摘要
基于经典梁理论,运用虚功原理和变分法推导了均匀变温场与横向均布荷载联合作用的功能梯度梁的几何非线性控制方程.考虑端部不可移夹紧边界条件,运用打靶法求解了该两点边值问题.当横向均布荷载为0时,考察了功能梯度梁的热屈曲临界升温和屈曲平衡路径.当均匀变温与横向均布荷载都不为0时,考察了功能梯度梁的荷载-挠度曲线.数值结果表明:随材料体积分数指数增加,梁的有量纲热屈曲临界升温显著减小,后屈曲变形显著增加;变温对功能梯度梁的荷载-挠度曲线影响非常显著.发现了功能梯度梁的双稳态构形及其转换现象,梁的最终平衡位形不但与变温及荷载参数有关,还与加载历程有关.
Based on the classical beam theory, the geometric nonlinear governing equations for FGM beams under uniform temperature field and uniform transverse loading were derived according to the principle of virtual work and the variational method. In view of the immovably clamped boundary conditions, the 2-point boundary value problem was solved with the shooting method. For the zero uniform transverse loading, the thermal buckling critical temperature and equilibrium path of the FGM beam were investigated. The load-deflection curves of the FGM beam were given for the nonzero uniform temperature and the nonzero transverse uniform loading. The numerical results show that, the dimensional thermal buckling critical temperature of the beam decreases significantly and the post-buckling deformation increases significantly with the material volume fraction index increases, and the temperature variation has a heavy influence on the load-deflection curves. The bistable configurations and the switch of the FGM beam were found. The final equilibrium shape of the beam is not only related to the variable temperature and loading parameters, but also to the loading process.
作者
王雪
赵伟东
WANG Xue;ZHAO Weidong(School of Civil Engineering, Qinghai University, Xining 810016, P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2019年第5期508-517,共10页
Applied Mathematics and Mechanics
基金
教育部春晖计划(Z2015057)
关键词
功能梯度梁
热-机械荷载
荷载-挠度曲线
双稳态构形
打靶法
functionally graded beam
thermomechanical loading
load-deflection curve
bistable configuration
shooting method
