简支圆板的非轴对称热弯曲  

Non-axisymmetrical Thermal Bending of Simply Supported Circular Plate

作　　者：董正筑[1] 彭维红[1] 李法善[1] 刘俊[1] 

机构地区：[1]中国矿业大学理学院,徐州221008

出　　处：《力学季刊》2008年第2期314-318,共5页Chinese Quarterly of Mechanics

基　　金：国家重点基础研究发展计划(2007CB209400);国家自然科学基金(50774077)

摘　　要：由于热弹性耦合问题的复杂性,能得到解析解的主要是轴对称问题和比较简单的问题。利用Green函数,根据双调和方程边值问题的边界积分公式和自然边界积分方程。在简支板的非轴对称问题的基础上,利用傅立叶级数及卷积的几个公式,求得了非轴对称变温边界条件下圆板的弯曲解,有较好的收敛速度和计算精度,计算过程相对简单。算例表明了方法的有效性。Due to the complexity of thermal elasitic problems, the analytic solutions have been obtained only for some axisymmetrical problems and simple problems. By using Green function, the boundary integral formula and natural boundary integral equation for the boundary value problems of biharmonic equation were obtained. Based on the bending solutions of simply supported circular plate under non-axisymmetrical load, by Fourier series and convolution formulae, the bending solutions under non-axisymmetrical thermal conditions were obtained. The formulas for computational accuracy, and the calculating process is the solutions have good convergence velocity and simple. The examples show the method is effective.

关 键 词：热弯曲 圆板 边界积分公式 自然边界积分方程 

分 类 号：O343[理学—固体力学] O242[理学—力学]