基于梯度有限元的异质材料实体优化设计

摘要

In order to achieve the optimal design of heterogeneous objects with the characteristic of spatially graded layout, the concept of two-phase graded finite elements is established. Lagrangian shape functions are employed to interpolate the volume fractions of the constituent materials. Adaptive lower bounds of the design variables are introduced to control the local gradients in the nodal neighborhoods. Method of moving asymptotes is used to solve the optimization problem for specific functionalities and objectives. A metal clip is analyzed and optimized to verify the feasibility and robustness of this approach.%针对具有空间分布梯度的异质材料实体的优化设计,建立了两相材料梯度有限元的概念,利用拉格朗日单元的形函数对体积分数进行插值,在节点邻域内引入设计变量自适应下界进行梯度控制,利用移动渐近线算法求解优化设计数学模型以使结构满足特定的功能和目标,以金属夹钳为算例验证了该方法的可行性和鲁棒性.