基于可行域调整的多相材料结构拓扑优化设计

针对多相材料结构柔顺度拓扑优化问题及其存在多个局部优化解的情况，提出一种新的多相材料结构柔顺度拓扑优化问题的求解方法， 并研究其获得多个局部优化解及寻找较好的优化解的能力。基于材料属性有理近似 （RAMP）模型，引入可行域调整技术，构建多相材料结构拓扑优化模型及近似优化模型。提出一种改进的交替主动相算法，该算法将多相材料结构拓扑近似优化模型分解为多个含2个主动相材料体积约束的系列二元相拓扑优化子模型，并利用光滑化对偶算法进行优化求解。与现有方法相比，采用多个不同的优化初始拓扑，提出的方法可找到更优的多相材料结构拓扑， 且为多相材料结构拓扑优化的多样性设计提供了一种有价值的思路与方法。

Multi-phase material struclural topology optimization design based on feasible domain adjustment

For the multi-phase material structural compliance topology optimization problem and the existence of multiple local optimization solutions, a new solution method is proposed, and the ability of the method to get multiple local optimization solutions and to find a better optimization solution are investigated. Based on the Rational Approximation of Material Properties (RAMP) model, the feasible domain adjustment technology is introduced to construct a model for multi-phase material structural topology optimization model and its approximate model. A modified alternating active-phase algrithom is proposed, in which the multi-phase material topology optimization problem is divided into some two-phase topology optimization sub-problems, which may include two real material volume constraints. And the sub-problems are solved by the smooth dual algorithm. Compared with the existed methods, the proposed method can obtain a different local optimal topology starting from a different initial topology, and can also obtain a better local optimal multi-phase material topology by using various initial topologies. And the proposed method gives a valuable idea and a multiple design approach to solve the multi-material structural topology optimization problem.