平面框架结构的几何非线性问题打靶法求解

Solution of geometrically non-linear problem of planar frame structure with numerical shooting method

基于弹性曲梁平面大变形问题的精确几何非线性理论,建立简单平面框架结构在静载荷作用下弯曲问题的无量纲控制方程和边界条件,其中基本未知量均被表示为变形前的轴线坐标的函数.采用打靶法求解非线性常微分方程的两点边值问题,得到不同框架结构的大变形平衡构形.所提出的理论和方法可以用于分析平面简单框架结构在各种载荷作用下的大变形问题.

Based on an exact geometric nonlinear theory of large deformation of planar elastic curved beams,the dimensionless equations and boundary conditions governing the nonlinear bending of a simple planar frame structure subjected to static loads were set up,in which the basic unknown was expressed as function of axial coorelinates before the deformation.By using shooting method to solve two-point boundary value problem of nonlinear ordinary differential equations,large deformation equilibrium configurations of different simple frames were obtained.The theory and method presented could be used to analyze large deformation of planar simple frames with a variety of geometries and loadings.