双模量材料圆板热弯曲及热屈曲的研究  

Thermal bending and thermal buckling of bimodulous circular plate

作　　者：吴晓[1] 赵均海[2] 黄志刚[1] 

机构地区：[1]湖南文理学院土木建筑工程学院,常德415000 [2]长安大学建筑工程学院,西安710061

出　　处：《应用力学学报》2015年第4期549-555,701,共7页Chinese Journal of Applied Mechanics

基　　金：湖南省科技计划资助项目[2011]65;湖南"十二五"重点建设学科项目[2011]76

摘　　要：采用Galerkin原理研究了双模量材料圆板的热弯曲及热屈曲问题。建立了双模量材料圆板在热状态下的弯曲微分方程,选取Legendre多项式为试函数,采用Galerkin原理推导出了双模量材料圆板在周边为弹性支承时的热弯曲及热屈曲近似解,该近似解与有关文献计算结果的误差在2%左右,二者基本吻合,验证了本文方法的正确性。讨论分析了温度对双模量材料圆板热弯曲及热屈曲的影响,得到了随着温差增大,双模量材料圆板中点弯曲挠度也逐渐增大,屈曲临界温度随着弯曲挠度增大而减小的结论。算例研究表明:双模量材料周边为不可移简支或周边为径向不可移转动弹性约束圆板在均匀及非均匀温度场发生小挠度轴对称热屈曲是非线性变形,而周边固支圆板发生小挠度轴对称热屈曲却是线性变形;在均匀温度场中,各向同性材料周边为不可移简支或周边为径向不可移转动弹性约束圆板、周边固支圆板,发生小挠度轴对称热屈曲都是线性变形;在非均匀温度场中,各向同性材料周边为不可移简支或周边为径向不可移转动弹性约束圆板发生小挠度轴对称热屈曲是非线性变形,各向同性材料周边固支圆板发生小挠度轴对称热屈曲是线性变形。Thermal bending and buckling problems of bimodulous circular plate are studied by the Galerkin principle. Thermal bending differential equations for bimodulous circular plate are established and the Galerkin principle is used to derive approximate solutions of thermal bending and buckling problems of bimodulous circular plate with edge elastically restrained against rotation by taking Legendre's multinomial expansion as a trial function. Calculation errors between the approximate solutions and relevant literatures are less than 2%. Effects of temperature on thermal bending and buckling of bimodulous circular plate are analyzed. Results obtained show that the midpoint deflection of a bimodulous circular plate increases with the temperature difference and critical buckling temperature decreases with the deflection increasing. Numerical example shows the axisymmetric thermal buckling with small deflection of bimodulous circular plates with edge immovably simply supported or immovably elastically restrained against rotation in temperature field is nonlinear deformation under uniform or non-uniform temperature fields, but that of plates with edge clamped is linear deformation. The buckling of isotropic circular plates with edge immovably simply supported or immovably elastically restrained against rotation in uniform temperature field is linear deformation, but that of plates with edge immovably simply supported or immovably elastically restrained against rotation in non-uniform temperature field is nonlinear deformation, and that of plates with edge clamped in non-uniform temperature field is linear deformation.

关 键 词：双模量 材料 圆板 弯曲 屈曲 温度 

分 类 号：O343[理学—固体力学]