Effect of Internal Pressure on the Influence Coefficients of Spherical Shells

Uniform asymptotic solutions are found for the differential equations governing the symmetric bending of spherical shells of constant thickness subjected to self-equilibrating edge loads and internal pressure. The solutions include the effect of nonlinear coupling of the stresses and edge loads. These solutions are used to obtain expressions for the influence coefficients of both a spherical cap and the complementary portion of the sphere. The effect of the pressure coupling on these influence coefficients is presented graphically.

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Nonlinear Corrections for Edge Bending of Shells

Journal of Applied Mechanics ◽

10.1115/1.3153803 ◽

1980 ◽

Vol 47 (4) ◽

pp. 861-865 ◽

Cited By ~ 6

Author(s):

G. V. Ranjan ◽

C. R. Steele

Keyword(s):

Differential Equations ◽

Spherical Shell ◽

Asymptotic Expansions ◽

Axial Displacement ◽

Exponential Functions ◽

Spherical Cap ◽

Influence Coefficients ◽

Edge Loading ◽

General Geometry ◽

Edge Influence

Asymptotic expansions for self-equilibrating edge loading are derived in terms of exponential functions, from which formulas for the stiffness and flexibility edge influence coefficients are obtained, which include the quadratic nonlinear terms. The flexibility coefficients agree with those previously obtained by Van Dyke for the pressurized spherical shell and provide the generalization to general geometry and loading. In addition, the axial displacement is obtained. The nonlinear terms in the differential equations can be identified as “prestress” and “quadratic rotation.” To assess the importance of the latter, the problem of a pressurized spherical cap with roller supported edges is considered. Results show that whether the rotation at the edge is constrained or not, the quadratic rotation terms do not have a large effect on the axial displacement. The effect will be large for problems with small membrane stresses.

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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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A Comparison of Theoretical and Experimental Results From Spherical Shells With a Single Radially Attached Nozzle

Journal of Engineering for Power ◽

10.1115/1.3616684 ◽

1967 ◽

Vol 89 (3) ◽

pp. 333-338 ◽

Cited By ~ 5

Author(s):

F. J. Witt ◽

R. C. Gwaltney ◽

R. L. Maxwell ◽

R. W. Holland

Keyword(s):

Spherical Shell ◽

Internal Pressure ◽

Experimental Results ◽

Strain Gages ◽

Spherical Shells ◽

Axial Thrust ◽

Outside Diameter ◽

Theoretical Results

A series of steel models having single nozzles radially and nonradially attached to a spherical shell is presently being examined by means of strain gages. Parameters being studied are nozzle dimensions, length of internal nozzle protrusions, and angles of attachment. The loads are internal pressure and axial thrust and moment loadings on the nozzle. This paper presents both experimental and theoretical results from six of the configurations having radially attached nozzles for which the sphere dimensions are equal and the outside diameter of the attached nozzle is constant. In some instances the nozzle protrudes through the vessel.

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