悬臂压杆大变形的优化算法

Optimum Algorithm for Large Deformation of a Cantilever Under Pressure on Free End

提出一种解决几何非线性问题的优化算法,研究了悬臂压杆的几何非线性大变形问题.取悬臂压杆大变形后的平衡状态为研究对象,利用整体坐标系下的坐标关系式表示出自由端端点坐标,构建端点未知坐标的目标函数,确定悬臂压杆大变形的最优化问题,编制优化程序进行求解.通过分析典型算例,并同有限元方法计算结果相比较,表明本文算法在求解强非线性变形中的正确性,为处理复杂几何非线性大变形问题提供了有效的思想.

An optimum algorithm is proposed to solve the geometrically nonlinear problem of Large deformation of a cantilever under pressure on free end. The cantilever in equilibrium after large deformation is studied. The coordinates of the free end are given through coordinate transformation formulae so as to define an objective function in terms of unknown coordinates of the endpoint. Then, make sure of the optimization problem of the large deformation of the cantilever under pressure on free end. An optimized algorithm is thus programmed for the problem. A typical numerical example is given and the result is analyzed in comparison with that by FEM. It is revealed that the algorithm is reliable in solving he strongly geometrically nonlinear deformation problem, which provides a prospective idea to solve the geometrically nonlinear large deformation problems that are more complex.