FGM梁临界屈曲载荷的改进型GDQ法分析

Critical Buckling Loads analysis of FGM Beams by A Modified Generalized Differential Quadrature Method

研究了功能梯度材料(FGM)梁在轴向静载荷作用下的屈曲问题.首先,基于一阶剪切变形梁理论(FSBT),应用最小势能原理,建立了以轴向位移、挠度及转角为基本未知函数功能梯度Timoshenko梁屈曲的控制微分方程.其次,通过引入边界条件控制参数,采用一种改进型广义微分求积法(MGDQ)数值研究了4种典型边界功能梯度Timoshenko与Euler梁的屈曲特性.算例结果表明:本文的分析方法切实可行、行之有效.最后,着重分析了梁理论、边界条件、梯度变化指数、跨厚比对FGM梁临界屈曲载荷的影响.

The buckling of functionally graded material(FGM)beams subjected to static axial force was investigated.Firstly,based on the first-order shear deformation beam theory(FSBT),the buckling governing differential equations for FGM Timoshenko beams were derived by the principle of minimun potential energy,in which the basic unknown functions were axial displacement,deflection and rotation angle.Then,introducing boundary condition coefficients defined and applying a modified generalized differential quadrature(MGDQ)method,the buckling behaviors of FGM Timoshenko beams and also Euler ones under four different classical boundary conditions were analyzed.The availability and accuracy of the presented method were verified throughout several numerical examples.Finally,the effects of two types of beam theories,boundary conditions,material gradient indexes,and length-to-thickness ratio on the critical buckling loads were mainly discussed.