矩形夹层板稳定性分析

Stability Analysis of Rectangular Sandwich Plate

本文在Reissner理论基础上,应用功的互等定理推导了夹层矩形板稳定问题的基本解,在已推导出的夹层板基本解的基础上,利用功的互等法求解了两对边固定一边简支一边自由、两邻边简支另两邻边自由且角点支承、两邻边简支另两邻边自由且角点悬空三种不同边界条件下夹层板的稳定问题,给出了挠曲面方程及其对应的执行方程;进行了数值计算,并与有限元结果进行对照分析.结果表明:本文方法求解过程更简单,提供了一种求解夹层板稳定问题的新方法,计算结果对解决工程实际问题具有一定的参考价值.

Based on the Reissner theory and using the reciprocal principle, the fundamental solution to the stability problem of rectangular sandwich plates is derived. Based on the fundamental solution of sandwich plate that has been derived and using the reciprocal method, the stability problem of sandwich plate is solved for three different boundary conditions, i.e.,(i) two opposite edges clamped, one edge simply supported and the other edge free,(ii) two adjacent edges simply supported, the other two edges free with the corner points supported, and(iii) two adjacent edges simply supported, the other two edges free with the corner points suspended. The surface deflection equation and the execution equations are given. The results from numerical calculations are compared with that from the finite element simulations. The results show that the procedure of the proposed method is simpler and provides a new method for solving the stability problem of sandwich plates. The calculation results have certain reference value for engineering problems.