ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a 2/R0h

Applied Mathematics and Mechanics (English Edition) ›› 1988, Vol. 9 ›› Issue (4): 401-416.

ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a2/R₀h

陈国栋

Tianjin General Paint Factory, Tiajin

收稿日期:1985-04-02 出版日期:1988-04-18 发布日期:1988-04-18
通讯作者: Chien Wei-zang

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, Tiajin

Received:1985-04-02 Online:1988-04-18 Published:1988-04-18

摘要/Abstract

摘要： 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.

关键词: lip-shaped crack, strained reinforcement layer, concentrated load, remote load, eigenstrain, interfacial stress

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.

Key words: lip-shaped crack, strained reinforcement layer, concentrated load, remote load, eigenstrain, interfacial stress

陈国栋. 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 (English Edition), 1988, 9(4): 401-416.

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 (English Edition), 1988, 9(4): 401-416.

参考文献

[1] Chien, W.Z., Equations of symmetrical ring shells in complex quantities and their general solutions for slender ring shells, Journal of Qinghua University, 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] Novozhilov, V.V., the Theory of Thin Shells, Noordhoff, Groningen, The Netherlands (1959).
[5] Chien, W.Z., General solutions of axial symmetrical ring shells, Applied Mathematics and Mechanics, 1, 3 (1980).
[6] Chang, W., The state of stress in toroidal and similar shells with azimental rings under torsionally symmetrically stress, Science Report of National Tsinghua University, 5 (A) (1949), 289-349. (in Chinese).
[7] Zhao Hong-bin, Wu Zhen-hui and Shen Zhu-pei, The equations in complex variables under axial symmetric loads and their asymptotic solutions, Journal of Qinghua University,21, 2 (1981), 1-14. (in Chinese).
[8] Chien, W.Z., The Treatises of Applied Mathematics and Mechanics, Jiangsu Science and Technique Press, China (1980). (in Chinese).
[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.

ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a2/R₀h

ON SECOND ORDER ASYMPTOTIC SOLUTIONS OF AXIAL SYMMETRICAL PROBLEMS OF r>0 THIN UNIFORM CIRCULAR TOROIDAL SHELLS WITH A LARGE PARAMETER a2/R₀h

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