功能梯度Timoshenko梁的静力弯曲分析

Static bending analysis of functionally graded Timoshenko beam

基于Timoshenko梁变形理论,建立功能梯度材料梁在均布载荷作用下的弯曲控制方程,寻找均匀梁和非均匀梁的控制方程的相似性,将功能梯度材料梁的弯曲求解转化为均匀梁的弯曲求解与相似转换系数的计算。通过理论推导和相似性分析证明,功能梯度Timoshenko梁的弯曲解与同样尺寸、边界条件和载荷条件下的均匀材料Timoshenko梁的弯曲解成正比,这个比例常数完全由材料的非均性质参数确定。

Based on Timoshenko beam deformation theory,the governing equations for the problem were built up.The authors studied the similarities of governing equations between the homogeneous beam and the non-uniform beam,and then the problem of functional gradient materials beam bending was to solve bending of uniform beam and to calculate similarity coefficient of product.Through theoretical derivation and analysis of the similarity,we found that the bending solutions of functional gradient Timoshenko beam is proportional to uniform materials Timoshenko beam with the same size,boundary conditions and load conditions,This proportional factor was determined entirely by nature inhomogeneous parameter of material constants.