A THREE-DIMENSIONAL ELASTICITY SOLUTION FOR TWO-DIRECTIONAL FGM ANNULAR PLATES WITH NON-UNIFORM ELASTIC FOUNDATIONS SUBJECTED TO NORMAL AND SHEAR TRACTIONS

In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.     

功能梯度材料矩形板的三维静动态响应分析

基于线弹性理论的基本方程,选用3个位移分量和3个应力分量作为状态变量,利用状态空间法建立了功能梯度矩形板的三维状态方程. 考虑四边简支的边界条件,采用打靶法数值求解了材料常数沿板厚按幂率变化的弯曲问题和自由振动问题,为求解功能梯度材料三维弹性响应提供了一种方法. 并且给出了功能梯度材料三维矩形板的静动态响应受组分材料分布以及板厚长比变化的影响规律.      

梯度材料层状结构中的Love波

研究了功能梯度材料层状结构中Love波的传播特性对覆盖层中的剪切弹性模量沿厚度方向为指数函数和幂函数变化的两种函数形式,利用WKB方法分别求得了波传播问题的近似解析解,通过计算分析,得到了Love波在功能梯度材料层中传播的一些规律.     

功能梯度与均匀圆板静动态解之间的相似转换关系

基于经典板理论,研究了功能梯度材料圆板的轴对称弯曲、屈曲和自由振动解与相应的均匀材料圆板解之间的转换关系.通过消去拉-弯耦合项得到了以挠度函数表示的功能梯度圆板的弯曲、屈曲和自由振动控制方程.分析功能梯度圆板与均匀圆板的控制方程之间的相似性,得到了功能梯度材料圆板与均匀圆板的解之间解的相似转换关系,在假定FGM圆板的材料性质沿厚分别以幂函数和指数函数的度变规律后,给出了相应的转换系数的解析表达式.该系数集中反映了功能梯度圆板的材料非均匀性.在已知均匀材料圆板轴对称解的条件下,可将功能梯度材料圆板轴对称问题的求解转化为相似转换系数的计算问题.这一方法可为非均匀板的求解提供了十分便捷有效的途径,而且便于工程应用.     

A NEW HYBRID ELEMENT ANALYSIS FOR EXPONENTIALLY VARYING FGM BASED ON AN ASYMPTOTIC STRESS FIELD

A hybrid finite element for exponentially varying Fhnctionally Graded Material （FGM） is established based on a derived stress field for an intact plate. Elements with both single layer and two layers of gradient are presented. The general stress field is obtained through an asymptotic analysis coupled with Westergaard＇s stress function approach. With the aid of boundary collocation technique, convergence of the derived stress field is verified. Effectiveness and efficiency of the element is investigated through calculation and comparison. Based on that element, stress field of FGM plate under different loading cases is studied briefly.     

功能梯度复合材料板壳结构的弯曲、屈曲和振动

功能梯度材料通常是由两种如金属和陶瓷复合而成的一种新型非均匀复合材料.由于在这种材料中,各组份材料的体积含量在空间位置上是连续变化的,其物理性能没有突变,因而可较好地避免诸如在纤维增强复合材料中经常出现的层间应力问题或降低应力集中现象.功能梯度复合材料目前已被发展用来作高温环境下的结构构件.本文对功能梯度材料板壳结构分析的研究现状进行了评述, 集中讨论线性和非线性弯曲、屈曲和后屈曲、振动和动力响应.涉及各种边界条件下薄板壳和中厚板壳受热/机荷载作用的情况,并提出需要进一步研究的方向.图0参82      

AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions,axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper.The de- flections and stresses of the plates are presented.Numerical results show the well accuracy and convergence of the method.Compared with the finite element method,the semi-analytical nu- merical method is with great advantage in the computational efficiency.Moreover,study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials.Two-directional functionally graded material is a potential alter- native to the one-directional functionally graded material.And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.