计及不同剪切变形的功能梯度材料梁的弯曲分析

Bending Analysis of Functionally Graded Materials Beam Considering Different Shear Deformation Theory

研究矩形截面功能梯度材料(Functionally graded materials,FGM)梁在不同剪切变形理论下的静力弯曲问题。假设FGM梁由金属和陶瓷两种材料构成,其等效物性参数沿厚度方向连续变化,且遵从简单幂率变化规律。基于最小势能原理,建立以轴向位移、横向位移及转角为未知函数的FGM梁的运动微分方程组。对简支FGM梁,采用Fourier级数法获得5种剪切变形理论下FGM梁的挠度、轴向位移及转角曲线,分析梁的长高比、梯度指标对弯曲变形的影响,分析不同剪切变形理论下FGM梁的切应力和正应力的分布特性,并与均质材料梁的静力弯曲特性进行比较。给出FGM梁的中性轴位置随梯度指标的变化曲线并进行分析。

Static bending analysis of functionally graded materials （FGM） beam of rectangular cross section considering different shear deformation theory are presented. The FGM beams are assumed to be made of ceramics and metal, and the equivalent parameters of FGM are continuously variation across the beam thickness with a simple power law. Based on the principle of minimum potential energy, the differential equations for the FGM beam are obtained, in which the unknown functions are deflection, axial displacement and rotation angle. For simply supported FGM beam, considering 5 kinds of shear deformation theory, the curves of deflection, axial displacement and rotation angle of FGM beam are obtained respectively by the Fourier series method. The effect of length-to-height ratios and gradient index of the FGM beam on the bending deformation are discussed. The distribution characteristics of the shear stress and normal stress of FGM beams under different shear deformation theory are investigated. Then the static bending behaviors of beam with FGM and homogeneous material are compared. The curves between the neutral axis location and gradient index of FGM beam are given. The properties of the curves are analyzed.