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
DOI: 10.12677/AAM.2021.108288, PDF,  被引量    科研立项经费支持
作者: 李佳臻：内蒙古工业大学理学院，内蒙古 呼和浩特
关键词: 圆底扁薄球壳；Adomian分解法；非线性屈曲问题；Shallow Spherical Shell with Round Bottom； Adomian Decomposition Method； Nonlinear Stability Problem
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。
Abstract: 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.
文章引用：李佳臻. 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[J]. 应用数学进展, 2021, 10(8): 2766-2774. https://doi.org/10.12677/AAM.2021.108288

参考文献

[1] Way, S. (1934) Bending of Circular Plate with Large Deflection. A.S.M.E. Transactions, Applied Mechanics, 56, 627-636.
[2] Simons, R.M. (1956) A Power Series Solution of the Nonlinear Equations for Axisymmetrical Bending of Shallow Spherical Shells. Journal of Mathematical Physics, 35, 164-176. [Google Scholar] [CrossRef] 
[3] 赵伟东, 高士武, 马宏伟. 扁球壳在热-机械荷载作用下的稳定性分析[J]. 应用数学和力学, 2017, 38(10): 1146-1154.
[4] Xu, J.-C., Li, Y., Wang, F. and Liu, R.-H. (2010) Nonlinear Stability of Double-Deck Reticulated Circular Shallow Spherical Shell. Applied Mathematics and Mechanics, 31, 261-272. [Google Scholar] [CrossRef] 
[5] 顾淑贤. 扁球壳轴对称屈曲问题的样条函数解法[J]. 力学学报, 1987, 19(2): 179-185.
[6] 侯朝胜, 周伟毅. 夹层圆板和夹层扁球壳非线性弯曲的进一步研究[J]. 天津大学学报, 2009, 42(12): 1072-1077.
[7] 叶开沅, 顾淑贤. 在均布压力作用下圆底扁球壳的非线性稳定性[C]//1980年全国力学会议文集. 北京: 北京大学出版社, 1981: 280-287.
[8] Duan, J., An, J. and Xu, M.Y. (2007) Solution of System of Fractional Differential Equations by Adomian Decomposition Method. Applied Mathematics—A Journal of Chinese Universities, 22, 7-12. [Google Scholar] [CrossRef] 
[9] Duan, J.S. and Rach, R. (2011) A New Modification of the Adomian Decomposition Method for Solving Boundary Value Problems for Higher Order Nonlinear Differential Equations. Applied Mathematics and Computation, 218, 4090-4118. [Google Scholar] [CrossRef] 
[10] Wazwaz, A.-M. (2000) The Decomposition Method for Solving Higher Dimensional Initial Boundary Value Problems of Variable Coefficients. International Journal of Computer Mathematics, 76, 159-172. [Google Scholar] [CrossRef] 
[11] Wazwaz, A.M., Rach, R. and Duan, J.S. (2013) Adomian Decomposition Method for Solving the Volterra Integral Form of the Lane-Emden Equations with Initial Values and Boundary Conditions. Applied Mathematics and Computation, 219, 5004-5019. [Google Scholar] [CrossRef] 
[12] 温颖, 银山. 地下水流区域上的异质含水层模型的分段Adomian近似解[J]. 应用数学进展, 2017, 6(4): 435-441.
[13] Yun, Y., Temuer, C. and Duan, J. (2014) A Segmented and Weighted Adomian Decomposition Algorithm for Boundary Value Problem of Nonlinear Groundwater Equation. Mathematical Methods in the Applied Sciences, 37, 2406-2418. [Google Scholar] [CrossRef] 
[14] 李丹丹, 银山. 偏微分方程的满足部分边界条件的解的多样性[J]. 应用数学进展, 2018, 7(5): 617-621.
[15] Yun, Y.-S. and Liu, H. (2021) New Approximate Analytical Solution of the Large Deflection Problem of an Uniformly Loaded Thin Circular Plate with Edge Simply Hinged. Alexandria Engineering Journal, 60, 5765-5770. [Google Scholar] [CrossRef] 

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