Asymptotic solutions for finite deformation of thin shells of revolution with a small circular hole

Hubertus J. Weinitschke; Charles G. Lange

doi:10.1090/qam/910449

Asymptotic solutions for finite deformation of thin shells of revolution with a small circular hole

Quarterly of Applied Mathematics ◽

10.1090/qam/910449 ◽

1987 ◽

Vol 45 (3) ◽

pp. 401-417 ◽

Cited By ~ 5

Author(s):

Hubertus J. Weinitschke ◽

Charles G. Lange

Keyword(s):

Circular Hole ◽

Finite Deformation ◽

Asymptotic Solutions ◽

Thin Shells ◽

Shells Of Revolution

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On the Accuracy of Some Shell Solutions

Journal of Applied Mechanics ◽

10.1115/1.4012115 ◽

1959 ◽

Vol 26 (4) ◽

pp. 577-583

Author(s):

G. D. Galletly ◽

J. R. M. Radok

Keyword(s):

Negative Curvature ◽

Numerical Solutions ◽

Asymptotic Solutions ◽

Thin Shells ◽

Shells Of Revolution ◽

Equilibrium Equations ◽

Influence Coefficients ◽

Bending Loads ◽

Edge Influence

Abstract R. B. Dingle’s method [1] for finding asymptotic solutions of ordinary differential equations of a type such as occur in the bending theory of thin shells of revolution is presented in outline. This method leads to the same results as R. E. Langer’s method [2], recently used for problems of this kind, and permits a simple analytical and less formal interpretation of the asymptotic treatment of such equations. A comparison is given of edge influence coefficients due to bending loads, obtained by use of these asymptotic solutions and numerical integration of the equilibrium equations, respectively. The particular shells investigated are of the open-crown, ellipsoidal, and negative-curvature toroidal types. The results indicate that the agreement between these solutions is satisfactory. In the presence of uniform pressure, the use of the membrane solutions for the determination of the particular integrals appears to lead to acceptable results in the case of ellipsoidal shells. However, in the case of toroidal shells, the membrane and the numerical solutions disagree significantly.

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Influence Coefficients for Thin Smooth Shells of Revolution Subjected to Symmetric Loads

Journal of Applied Mechanics ◽

10.1115/1.3640551 ◽

1962 ◽

Vol 29 (2) ◽

pp. 335-339 ◽

Cited By ~ 7

Author(s):

B. R. Baker ◽

G. B. Cline

Keyword(s):

Differential Equations ◽

Asymptotic Integration ◽

Asymptotic Solutions ◽

Thin Shells ◽

Uniform Thickness ◽

Shells Of Revolution ◽

Influence Coefficients ◽

Independent Variable

The differential equations governing the deformation of shells of revolution of uniform thickness subjected to axisymmetric self-equilibrating edge loads are transformed into a form suitable for asymptotic integration. Asymptotic solutions are obtained for all sufficiently thin shells that possess a smooth meridian curve and that are spherical in the neighborhood of the apex. For design use, influence coefficients are derived and presented graphically as functions of the transformed independent variable ξ. The variation of ξ with the meridional tangent angle φ is given analytically and graphically for several common meridian curves—the parabola, the ellipse, and the sphere.

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