CAJ | 학술논문

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,这方法能普遍适用于各种荷载形式和支承条件.
제출용직접변분방법연구초정정소성량적최우설계문제.수학상타표술위일개구유불등식약속적범함겁치문제，응용랍격랑일승자법득도료최우소성설계적일조필요조건，병유차도출료최우성조건.당목표함수시소성겁한만구철함수시,증명료저일최우성조건야시최우해적충분조건.기우최우성조건가건립구해최우소성량적일반방법,저방법능보편괄용우각충하재형식화지승조건.
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.