论日本江户时期“怀德书院”的教育

基于独立连续映射方法（Independent Continuous and Mapping，ICM），实现功能梯度材料（Functionally Graded Material，FGM）结构的拓扑优化设计.通过引入过滤函数，构建FGM-ICM材料模型.结合梯度位移函数，建立以结构质量最小化为目标、以位移为约束条件的功能梯度材料结构拓扑优化近似显式模型.采用线性衰减的过滤方法避免棋盘格现象和网格依赖性问题.另外，为得到边界清晰的拓扑构型，设计拓扑变量阈值动态调整策略（Dynamic Adjustment Strategy for Variable Threshold，DASVT），消除了拓扑变量阈值取值的盲目性.通过数值算例验证了该方法的可行性和有效性，最终实现了功能梯度材料结构ICM拓扑优化设计.

ICM Topology Optimization Method of Functionally Graded Structures Considering Displacement Constraint

Topology optimization of functionally graded material structure was presented based on independent continuous and mapping method. By introducing the filter function, the FGM-ICM model was constructed. Combined with the gradient displacement function, the approximate explicit model for ICM structural topology optimization of FGM was established. The filter method of linear attenuation was adopted to avoid the checkerboards and mesh dependency problem. Meanwhile, in order to obtain the clear topological configuration, the dynamic adjustment strategy for the topological variable threshold was proposed. The results of numerical examples demonstrate that the proposed analysis method can effectively realize the structural topological optimization of FGM.