摘要
现有的拱的平面内稳定理论有很大分歧。本文采用平截面假定,未作任何近似地采用了有限变形理论中的应变位移关系,完整地考虑了横向应力和剪应力的二阶效应,用虚功原理推导了拱的平面内非线性分析的平衡方程。之所以引入横向应力的非线性效应,是因为保持平衡所需的各应力分量的二阶效应会部分相互抵消,忽略其中任何一个都可能导致不正确的结果。文中还给出了内力采用线性分析结果的近似非线性分析方程,可以用于绝大多数工程问题的求解。对拱的内力和位移的线性问题进行了精确求解,代入非线性方程后得到了圆弧拱屈曲分析的平衡微分方程。用Galerkin法求得了考虑/不考虑拱内弯矩和剪力影响、考虑/不考虑屈曲前变形影响的临界荷载,并讨论了拱轴不可伸长假定的影响。系统地与前人的研究进行了比较。
Current theories for arch buckling analysis have great differences. Based on the Bernoullis assumption, a new theory for nonlinear analysis of circular arches is proposed. The finite displacement theory for strain-displacement relation is adopted. The nonlinearity of the shear and the transverse stresses is considered. It is believed that the nonlinear effects of various stresses, which are in equilibrium prior to buckling, will cancel each other partially, so neglecting any one of these stresses will lead to unwanted terms in the equilibrium equations. Employing the internal forces in linear analysis, a set of linearized equations suitable for buckling analysis of arches are derived. A detailed analysis of the buckling of circular arches under uniform radial load is conducted. The results of the linear analysis are substituted into the nonlinear equations to obtain a set of equations which are solved using Galerkin technique. The effect of pre-buckling deformation is included. Various assumptions often used by previous researchers, especially the inextensional assumption of the arch axis, are discussed. A comprehensive comparison of various theories is provided.
出处
《工程力学》
EI
CSCD
北大核心
2005年第1期93-101,共9页
Engineering Mechanics
关键词
拱
稳定性
非线性分析
应力
屈曲
arch
stability
nonlinear analysis
stress
buckling
