最小位移类桁架连续体拓扑设计优化

为将拓扑优化中的柔度最小化问题拓展到一般位移最小化问题,用有限元划分设计域,采用类桁架连续体材料模型,并假设杆件在设计域内连续分布.将杆件在节点位置的密度和方向作为设计变量,将指定位置和方向的位移作为目标函数,采用基于目标函数梯度的优化准则法,通过优化杆件的连续分布场形成拓扑优化的类桁架连续体.该方法可结合结构力学的基本概念,选择部分杆件形成拓扑优化刚架.

Topology design optimization on truss like continuum with minimum displacement

To expand flexibility minimization problem in topology optimization to general displacement minimization problem,the design domain is meshed by finite elements and the truss-like continuum is used as the material model,and the rods are assumed to distribute continuously in design domain.The density and orientation of rod at node position are selected as design variables.The displacement along the specific direction is selected as the objective function.The continuum distribution field of members is optimized to form truss-like continuum by optimality criteria method based on the gradient of objective function.By the aid of structural mechanics conception,the parts of members are remained to form topology optimization frame.