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。
Micro-mass sensors have attracted increasing attention in the field of biomolecular and chemical detec- tion. It has been found that the size, shape, and geometry of the structure may affect the performance of the sensor. As a result, a topology optimization methodology is proposed in this paper for the design of micro-mass sensors. A phase- field function controlled by nodal variables and finite element shape functions is used to describe the configuration of a sen- sor in the constructed optimization problem. The design goal is to maximize the mass detection sensitivity. On the basis of these formulations, an optimization algorithm is constructed using the finite element method and the method of moving asymptotes. Numerical examples are presented to demon- strate the validity of the proposed problem formulation. The results suggest that the performance of the micro-mass sensor can be improved by using the proposed approach.
