New Solutions of Novozhilov’s Equation of Toroidal Shells

Dong Ming-de

Volume 6 Issue 5

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(5): 401-413

Dong Ming-de. New Solutions of Novozhilov’s Equation of Toroidal Shells[J]. Applied Mathematics and Mechanics, 1985, 6(5): 401-413.

Citation:

Dong Ming-de. New Solutions of Novozhilov’s Equation of Toroidal Shells[J]. Applied Mathematics and Mechanics, 1985, 6(5): 401-413.

Citation:

Dong Ming-de. New Solutions of Novozhilov’s Equation of Toroidal Shells[J]. Applied Mathematics and Mechanics, 1985, 6(5): 401-413.

PDF( 683 KB)

New Solutions of Novozhilov’s Equation of Toroidal Shells

Dong Ming-de

Institute of Theoretical Institute of Physics, Academia Sinica, Beijing

Received Date: 1983-08-04
Publish Date: 1985-05-15

Abstract

Abstract

New solutions are obtained for Novozhilov's equation of toreidal shells having general slenderness ratio 0<a<1(a=a/R). In contrast to the results by continued fractiontechnique, the exponents and expansion coefficients of our series solutions are all closed and explicit. The series satisfies shell equation identically. Convergence proof is also demonstrated.Explicit expressions for boundary effect and monodromy indices are also given. Finally, we discuss the possibility of applying the present method to solve the fundamental system of equations for elastic shells with rotational symmetry.

FullText(HTML)

References(6)

References

[1]	Novozhilov,V,V.,Theory of Thin Shells(1951),(俄文),第四章(及其中引用的文献).
[2]	钱伟长、郑思棵,轴对称圆环壳的一般解,应用数学和力学,(1980),287-300.
[3]	钱伟长、郑思裸,半圆弧波纹管的计算—环壳一般解的应用,应用数学和力学,2,1(1981),97-111.
[4]	董明德,Poincar非正则积分问题(讲义,待出版).
[5]	Dong Ming-de,(a)Non-perturbative solutions of Bloch-Mathieu Hamiltonian system.
[6]	Physics Letters,97A,7,Sep,(1983),275一279.(b)The problem of secular terms:Non-perturbative analysis of the Hill-Bloch system,ibid.,98A,4 Oct,(I983),156-160.

Relative Articles

[1]	Taogetusang. New 2-Soliton Solutions to the Arbitrary Order Nonlinear Camassa-Holm Equation[J]. Applied Mathematics and Mechanics, 2017, 38(5): 553-560. doi: 10.21656/1000-0887.370211
[2]	ZHANG Jian, YE Jian-shu, ZHAO Xin-ming. Dynamic Bayesian Estimation of Displacement Parameters of Continuous Curve Box Based on Novozhilov Theory[J]. Applied Mathematics and Mechanics, 2007, 28(1): 77-84.
[3]	FU Zun-tao, LIU Shi-da, LIU Shi-kuo, ZHAO Qiang. New Exact Solutions to KdV Equations With Variable Coefficients or Forcing[J]. Applied Mathematics and Mechanics, 2004, 25(1): 67-73.
[4]	Zhang Yinyi. Torsional Buckling of Spherical Shells Under Circumferential Shear Loads[J]. Applied Mathematics and Mechanics, 1999, 20(4): 405-410.
[5]	Zhu Weiping, Huang Qian, Guo Ping. Complex Equations of Flexible Circular Ring Shells Overall-Bending in a Meridian Plane and General Solution for the Slender Ring Shells[J]. Applied Mathematics and Mechanics, 1999, 20(9): 889-895.
[6]	Zhang Ruojing. Novel Solutions of Toroidal Shells Under Axisymmetric Loading[J]. Applied Mathematics and Mechanics, 1999, 20(5): 491-498.
[7]	Lü Enling. A New Solution to Structural Fuzzy Finite Element Equilibrium Equations(SFFEEE)[J]. Applied Mathematics and Mechanics, 1997, 18(4): 361-366.
[8]	Xu Rong-liang, Zhou Guo-cai, Sun Zhao. The Existence of Limit Cycles For The System X=Q(X,y),y=p(X)[J]. Applied Mathematics and Mechanics, 1995, 16(1): 53-59.
[9]	Xie Guanmo, Luo Dongping. Analytical Solution of Radiated Sound Pressure of Ring-Stiffened Cylindrical Shells in Fluid Medium[J]. Applied Mathematics and Mechanics, 1995, 16(12): 1061-1066.
[10]	Zhao Xing-hua. Stress-Anlysis of Thick Ring Shell Sumitted to the Action of Internal Pressure[J]. Applied Mathematics and Mechanics, 1994, 15(12): 1047-1055.
[11]	Zhao Xing-hua. The Asymptotic Solving Equations of Thick Ring Shell and it’s Solution under Moment M₀[J]. Applied Mathematics and Mechanics, 1994, 15(11): 951-962.
[12]	Ding Zhong-man, Wang Zhi-qing. The New Solution for the Axially Symmetrical Laminar Boundary Layer Equations between Two Parallelf Spherical Surfaces[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1075-1080.
[13]	Huang An-ji, Cao Deng-qing. On the Existence of Limit Cycles of Liénard Equation[J]. Applied Mathematics and Mechanics, 1990, 11(2): 119-130.
[14]	He Fu-bao, Yu Zhi-meng. The Initial Post-Buckling Behavior of Ring Stiffened Shells under Hydrostatic Pressure[J]. Applied Mathematics and Mechanics, 1988, 9(11): 951-962.
[15]	Ye Kai-yuan, Ji Zhen-yi. Free Vibration of Nonlinear Deformation Ring-and Stringer Stiffened Nonuniform Cylindrical Shell[J]. Applied Mathematics and Mechanics, 1988, 9(11): 963-974.
[16]	Wang Zhi-qing, Shang Er-bing. The New Solutions for Two Kinds of Axially Symmetrical Laminar Boundary Layer Equations[J]. Applied Mathematics and Mechanics, 1988, 9(1): 57-62.
[17]	Li Long-yuan. A Perturbation Solution of Free Vibration of Cylindrical Shells with Ring-Stiffeners[J]. Applied Mathematics and Mechanics, 1987, 8(3): 277-286.
[18]	Chien Wei-zhang, Fan Da-jun, Hwang Qien. Comparison of the Calculations of Three-Convolution Circular Arc Corrugated Diaphragms by Toroidal Shell Theory and by Orthogonal Anisotropy Plate Theory[J]. Applied Mathematics and Mechanics, 1984, 5(1): 41-48.
[19]	Dong Ming-de. New Method of Solving Lame-Helmholtz Equation and Ellipsoidal Wave Functions[J]. Applied Mathematics and Mechanics, 1984, 5(2): 167-178.
[20]	Chien Wei-zang, Zheng Si-liang. Calculations for Semi-Circular Arc Type Corrugated Tube——Applications of General Solutions of Ring Shell Eguation[J]. Applied Mathematics and Mechanics, 1981, 2(1): 97-111.