复合材料多层厚板的精化高阶理论及其有限元法

A REFINED HIGHER-ORDER THEORY AND ITS FINITE ELEMNT METHOD FOR THICK LAMINATED PLATES

  • 摘要: 本文提出了一种经过改进的复合材料多层厚板的精化高阶剪切变形理论,采用Legendre多项式来逼近位移场沿厚度方向的分布,较好地模拟了横向剪切变形和层间拉、压变形,利用层板上,下自由表面横向剪应力为零的边界条件,对所假定的位移场作了化简,在此基础上构造了相应的有限元.文中通过一些典型算例,与Pagano的弹性力学精确解9以及其他高阶理论的解作了比较,说明本文的精化高阶剪切变形理论及其相应的有限元具有精度高和收敛快的优点.

     

    Abstract: In order to improva the accuracy of the shear deformation theory of thick laminated plates,an improved higher order theory is developed.The Legendre polynomials are introduced into the approximate displace ment distributions across the plate thickness,and a finite element model is suggested from the original equations.This theory has the same independent arguments as that in the second order shear deformation Yheory proposed by Whitney,Sun,and Engblom,etal.,but proposes the parabolic distribution of the transverse shear strains-through the thickness of the plate.The accuracy of the present theory is examined by applying it to bending problems of laminated plates which was solved exactly by Pagano.The results are compared with three-dimensional elasticity solutions,the second order shear deformation theory and some other higher order shear deformation theory solutions.The present theory shows the deflections and stress more accurately than that obtained from the previous works in the structural analysis of laminated plate with small apan with respect to thickness.

     

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