DQ法求解FGM Levinson梁的静态弯曲问题

Static Bending Solutions of Functionally Graded Material Levinson Beams Based on Differential Quadrature Method

基于高阶剪切变形理论,采用微分求积法(DQM)研究了功能梯度材料Levinson梁的静态弯曲解,并与Timoshenko梁的弯曲解进行了比较。考虑功能梯度梁的材料性质沿厚度方向按照幂函数连续变化,建立了梁的无量纲控制方程,给出了均布载荷作用下,长细比为10时,相同尺寸的梁在3种常见的边界条件下功能梯度Levinson梁的无量纲挠度随梯度指数p的变化规律以及不同边界条件下功能梯度材料Levinson梁的无量纲挠度随长细比的变化规律。

Based on the higher-order shear deformation theory, this paper gets static bending solutions of FGM Levinson beams by differential quadrature method and then compares those with the Timoshenko beams bending so-lutions. The non-dimensional governing equations of FGM beams are derived by considering the material properties which vary continuously in the thickness direction based on power law exponent, and the non-dimensional deflection of three common boundary conditions are derived by considering the material properties varying with the power law exponent in the thickness direction while the slenderness ratio is ten. The non-dimensional deflections of FGM Levinson beams for the different boundary conditions are also illustrated at varied slenderness ratio.