超静定梁的最优塑性设计

Optimal Plastic Design of Statically Indeterminate Beams

提出用直接变分方法研究超静定塑性梁的最优设计问题 .数学上它表述为一个具有不等式约束的泛函极值问题 ,应用拉格朗日乘子法得到了最优塑性设计的一组必要条件 ,并由此导出了最优性条件 .当目标函数是塑性极限弯矩凸函数时 ,证明了这一最优性条件也是最优解的充分条件 .基于最优性条件可建立求解最优塑性梁的一般方法 。

A method of direct variation is presented for the investigation of the optimal design of statically indeterminate plastic beams in this paper.Mathematically it is formulated as a functional extreme problem with ineqrality constraints.The necessary conditions for the optimal plastic design are obtained by means of the Lagrange multiplier method,and then the optimality conditions are derived.It is proved that the optimality conditions are also sufficient if the objective function is a convex function of the plastic limit bending moment.A universal method for finding optimal plastic beams can be developed based on the optimality conditions.The method proposed in the paper is applicable to any kind of loadings and support conditions.