三边简支一边固支正交异性矩形叠层厚板的精确解

基于三维弹性力学基本方程，应用状态空间法求解三边简支一边固支正交异性矩形单层和叠层厚板静力问题。把固支边上的边界位移函数作为状态变量引入状态方程，使状态方程从非齐次的变为齐次的，得到了该问题的三维精确解。所得到的解不仅严格满足三维弹性力学基本方程，而且严格满足全部边界条件。此外，对固支边的应力提出了新的计算方法，能够得到更精确的边界应力。算例表明：该文解与有限元解吻合很好，在固支边处依然具有很高的精度；而且随着厚宽比的增大，精度并不降低。

EXACT SOLUTIONS OF ORTHOTROPIC RECTANGULAR THICK LAMINATES WITH THREE EDGES SIMPLY SUPPORTED AND THE OTHER ONE CLAMPED

Based on the three-dimensional basic equations of elasticity, the state space method is used to solve the Orthotropic rectangular thick single and laminated plates with three edges simply supported and the other one clamped under static loads. Boundary displacement functions are treated as state variables and introduced into state equations, thus the state equations become homogeneous. The three-dimensional exact solutions are presented. Not only the three-dimensional basic equations of elasticity but also all boundary conditions are satisfied strictly. Additionally, a new calculating method of the stresses on the clamped edge is proposed and more exact boundary stresses can be obtained. The results of two examples show that the solutions obtained in this paper are consistent with FEM ones and the stresses on the clamped edge also have high precision. Furthermore, the precision of the solutions does not decrease when the ratio of the thickness to the width increases.