各种边界条件下对称层合板的弯曲问题

由一般对称层合板弯曲控制方程，导出了一个简单而完备的级数序列的通解，通过边界配点最小二乘法求得问题的解。文中给出了位移和内力的矩阵显表达式，论述了形成线性方程组的具体方法，用本文方法计算了几个算例，其中包括圆形、矩形和角形等层合板。结果表明：本文方法既简单、通用、又精确。

A BENDING ANALYSIS OF SYMMETRIC LAMINATED PLATES UNDER VARIOUS BOUNDARY CONDITIONS

The bending governing equation of symmetric liaminate plates is analyzed and a simple yet perfect sequence corresponding to the general solution is derived,by applying the discrete least squares to the boundary conditions. The sequence can approximate the exact solution of the plates with various support conditions and shapes of boundary. The explicit expressions of displacements and internal forces are given in the form of matrix and the process to form the linear algebraic equations is described. Several groups of representative examples are calculated. The examples include circular, square and triangular plates. Numerical results demonstrate that the method is not only simply and generally applicable but also accurate.