横向非均匀温度场作用的FGM夹层圆板热屈曲分析  

Thermal Buckling Analysis of FGM Sandwich Circular Plates Under Transverse Nonuniform Temperature Field Actions

作　　者：龚雪蓓 赵伟东[1,2] 郭冬梅 GONG Xuebei;ZHAO Weidong;GUO Dongmei(School of Civil Engineering,Qinghai University,Xining 810016,P.R.China;Qinghai Provincial Key Laboratory of Energy-Saving Building Materials and Engineering Safety,Xining 810016,P.R.China)

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

出　　处：《应用数学和力学》2023年第4期419-430,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(52168053)。

摘　　要：基于von Kármán几何非线性板理论,导出了受横向非均匀温度场作用的幂律型功能梯度材料(FGM)夹层圆板的位移型几何非线性控制方程.考虑不可移夹紧边界条件,通过求解线性特征值问题,得到了系统的有量纲临界屈曲温度差解析公式.另外,运用打靶法计算了非线性常微分方程两点边值问题.考察了几何参数、组分材料特性、梯度指数、温度场参数和层厚比对FGM夹层圆板的临界屈曲温度差、热过屈曲平衡路径和平衡构形的影响.当厚径比、梯度层相对厚度和梯度指数增加时,FGM夹层圆板临界屈曲温度差均单调增加;当半径和总厚度给定时,随FGM层相对厚度增加,FGM夹层圆板后屈曲变形显著减小.Based on the von Kármán geometric nonlinear plate theory,the displacement-type geometric nonlinear governing equations for FGM sandwich circular plates under transverse nonlinear temperature field actions were derived.With the immovable clamped boundary condition,the analytical formula for dimensional critical buckling temperature differences of the system was obtained from the solution of the linear eigenvalue problem.Moreover,the 2-point boundary value problem of ordinary differential equations was solved with the shooting method.The effects of geometric parameters,constituent material properties,gradient indexes,temperature field parameters and layer-thickness ratios on the critical buckling temperature differences,the thermal postbuckling equilibrium paths,and the buckling equilibrium configurations of FGM sandwich circular plates,were investigated.The results show that,with the increases of the thickness-radius ratio,the relative thickness of the FGM layer and the gradient index,the FGM sandwich circular plate's critical buckling temperature difference will increase monotonically.Given a fixed radius and a fixed total thickness,the postbuckling deformation of the FGM sandwich circular plate will decrease significantly with the relative thickness of the FGM layer.

关 键 词：功能梯度材料 夹层圆板 非均匀温度场 热屈曲 打靶法 

分 类 号：TU43[建筑科学—岩土工程]