弹性地基上双曲率扁壳的优化设计问题

本文讨论位于弹性地基上的双曲率扁壳优化设计的一个方法。其实质是取扁壳的初始挠曲函数作为待求的控制函数或设计变量,以载荷的势能作为判定双曲率扁壳优化设计的质量准则,故势能泛函即为目标函数,而优化条件及等周条件均作为约束条件,从而得到本问题优化设计的必要条件。同时引入一共轭函数,最后将问题归结为求解共轭函数的微分方程及初始挠曲函数两个边值问题。

On Problems of Optimal Design of Shallow Shell with Double Curvature on Elastic Foundation

The present paper discusses a method of optimal design of the shallow shell, with double curvature on the elastic foundation, Substantially we take the initial flexural function as the control function or design variable which will be found and the potential energy of the eternal loads as the criterion of quality of the optimal design of the shallow shell with double curvature, therefore the functional of the potential energy will be aim function, The optimal conditions and the isoperimetric conditions belong to the constrained conditions, thus we obtain the necessary conditions of the optimal design for the given problems, at the same time the conjugate function is introduced, then the problems are reduced to the solutions of two boundary value problems for the differential equation of conjugate function and tba initial fleeural function.