面内功能梯度矩形板的近似理论与解答

提出了面内功能梯度矩形板在竖向载荷作用下的近似 理论与解析解. 假设材料常数在面内x轴方向按指数规 律变化.引入了板理论的Reissner-Mindlin假设, 并考虑了板中面上的剪切变形的影响.推导了板在平行于y轴的两边简支, 平行于x轴方向的两边简支或固支情况下中性层法线转角和挠度用Fourier级数表示的解.讨论了退化为Kirchhoff假设下经典薄板理论的解的情况.提供了经典薄板理论在和Reissner-Mindlin假设下的算例并与三维有限元的计算结果进行了比较, 说明了该方法在厚板情况下也是相当精确的.

APPROXIMATE THEORY AND ANALYTICAL SOLUTION FOR RECTANGULAR PLATES WITH IN-PLANE STIFFNESS GRADIENT

Approximate theory for rectangular plates with in-plane stiffness gradient subjected to transverse loading is established. In this theory, Reissner-Mindlin assumption is introduced, and the shear deformation in the mid-surface of the plate is considered. Material properties of the plates vary exponentially in the direction parallel to one pair of edges. Analytical solution in the cases that one pair of edges of the plate is simply supported and the other pair is fixed or simply supported is obtained. It is indicated that this solution can degenerate into the classical solution of thin plates based on the well-known Kirchhoff assumption if the shear deformation in the mid-surface is ignored. The numerical results of this solution are given and compared with those from 3D finite element solution by means of PATRAN code. It shows that the precision of this solution is still high even for thick plates.