On Second Order Asymptotic Solutions of Axial Symmetrical Problems of r>0 Thin Uniform Circular Toroidal Shells with a Large Parameter a<sup>2</sup>/R<sub>0</sub>h

Chen Guo-dong

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Chen Guo-dong. On Second Order Asymptotic Solutions of Axial Symmetrical Problems of r>0 Thin Uniform Circular Toroidal Shells with a Large Parameter a2/R0h[J]. Applied Mathematics and Mechanics, 1988, 9(4): 365-378.

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Chen Guo-dong. On Second Order Asymptotic Solutions of Axial Symmetrical Problems of r>0 Thin Uniform Circular Toroidal Shells with a Large Parameter a²/R₀h[J]. Applied Mathematics and Mechanics, 1988, 9(4): 365-378.

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On Second Order Asymptotic Solutions of Axial Symmetrical Problems of r>0 Thin Uniform Circular Toroidal Shells with a Large Parameter a²/R₀h

Chen Guo-dong

Tianjin General Paint Factory, Tianjin

Received Date: 1985-04-02
Publish Date: 1988-04-15

Abstract

Abstract

According to the classital shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a²/R₀h.In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.

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References(14)

References

[1]	钱伟长,轴对称圆环壳的复变量方程和轴对称细环壳的一般解,清华大学学报,19,1(1979),27-47.
[2]	Tölke,F.,Zur Integration der Differentialgeichungen der Rotationsschale,lngenieur Archiv,9 (1938),282-288.
[3]	Clark,R.A.,On the theory of thin elastic toroidal shells,J.Math.Phys.,29 (1950),146-178.
[4]	Новожилов В.В.,Теорця Тонкцх Оболочек,ГИСЛ(1951).
[5]	钱伟长,轴对称圆环壳一般解,应用数学和力学,1,3 (1980),287-300.
[6]	张维,承受轴对称载荷的圆环壳和带顶点的壳的应力状态,国立清华大学科学报告,5(A)(1949),289-349.
[7]	赵鸿宾、吴振辉、沈祖培,圆环壳在承受轴对称载荷时的复变量方程和渐近解法,清华大学学报,21,2 (1981), 1-14.
[8]	钱伟长,《应用数学和力学论文集》,江苏科技出版社(1980).
[9]	Desilva,C.N.and P.M.Naghdi,Asymptotic solutions of a class of elastic shells of revolution with variable thickness,Q.Appl.Math.,15,2 (1957),169-182.
[10]	Clark,R.A.,Asymptotic solutions of toroidal shell problems,Q.Appl.Math.,16,1 (1958),47-60.
[11]	Tumarkin,S.A.,Asymptotic solution of a linear nonhomogeneous second order differential equatlon with a transition point and its application to the computations of toroidal shells and propeller blades,Prikl.Mate.i.Mekh.,29 (1959),1549-1569.
[12]	Chen Guo-dong,Exact solutions of toroidal shells in.pressure vessels and piping,Int.J.Pres.Ves.and Piping,19,2 (1985),101-116.
[13]	Chen Guo-dong,The uniformly valid asymptotic solutions for spherical thin shells with constant thickness under edge loads,Proceedings of the Fifth Engineering Mechanics Division Specialty Conference ASCE,Aug.(1984),261-269.
[14]	Chen Guo-dong,The uniformly valid asymptotic solution of ellipsoidal shell heads in pressure vessels,J.Pressure Vessel Technol.,Trans.ASME,107,1 (1985),92-97.