一阶剪切理论下功能梯度梁与均匀梁静态解之间的相似关系  

ANALOGOUS RELATIONSHIP BETWEEN THE STATIC SOLUTIONS OF FUNCTIONALLY GRADED BEAMS AND HOMOGENOUS BEAMS BASED ON THE FIRST-ORDER SHEAR DEFORMATION THEORY

作　　者：徐华[1] 李世荣[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》2012年第4期161-167,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10872083);教育部博士点基金项目(200807310002)

摘　　要：基于一阶剪切理论,研究了功能梯度材料Timoshenko梁的静态弯曲解与对应的均匀材料梁的解的线性转换关系。通过比较功能梯度材料梁和均匀材料梁的无量纲控制方程,发现了它们弯曲解的线性相关性。在给定材料弹性模量沿横向非均匀变化规律后,可将功能梯度材料Timoshenko梁在静载荷作用下的弯曲变形解用相同尺寸、相同载荷以及相同边界条件下的均匀材料Timoshenko梁的弯曲变形解线性表示。这样,可将非均匀Timoshenko梁弯曲问题的求解转化为对应的均匀材料Timoshenko梁弯曲问题的求解和转换系数的计算,从而使得求解过程得以简化。Based on the first order shear deformation theory,linear transformative relation between the static bending solution of the functionally graded Timoshenko beams and the corresponding homogenous material beams were analyzed.Through comparing non-dimensional governing equations of functionally graded material beams and the corresponding homogenous beams,linearly dependant relation between their bending solutions was found.When the law of variation of the elastic modulus in the lateral direction is specified,the bending solution of the FGM Timoshenko beams can be linearly expressed by that of homogenous beams with the same geometry,the same loadings and the same constraints.Consequently,solutions of the bending problem of a non-homogenous Timoshenko beam can be reduced to that of a homogenous one and the calculation of the transition parameters,which simplifies the solution procedure.

关 键 词：功能梯度材料 TIMOSHENKO梁 弯曲 相似转换 解析解 

分 类 号：TU318[建筑科学—结构工程] TU323.3