弹性地基上加热弹性圆板的热过屈曲及临界屈曲模态跃迁  

THERMAL POST-BUCKLING AND THE CRITICAL BUCKLING MODE TRANSITION OF HEATED ELASTIC CIRCULAR PLATES ON ELSSTIC FOUNDATION

作　　者：李世荣[1] 郁汶山[1] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《工程力学》2007年第5期63-66,28,共5页Engineering Mechanics

基　　金：国家自然科学基金资助项目(10472039)

摘　　要：基于von Kármán薄板理论建立了Winkler弹性基础上弹性圆板在均匀升温下的轴对称热过屈曲控制方程。这是一组以中面位移为基本未知量的非线性常微分方程,其中包含了温度载荷和弹性地基刚度两个参数。采用打靶法数值求解相应的非线性两点边值问题,获得了周边不可移简支圆板的热屈曲及热过屈曲响应。绘出了前三阶屈曲模态对应的临界温度载荷随地基参数连续变化的特性曲线,获得了反映临界热屈曲模态跃迁特性的地基参数值。给出了弹性圆板按一阶模态失稳后的热过屈曲平衡路径和平衡构形,分析了地基刚度参数对临界屈曲温度载荷以及过屈曲平衡构形的影响。Based on the von Karman thin plate theory the governing equations in terms of the displacements of the middle plane are formulated for an elastic circular plate on Winkler elastic foundation, in which the two parameters of thermal loading and elastic foundation stiffness are included. By using the shooting method the corresponding two-point boundary value problem for nonlinear ordinary differential equations are solved numerically and the thermal buckling and post-buckling responses for the circular plate with immovably simply supported edges are obtained. Characteristic curves of the critical temperature loads for the anterior third-order buckling modes varying continuously with the foundation stiffness are plotted and the values of transition foundation stiffness between different modes are evaluated. Post-buckling equilibrium paths and configurations for the first-order buckling mode are presented and the effects of the foundation stiffness on the critical buckling temperature and the post-buckling configurations are analyzed.

关 键 词：圆板 弹性基础 热屈曲 临界温度 模态跃迁 

分 类 号：O343[理学—固体力学]