横向非均匀温度场作用的FGM夹层梁热屈曲分析  

Thermal buckling analysis of FGM sandwich beams under the actionof transverse non - uniform temperature field

作　　者：李成龙 赵伟东 LI Chenglong;ZHAO Weidong(School of Civil Engineering and Water Resources,Qinghai University,Xining 810016,China;Qinghai Key Laboratory of Energy-saving Building Materials and Engineering Safety,Xining 810016,China)

机构地区：[1]青海大学土木水利学院,青海西宁810016 [2]青海省建筑节能材料与工程安全重点实验室,青海西宁810016

出　　处：《青海大学学报》2024年第2期60-67,共8页Journal of Qinghai University

基　　金：国家自然科学基金项目(52168053)。

摘　　要：基于经典几何非线性梁理论,推导了受横向非均匀升温作用的FGM夹层梁热屈曲控制方程。对于端部夹紧边界条件梁,随着温度升高,梁发生分支屈曲,考虑到分支屈曲临界状态变形较小,将非线性边值问题退化成线性特征值问题,通过求线性特征值问题,得到了有量纲临界屈曲温度差解析解。另外,运用打靶法计算非线性边值问题,得到了热过屈曲平衡路径和平衡构型。利用算例探究层厚比、梯度指数、温度场级数项数目对FGM夹层梁热过屈曲平衡路径和平衡构型的影响。结果表明:当梯度层相对厚度和梯度指数增加时,FGM夹层梁临界屈曲温度差均增加。The thermal buckling governing equation of functionally gradient materials(FGM)sand-wich beams subjected to transverse non-uniform heating is derived in view of the classical geomet-ric non-linear beam theory.For the end clamped boundary condition beam,the beam undergoes branch buckling as the temperature increases.Considering the small deformation corresponding to the critical state of branch buckling,the problem of nonlinear boundary value is reduced to a linear ei-genvalue problem.The analytical solution of dimensional critical buckling temperature difference of the system is obtained by solving the linear eigenvalue problem.The non-linear boundary value problem is calculated by shooting method.In addition,the thermal post-buckling equilibrium path and equilibrium configuration of the system are obtained as well.The effects of layer thickness ratio,gradient index,temperature field and geometric parameters on the thermal post-buckling equilibrium path and equilibrium configuration of FGM sandwich beams are investigated by examples.The results show that the critical buckling temperature difference of FGM sandwich beam increases when the relative thickness and gradient index of the gradient layer increase.

关 键 词：功能梯度材料 夹层梁 非均匀升温 热屈曲 打靶法 

分 类 号：TU311[建筑科学—结构工程]