结构最大刚度拓扑优化的隐式方法

An Implicit Topology Optimization Method for the Maximum Structural Stiffness

提出了结构在力、位移以及力与位移混合作用方式下结构最大刚度拓扑优化的一般性设计方法。设计目标为最大化结构的最小总势能,设计变量为单元的密度。通过SIMP(solid isotropic materials with penalization)准则建立设计变量与结构性能之间的关系。通过KKT(Karush-Kuhn-Tucker)条件推导了优化问题的最优解条件;并给出了基于最优解条件的变量迭代格式。迭代格式不显含目标函数,是一种隐式的求解方法。数值算例表明,对于结构承受力、位移以及力和位移混合作用时均能够获得准确结果,且方法具有简洁高效的特点。

A general topology optimization method was proposed for a structure subjected to the force,the displacement and the mixed loading of force and displacement to maximize the structural stiffness.The objective function is the maximization of the structural minimum total potential energy and the design variable is the density of an element.The SIMP （solid isotropic materials with penalization） proposition is used to relate the density and the structural properties.Moreover,the optimal criterion is derived through the KKT （Karush-Kuhn-Tucker） condition.Based on this criterion,the iteration scheme of variables is shown.The objective function is not included explicitly in this scheme; hence,it is an implicit method.Numerical examples show that the present method can obtain the accurate results for structures subjected to force,displacement and the mix action of force and displacement.Also,the method is simple and efficient.