单侧接触约束下桁架拓扑优化的若干结果

对考虑应力和无摩擦单侧接触位移约束的桁架拓扑优化问题进行了研究，采用解析方法，通过对典型算例不同初始接触间隙下的拓扑优化解的讨论，发现这一优化问题中存在解不唯一现象，研究也表明，接触状态对结构拓扑有一定影响，不同初始接触间隙可能导致不同的拓扑结构，对利用数值方法该问题进行了研究，为克服结构拓扑优化中奇异最优解问题，采用ε松弛方法建立桁架拓扑优化模型列式，并利用双层优化方法求解本拓扑优化问题，第一层，通过求解与原接触问题等价的二次规划问题来进行结构接触分析；第二层，利用第一层得到的位移及应力，采用ε-松弛方法进行结构拓扑优化。

SOME RESULTS ON OPTIMAL TOPOLOGY DESIGN OF TRUSS WITH UNILATERAL CONTACT CONSTRAINTS

The optimal topology design of truss structures concerni ngstress and frictionless unilateral contact displacement constraints is invest igated. The existence of ununique optimal solution under contact gaps is found. It shows that the contact conditions has an effect on structural topology, and different initial contact gaps may lead to different structural topologies. To a void the singular optima in structural topology optimization in multiple loading cases, an ε-relaxed method is adopted to establish the relaxing topology optimization formulations. The problem is solved by means of a two-level optimi zation method. In the first sublevel, the solution of the frictionless unilatera l contact problem is obtained by solving an equivalent quadratic programming. In the second sublevel, topology optimization of truss is carried out by an ε -relaxed method. The validity of the method proposed is verified by computation al results.