摘要
描述几何大变形问题的方程式为非线性微分方程,该方程不能应用叠加原理求解,且当荷载复杂、柔性结构杆件的截面变化时其求解更加复杂.基于拟线性等效系统的原理,提出了简化的拟线性等效系统,通过试差法确定水平位移Δ,将非线性弯矩和刚度转化为线性问题,从而将欧拉-贝努利方程转化为线性问题,并且在梁中推广了拟线性等效系统.实例验证表明拟线性等效系统简化方法得当、计算结果满足精度要求.
A nonlinear differential equations, which describes the problem of geometric large deformation, can＇t be solved by applying superposition principle, particularly when the loads are complicated and the section of flexible structure is alterable, and the problem＇s solution is more complex. Thus,based on the principle of imitate-linearity equal system,the basic idea of simplification＇s imitate-linearity equal system is presented to solve the problem. Nonlinear Analysis of the moment and stiffness are transformed into linear problems by tring difference method to determine horizontal displacement values, so Euler-Bernoulli equation that is a second-order nonlinear differential equations is transformed into linear one, and simplification＇s imitate-linearity equal system is also generalized to the multi horizontal displacement variable beam system. At last, an example shows that the simplification method is proper and the results posses enough precision.
出处
《武汉理工大学学报（交通科学与工程版）》
2008年第5期963-966,共4页
Journal of Wuhan University of Technology（Transportation Science & Engineering）
基金
高等学校博士学科专项科研基金项目资助(批准号:20050611002)
关键词
简化拟线性等效系统
试差法
欧拉方程
simplification＇s imitate-linearity equal system
try difference method
Euler-equation
