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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。
Based on the basic equations of three - dimensional elastic mechanics, the static state problem of single rectangular and laminated thick plates with clamped orthotropic anisotropy is solved by the state space method. The boundary displacement function on the solid support side is introduced into the state equation as a state variable, and the state equation is changed from inhomogeneous to homogeneous. The exact three-dimensional solution of the problem is obtained. The obtained solution not only satisfies the basic equations of three-dimensional elastic mechanics strictly, but also satisfies all the boundary conditions strictly. In addition, a new calculation method is proposed for the stress of the clamped edge to get more accurate boundary stress. The example shows that the solution agrees very well with the finite element solution and still has a high precision at the support and support points. And as the aspect ratio increases, the precision does not decrease.