叠层双曲率厚壳静、动态问题的分析解

本文抛弃任何有关位移或应力分布的假设,在正交曲线坐标系下,对正交异性双曲率厚壳建立其状态方程。根据层问应力和位移协调条件,对具有正交异性层的周边简支的层合双曲丰厚壳的静力和动力问题,利用Cayley-Hamilton定理一次求解全部未知量。无论层数多少,最后都归结为只需求解三元一次代数方程组。此解满足所有弹性力学基本方程,并计及了全部弹性常数。可得到任意需要的精度。数值结果与文献3]及6]作了对比,结论令人满意。

ANALYTICAL SOLUTIONS OF STATICS AND DYNAMICS FOR THICK DOUBLY CURVED LAMINATED SHELLS

No any simplifying hypothesis about displacement models or stress distribution being introduced, the state equations for the orthotropic thick doubly curved shells are established in an orthogonal curvilinear coordinate system. According to the compatibility conditions of stresses and displacements at the interfaces among the layers, the analytical solutions of the statics and dynamics for the simply supported thick do-ubly curved shells with orthotropic layers are presented.All unknown quantities can be obtained by means of. Cayly-Hamilton theorem. No matter how many layers are considered, the final problem always leads to solving a set of linear algebraic equations of third order. The solutions can satisfy every equation of elasticity, and all the nine elastic constants can be taken into account. The arbitrary pnecision needed by us can be obtained. Numerical results are compared with those of References C3] and 6], The conclutions are satisfactory.