The resistance of a liquid to a nonsymmetric deformation of a cylinder and a sphere

1972 ◽  
Vol 7 (5) ◽  
pp. 769-775
Author(s):  
N. A. Slezkin
Keyword(s):  
Nonsymmetric Deformation

Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution

1992 ◽  
Vol 59 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Charles R. Steele ◽  
Yoon Young Kim
Keyword(s):  
Variational Principle ◽  
Equations Of State ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Shells Of Revolution ◽  
Elastic Bodies ◽  
Mixed Variational Principle ◽  
Stress Components ◽  
Independent Variable ◽  
Nonsymmetric Deformation

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.

Nonsymmetric Deformation of Dome-Shaped Shells of Revolution

1962 ◽  
Vol 29 (2) ◽  
pp. 353-361 ◽  
Author(s):  
C. R. Steele
Keyword(s):  
Integral Equation ◽  
Axial Force ◽  
Circumferential Direction ◽  
Trial And Error ◽  
Shells Of Revolution ◽  
Side Force ◽  
Trial And Error Method ◽  
Error Method ◽  
Nonsymmetric Deformation

Bending solutions that are uniformly valid in both shallow and nonshallow regions of a dome with arbitrary meridian are determined for edge loads that vary sinusoidally in the circumferential direction. The membrane and inextensional deformation solutions are obtained in terms of a function which satisfies a simple integral equation which eliminates the usual trial-and-error method of isolating the solutions that are regular at the apex. For a specific application, curves and formulas are obtained for the stresses and deformations of a dome with rigid rings clamped to the edges under the action of axial force, side force, and tilting moment.

Nonsymmetric Buckling of Plate-End Pressure Vessels

1989 ◽  
Vol 111 (3) ◽  
pp. 304-311 ◽  
Author(s):  
J. G. Teng ◽  
J. M. Rotter
Keyword(s):  
Flat Plate ◽  
Large Deformations ◽  
Deformation Mode ◽  
Pressure Vessels ◽  
Plastic Behavior ◽  
Geometrically Nonlinear ◽  
End Plate ◽  
Local Stresses ◽  
Nonlinear Elastic ◽  
Nonsymmetric Deformation

Small cylindrical pressure vessels are often constructed with a circular flat plate end closure. The end-plate undergoes large deformations under working loads. High local stresses develop at the junction between the cylinder and end-plate, causing yield under proof loading. The compressive circumferential stresses at the junction may lead to bifurcation into a nonsymmetric deformation mode. This study explores the geometrically nonlinear elastic-plastic behavior of plate-end pressure vessels. The form of the axisymmetric prebuckling path is investigated, showing the strongly stiffening nature of the response. Bifurcation of the closure into a nonsymmetric mode is then studied.

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