简支梁大变形的优化算法

提出一种求解几何非线性问题的优化算法,并研究了简支梁的几何非线性大变形问题。首先取简支梁大变形后的平衡状态为研究对象,分别创建它的变分模型和微分模型;然后基于微分模型,通过动坐标的迭代关系式求得微段端点坐标,构建微段端点未知坐标的目标函数;最后确定简支梁几何非线性大变形的最优化问题,并编制相应优化程序进行求解。通过分析典型算例,并同有限元方法的计算结果相比较,表明提出的优化算法在求解强几何非线性大变形问题中的正确性,为处理几何非线性大变形问题提供了一种新方法。

Optimum Algorithm for Large Deformation of Simply-supported Beam

An optimum algorithm is proposed to solve the geometrically nonlinear problem for a simply-supported beam with large deformation.The variational model and the differential model are respectively established.Based on the differential model,the endpoints coordinates of slight segments are given via coordinate transformation formulae to define an objective function in terms of unknown coordinates of the endpoints coordinates of slight segments.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 for solving the strongly geometrically nonlinear deformation problem to offer a new way for geometrically nonlinear problems.