变厚度圆柱壳的强度优化设计

Optimum design of cylindrical shell with nonuniform wall thickness

对在任意轴对称分布荷载作用下体积保持常数的变厚度圆柱壳的强度优化设计问题进行了研究。当中面形状固定时 ,采用阶梯折算法 ,用传递矩阵导出了变厚度圆柱壳的初参数解的显式表达式。根据Huber-Mises-Hencky强度准则 ,将变厚度圆柱壳的强度优化转化为极小化当量应力的非线性规划问题 ,并采用投影梯度法建立了问题的优化方法。文中对几个典型问题进行了计算。与等厚度圆柱壳相比较 ,优化圆柱壳的最大当量应力得到了显著降低。

A strength optimal design problem of the cylindrical shell with nonuniform wall thickness is studied. If the middle surface of the shell is known, the equilibrium equations of the cylindrical shell under arbitrarily axisymmtrically distributed load are solved by using the stepped reduction method, and its solutions of explicit formulation arc obtained. Based on the Huber-Mises-Henckey failure hypothesis, the optimal problem with the condition of constant volume is reduced to a nonlinear programming problem in which the objective function is the maximum reduced stresses of the cylindrical shell, and an optimal method is established in terms of the projective gradient method. Finally, some typical problems are calculated. In contrast with the uniform shell, the maximum reduced stresses of the optimal shell are reduced greatly. Those results may be used to design the ribs of cylindrical shell.