均布载荷作用下圆底扁薄球壳非线性屈曲问题的新解析解  

A New Analytical Solution for the Nonlinear Buckling of Shallow Thin Spherical Shells with Circular Bottom under Uniformly Distributed Loads

作　　者：李佳臻 

机构地区：[1]内蒙古工业大学理学院,内蒙古 呼和浩特

出　　处：《应用数学进展》2021年第8期2766-2774,共9页Advances in Applied Mathematics

摘　　要：本文中考虑了在均布载荷作用下,周边固定的圆底扁薄球壳的非线性屈曲问题。我们利用Adomian分解法得到了该非线性屈曲问题的新解析近似解。基于新解析解讨论了具有各种k值对应的中心挠度与载荷的特征曲线。得到的结果与修正迭代法得到的结果非常吻合,便说明得到的新解析解的有效性和准确性。Nonlinear buckling problem of shallow thin spherical shell with circular bottom and fixed periphery under uniform load is considered in this paper. We use the Adomian decomposition method to obtain a new analytical approximate solution to the nonlinear buckling problem. Based on the new analytical solution, the characteristic curves of center deflection and load corresponding to various k values are discussed. The results obtained in this paper are very consistent with the results obtained by the modified iterative method, which shows the validity and accuracy of the new analytical solution obtained.

关 键 词：圆底扁薄球壳 ADOMIAN分解法 非线性屈曲问题 

分 类 号：G63[文化科学—教育学]