基于状态方程矩形层合板多种边界条件下的解析解

以边界位移函数方法为基础，推导了矩形层合板多种边界条件下的非齐次状态方程和定解条件.将非齐次状态方程增维齐次化，可避免积分时可能出现的数值病态问题，并简化了计算过程.边界位移沿厚度方向非线性分布假设可以适当减少数值结果收敛要求的薄层数.数值结果可作为其它数值法或半解析法的标准解.该文的方法可为分析更加复杂的边界条件问题提供参考.

Analytical Solutions of Rectangular Laminated Plates Under Various Boundary Conditions in the State Space

Based upon the method of boundary displacement functions, the non-homogeneous state equations and the control equations for the solutions of rectangular laminated plates under various boundary conditions were derived. Through dimension expansion, the non-homogeneous equations were converted to homogeneous equations, thus the possible problems of numerical ill-conditions were avoided, and the calculation process was simplified for the homogeneous equations. An introduction of the hypothesis of nonlinear boundary displacement distribution along the thickness direction reasonably decreased the number of sub-layers for the convergence of numerical results. The numerical results in the examples provide standard referential solutions for other numerical or semi-analytical methods. The present method is suitable for the problems under more complex boundary conditions.