具有自由边的层合开口柱壳弯曲问题的解析解

从三维弹性力学基本方程出发，通过假设自由边的边界位移函数并选择适当的级数形式解函数，建立了正交异性层合开口柱壳的状态方程，给出了具有自由的层合开口柱壳的解析解．此解计及了正交异性材料的所有弹性常数，且满足层合壳的基本方程和层间连续条件．为证实本文方法的有效性，给出了数值算例，并与解析解和半解析解模型的结果作了对比，结果令人满意．

Analytical Solution to the Bending Problem of Laminated Open Cylindrical Shells With Free Edges

Based on 3D fundamental equations of elasticity and by assuming boundary displacement functions associated with free edges and selecting appropriate series form solutions, state equation for orthotropic laminated open cylindrical shells is established and an analytical solution for the laminated shells with free edges is presented. The solution given takes into account all elastic constants for orthotropic materials. Furthermore, all fundamental equations of elasticity and continuity conditions between plies of the laminates are satisfied. To illustrate the effectiveness of the present method, numerical examples are calculated and compared with analytical and semi-analytical models. Satisfactory results are obtained.