2D analysis of laminated composite and sandwich plates using a new fifth-order plate theory

Abstract In the present paper, a new fifth-order shear and normal deformation theory (FOSNDT) is developed for the bi-directional bending analysis of laminated composite and sandwich plates subjected to transverse loads. This theory considered the effects of both transverse shear and normal deformations. In-plane displacements use a polynomial shape function expanded up to fifth-order in terms of the thickness coordinate to properly account the effect of transverse shear deformation. Transverse displacement is the function of x, y and z- coordinates to account the effect of transverse normal deformations i.e. thickness stretching. Hence, the present theory involves nine unknowns in the displacement field. The present theory does not require a problem dependent shear correction factor as it satisfies traction free boundary conditions at top and bottom surfaces of the plate. The governing differential equations and associated boundary conditions are obtained using the principle of virtual work. The plate is analysed for simply supported boundary conditions using Navier’s solution technique. To prove the efficiency of the present theory, the non-dimensional displacements and stresses obtained for laminated composite and sandwich plates are compared with existing exact elasticity solutions and other theories. It is observed from the comparision that the displacements and stresses obtained by the present theory are in excellent agreement with the results obtained by exact elasticity solutions compared to other higher-order plate theories available in the literature.

摘要 本文提出一种新的五阶剪切与正变形理论（Fifth-order Shear and Normal Deformation Theory, FOSNDT），用于承受横向载荷的层合复合材料板与夹层板的双向弯曲分析。该理论同时考虑横向剪切变形与横向正变形的双重效应。面内位移采用以厚度坐标为变量展开至五阶的多项式形函数，以精准表征横向剪切变形的影响；横向位移为x、y、z坐标的多元函数，用于考虑横向正变形即厚度拉伸效应。因此，本理论的位移场包含九个未知量。本理论无需采用与具体问题相关的剪切修正因子，因其天然满足板上下表面的无牵引边界条件。通过虚功原理推导得到控制微分方程及对应的边界条件。采用纳维解法对简支边界条件下的板结构进行分析。为验证本理论的有效性，将层合复合材料板与夹层板的无量纲位移和应力结果，与现有精确弹性解及其他经典理论的结果开展对比。对比结果表明，相较于文献中已有的其他高阶板理论，本理论所得位移与应力结果与精确弹性解的吻合度极佳。