结构柔顺度拓扑优化的倒变量准则

Reciprocal criterion of structural compliance topology optimization

针对在工程中广泛应用于最大化结构刚度设计的最小化结构柔顺度拓扑优化问题,应用连续体拓扑优化SIMP法,基于倒变量建立了优化模型;应用K-T条件建立了相应的优化准则,并提出了柔顺度过滤方法消除棋盘格现象及网格依赖等数值问题。应用不同的网格,与原准则法及MMA法进行了算法效率比较,与敏度过滤法及密度过滤法进行了优化求解结果及效率的比较。所附MATLAB程序测试表明:所提方法迭代次数最少、运行时间最短,随问题规模增大迭代次数不会增加;与原准则法相比,不用设置运动极限参数,适合求解大规模工程问题。

To the minimizing structural compliance problems which widely occur in engineerings for a maximum structural stiffness design,an optimization model with reciprocal variables was established by the SIMP method.An optimality criterion is proposed by the K-T condition.Compliance filtering method is proposed to eliminate numerical problems such as checkerboard patterns and mesh dependency problems.With different scales of optimization problems,the solution efficiency is compared with the original criteria method and MMA method;and the optimal results and solution efficiency are compared with the ones of sensitivity filtering method and density filtering method.A MATLAB program of the presented method is applied in the paper and several numerical examples are illustrated.It shows from examples that the presented method has least iterations and shortest time among the compared methods,and the number of iterations doesn’t increase while the scale of optimization problems increases.Compared with the original criteria method,the moving limits are not necessary for the presented method.Therefore,it is suitable for large-scale engineering problems.