NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS

Applied Mathematics and Mechanics (English Edition) ›› 1993, Vol. 14 ›› Issue (11): 1023-1031.

NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS

牛忠荣

Institute of Applied Mechanics, Hcfei University of Technology, Hefei

收稿日期:1992-10-05 出版日期:1993-11-18 发布日期:1993-11-18
通讯作者: He Fu-bao

NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS

Niu Zhong-rong

Institute of Applied Mechanics, Hcfei University of Technology, Hefei

Received:1992-10-05 Online:1993-11-18 Published:1993-11-18

摘要/Abstract

摘要： Based on the differential equation of the nonlinear bending of shallow spherical shells with variable thickness under axisymmetrical loads, this paper studies the numerical solution of the nonlinear differential equation by means of interpolating matrix method. The analysis of the results indicates that the suggested method is easy to implement and obtains the same high accuracy for both the displacements and the internal forces.

关键词: shallow spherical shell, variable thickness, nonlinear analysis, interpolating matrix method

Abstract: Based on the differential equation of the nonlinear bending of shallow spherical shells with variable thickness under axisymmetrical loads, this paper studies the numerical solution of the nonlinear differential equation by means of interpolating matrix method. The analysis of the results indicates that the suggested method is easy to implement and obtains the same high accuracy for both the displacements and the internal forces.

Key words: shallow spherical shell, variable thickness, nonlinear analysis, interpolating matrix method

牛忠荣. NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS[J]. Applied Mathematics and Mechanics (English Edition), 1993, 14(11): 1023-1031.

Niu Zhong-rong . NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS[J]. Applied Mathematics and Mechanics (English Edition), 1993, 14(11): 1023-1031.

[1]	Minghao ZHAO, Zelong MA, Chunsheng LU, Qiaoyun ZHANG. Application of the homotopy analysis method to nonlinear characteristics of a piezoelectric semiconductor fiber[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 665-676.
[2]	Rong WANG, Guohua NIE. Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1825-1836.
[3]	Yongan ZHU, Fan WANG, Renhuai LIU. Nonlinear stability of sensor elastic element—corrugated shallow spherical shell in coupled multi-field[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 877-888.
[4]	M. M. KHADER;A. M. MEGAHED. Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity, and thermal radiation[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1387-1400.
[5]	李善倾袁鸿. Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(5): 635-642.
[6]	徐加初李勇王璠刘人怀. Nonlinear stability of double-deck reticulated circular shallow spherical shell[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(3): 279-290.
[7]	黄家寅. UNIFORMLY VALID ASYMPTOTIC SOLUTIONS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE OF FOUR CLAMPED EDGES WITH VARIABLE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 817-826.
[8]	黄家寅. BASIC EQUATIONS OF THE PROBLEM OF THE NONLINEAR UNSYMMETRICAL BENDING FOR ORTHOTROPIC RECTANGULAR THIN PLATE WITH VARIABLE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(7): 812-816.
[9]	王永岗;戴诗亮. THERMOELASTICALLY COUPLED AXISYMMETRIC NONLINEAR VIBRATION OF SHALLOW SPHERICAL AND CONICAL SHELLS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(4): 430-439.
[10]	刘颖范;陈晓红. SOME RESULTS ON CONTINUOUS TYPE CONDITIONAL INPUT-OUTPUT EQUATION-FIXED POINT AND SURJECTIVITY METHODS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(3): 358-366.
[11]	康盛亮. THE METHOD OF MULTIPLE SCALES APPLIED TO THE NONLINEAR STABILITY PROBLEM OF A TRUNCATED SHALLOW SPHERICAL SHELL OF VARIABLE THICKNESS WITH THE LARGE GEOMETRICAL PARAMETER[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(10): 1198-1209.
[12]	徐加初;王乘;刘人怀. NONLINEAR STABILITY OF TRUNCATED SHALLOW CONICAL SANDWICH SHELL WITH VARIABLE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(9): 977-986.
[13]	骆少明;张湘伟;蔡永昌. THE VARIATIONAL PRINCIPLES AND APPLICATION OF NONLINEAR NUMERICAL MANIFOLD METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(12): 1401-1406.
[14]	王永岗;王新志;宋慧芳. NONLINEAR FREE VIBRATION OF ORTHOTROPIC SHALLOW SHELLS OF REVOLUTION UNDER THE STATIC LOADS[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(6): 585-591.
[15]	黄家寅;秦圣立;许小平. THE PROBLEM OF THE NON-LINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR THIN PLATE WITH VARIABLE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(3): 279-295.

NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS

NONLINEAR BENDING OF THE SHALLOW SPHERICAL SHELLS WITH VARIABLE THICKNESS UNDER AXISYMMETRICAL LOADS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价