对称层合圆柱正交异性中心开孔扁球壳的非线性屈曲

Nonlinear Buckling of Cylinder-Orthotropic Layered and Shallow Shell with a Hole at Center

在非线性线屈曲理论基础上，考虑对称线布载荷作用形式，导得相应控制方程，以分析中心开孔，即外边缘固定，以及内边缘悬空的复合材料扁球壳非线性屈曲稳定性问题。为了求解本文的非线性屈曲问题，获得临界载荷计算公式，本文采用修正迭代法，即第一次迭代将非线性项略去，第二次迭代将第一次迭代结果作为已知量代入非线性项来获得临界载荷的解析计算公式。最后，本文以实例分析讨论了横向剪切变形、开孔大小、线布载荷位置和几何参数对临界载荷的影响。

Based on the theory of nonlinear buckling, governing equations are developed by considering the symmetrical linear load. A composite shallow shell with a center hole, whose interior boundary is free, and exterior boundary is fixed, is considered to study its nonlinear buckling problem. In order to solve the nonlinear buckling problem and obtain the formula of a critical load, an iterative-modified method, with the nonlinear item neglected in the first iteration, and the nonlinear item of ,the second iteration replaced by the result of the first iteration is applied to obtaining the analytical formula of the critical load. Meanwhile, the iterative process is too complicated, so that all the polynomial items expressing ψ ,S,P,Φ di etc are neglected. Finally, some examples are given to show the effect of shearing deformation, the hole size, the position of linear load and the geometrical parameter on the critical load.