功能梯度Levinson圆板弯曲解的均匀化和经典化表示  

HOMOGENIZED AND CLASSICAL EXPRESSIONS FOR BENDING SOLUTIONS OFFUNCTIONALLY GRADED LEVINSON CIRCULAR PLATES

作　　者：万泽青[1] 李世荣[1] 李秋全[1] 

机构地区：[1]扬州大学建筑科学与工程学院,江苏扬州225127

出　　处：《工程力学》2015年第1期10-16,35,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(11272278);江苏省研究生科研创新计划项目(CXZZ13_0898)

摘　　要：基于Levinson三阶剪切变形理论,研究了材料性质沿厚度任意连续变化的功能梯度材料圆板的轴对称弯曲问题。首先,建立了功能梯度材料圆板在Levinson板理论下轴对称弯曲问题位移形式的控制微分方程,其中考虑了拉-弯耦合和三阶剪切变形效应。然后,利用载荷等效关系以及均匀板的经典理论控制微分方程,导出功能梯度圆板在Levinson剪切变形理论下弯曲解与经典理论下均匀圆板的挠度之间的解析转换关系,给出了转换系数的计算公式。由此,可将功能梯度材料圆板在Levinson三阶剪切理论下的弯曲问题转化为相应均匀薄圆板在经典理论下的弯曲问题求解,以及转换系数的计算问题。Based on Levinson's third-order shear deformation plate theory, axisymmetrical bending of functionally graded material(FGM) circular plates with arbitrary material property variation through the thickness was investigated. First,differential equations were formulated in terms of the displacements governing the axisymmetric bending of the FGM plate under Levinson plate theory. The effects of tension-bending coupling and third-order shear deformation were included in these equations. Then, by using load equivalence relations and the governing differential equation of a homogenous classical plate, the analytical transitional relationship between solutions of FGM circular plates based on the Levinson plate theory and those of the corresponding homogenous ones based on classical plate theory were derived. The analytical formulations of the transition coefficients were given in the expressions. As a result, solutions to static bending of FGM Levinson circular plates can be transformed into those of the corresponding homogenous plates based on classical plate theory and the calculation of the transformation coefficients.

关 键 词：功能梯度圆板 Levinson板理论 轴对称 弯曲解 转换系数 

分 类 号：O343[理学—固体力学]