Continuum Structures Using Hybrid Element of Non-uniform Thickness

提出了以节点厚度为设计变量、基于变厚度杂交有限元的二维连续体结构拓扑优化设计模型。考虑了以柔顺度作为目标函数、体积作为约束条件的刚度最大化拓扑优化问题,推导了基于节点变厚度杂交元的连续体结构敏度计算的解析表达式,并采用优化准则法进行迭代求解。对MBB梁等典型问题所做算例结果表明,无需采用敏度过滤等特殊处理,该方法也能给出具有清晰边界的拓扑优化结果,验证了方法的有效性和优越性。

A topology optimization model based on nodal thickness with penalization exponent is proposed for 2D continuum structures. In this formulation, the thickness is used as the design variable and a hybrid element for 2D membrane of non-uniform thickness is applied for the finite element analysis. Analytical expressions have been derived for sensitivity analysis and an iterative solution algorithm based on optimality criteria also presented. The numerical results with classical problems such as MBB beam show that, while no special techniques like sensitivity filtering are employed, the topologies obtained are still clear and reasonable, demonstrating the effectiveness and superiority of the new method.