计入横向剪切变形时层合板位移差分解法

在考虑横向剪切变形对层合板弹性解的影响时，本文提出一种数值计算方法。由边界条件给出边界结点位移的表达式，根据薄板的经典理论和一阶横向剪切变形理论导出位移增量所满足的平衡微分方程，引用经典理论计算的横向剪力修正了荷载列阵。致使在较粗的网格划分时、宽广的层合板长厚比范围内，仍能得到与解析解颇为一致的数值解。

A Finite Difference Solution of The Displacement of Laminate on Taking Account of Transverse Shear

In consideration of the influence of transverse shear on elastic solutions of laminate, this paperputs forward a numerical method. The expressions of displacement of node on boundary were determined by boundary condition. On the basis of classical theory of sheet and first order transverse sheartheory, equlibrium differential equations for displacement increments were developed. The array ofload was modified by shear force from classical theory. Although mesh being cruder and over a widerange of length/thick ratio of laminate, numerical solutions are in good coincidence with analytical results.