Admissible Singular Solutions and the Hypercircle Method in Shallow Shell Theory

1977 ◽  
Vol 44 (1) ◽  
pp. 117-122 ◽  
Author(s):  
H. Antes
Keyword(s):  
Exact Solution ◽  
Singular Point ◽  
Iterative Procedure ◽  
Shallow Shell ◽  
Shell Theory ◽  
Plate Theory ◽  
Singular Solutions ◽  
Admissible Solutions ◽  
Shell Equations

The object of this study is the construction of geometrically and statically admissible solutions of the basic shallow shell equations in the case of singular loads, especially for the use in the hypersphere theorems. An iterative procedure extends known solutions of plate theory to the classical and an improved shallow shell theory. The results contain all important terms of the exact solution near the singular point.

An Upper Bound on the Error in Linear Quasi-Shallow Shell Theory

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Upper Bound ◽  
Shallow Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Energy Norm ◽  
Shell Equations

For a completely clamped elastic shell, an explicit upper bound is derived for the error in the energy norm of a solution of the linear, quasi-shallow shell equations as compared to the corresponding solution of the Sanders-Koiter equations.

Point Load on a Shallow Elliptic Paraboloid

1966 ◽  
Vol 33 (3) ◽  
pp. 575-585 ◽  
Author(s):  
Kevin Forsberg ◽  
Wilhelm Flu¨gge
Keyword(s):  
Power Series ◽  
Axial Symmetry ◽  
Shallow Shell ◽  
Point Load ◽  
Singular Solutions ◽  
Elliptic Paraboloid ◽  
Concentrated Loading ◽  
Shell Equations ◽  
Shell Geometry ◽  
Thin Shallow Shell

The present work is a study of a thin shallow shell having a specific type of deviation from axial symmetry, i.e., the portion of an elliptic paraboloid near its vertex. The singular solutions to the homogeneous shallow-shell equations are expressed as power series in terms of a parameter γ, which is a measure of the deviation of the shell geometry from axial symmetry. These singular solutions can be directly related to concentrated loading at the vertex of the shell. The solution converges in the range γ = 0 (sphere) to γ = 1/2 (cylinder). Detailed graphical results are presented for the stress resultants and radial deflection of a shell subjected to a point load at its vertex.

Singular Solutions to the Shallow Shell Equations

1970 ◽  
Vol 37 (2) ◽  
pp. 361-366 ◽  
Author(s):  
J. Lyell Sanders
Keyword(s):  
Closed Form ◽  
Theoretical Investigation ◽  
Shallow Shell ◽  
Fourier Transforms ◽  
Complex Form ◽  
Middle Surface ◽  
Singular Solutions ◽  
Concentrated Loads ◽  
Shell Equations ◽  
Complete Solutions

The paper contains a theoretical investigation of those multivalued singular solutions to the shallow shell equations which correspond physically to concentrated loads and dislocations. Use of the shell equations in complex form permits a unified treatment of the load and dislocation problems. The analysis is limited to the case of shells with a quadratic middle surface, and Fourier transforms of the solutions are obtained. Complete solutions in closed form in the case of a shallow sphere are given in the Appendix, including some results not previously published.

Transverse Bending of Cross-Ply Laminated Circular Cylindrical Plates

1976 ◽  
Vol 18 (2) ◽  
pp. 53-56 ◽  
Author(s):  
P. K. Sinha ◽  
A. K. Rath
Keyword(s):  
Aspect Ratio ◽  
Transverse Shear ◽  
Shallow Shell ◽  
Shell Theory ◽  
Plate Theory ◽  
Transverse Shear Deformation ◽  
Laminated Plate ◽  
Simply Supported ◽  
Transverse Bending ◽  
Plate Curvature

The paper deals with the transverse bending of simply supported, circular, cylindrical plates consisting of cross-ply laminates with arbitrary sequences of 0° and 90° plies. The analysis is carried out within the framework of laminated-plate theory and shallow-shell theory, where the effect of transverse shear deformation is considered. The non-dimensional deflection parameters are computed for panels consisting of antisymmetric graphite-epoxy plies. The influence of the coupling between bending and extension, the plate curvature and the aspect ratio are studied and discussed.

Comparison of Beam and Shell Theories for the Vibrations of Thin Turbomachinery Blades

1983 ◽  
Vol 105 (2) ◽  
pp. 383-392 ◽  
Author(s):  
A. W. Leissa ◽  
M. S. Ewing
Keyword(s):  
Shallow Shell ◽  
Shell Theory ◽  
Free Vibrations ◽  
Two Dimensional ◽  
Analysis Method ◽  
One Dimensional ◽  
Low Aspect Ratio ◽  
Turbomachinery Blades ◽  
Dimensional Analysis Method ◽  
Beam Theories

A great deal of published literature exists which analyzes the free vibrations of turbomachinery blades by means of one-dimensional beam theories. Recently, a more accurate, two-dimensional analysis method has been developed based upon shallow shell theory. The present paper summarizes the two types of theories and makes quantitative comparisons of frequencies obtained by them. Numerical results are presented for cambered and/or twisted blades of uniform thickness. Significant differences between the theories are found to occur, especially for low aspect ratio blades. The causes of these differences are discussed.

Pressurized Cylindrical Shell With a Rigid Circular Inclusion

1978 ◽  
Vol 100 (2) ◽  
pp. 158-163 ◽  
Author(s):  
D. H. Bonde ◽  
K. P. Rao
Keyword(s):  
Differential Equation ◽  
Cylindrical Shell ◽  
Shallow Shell ◽  
Circular Inclusion ◽  
Hankel Functions ◽  
Curvature Parameter ◽  
Shell Equations ◽  
Limiting Case ◽  
Rigid Circular Inclusion ◽  
Good Agreement

The effect of a rigid circular inclusion on stresses in a cylindrical shell subjected to internal pressure has been studied. The two linear shallow shell equations governing the behavior of a cylindrical shell are converted into a single differential equation involving a curvature parameter and a potential function in nondimensionalized form. The solution in terms of Hankel functions is used to find membrane and bending stressses. Boundary conditions at the inclusion shell junction are expressed in a simple form involving the in-plane strains and change of curvature. Good agreement has been obtained for the limiting case of a flat plate. The shell results are plotted in nondimensional form for ready use.

A Review of Tubular Conical Transition Strength Design Equations

2020 ◽  
Author(s):  
Albert Ku ◽  
Jieyan Chen ◽  
Bernard Cyprian
Keyword(s):  
Thin Shell ◽  
Shell Theory ◽  
Yield Criterion ◽  
Plasticity Theory ◽  
Transition Strength ◽  
Ultimate Capacity ◽  
Design Standards ◽  
Fem Simulations ◽  
Column Type ◽  
Shell Equations

Abstract This paper consists of two parts. Part one presents a thin-shell analytical solution for calculating the conical transition junction loads. Design equations as contained in the current offshore standards are based on Boardman’s 1940s papers with beam-column type of solutions. Recently, Lotsberg presented a solution based on shell theory, in which both the tubular and the cone were treated with cylindrical shell equations. The new solution as presented in this paper is based on both cylindrical and conical shell theories. Accuracies of these various derivations will be compared and checked against FEM simulations. Part 2 of this paper is concerned with the ultimate capacity equations of conical transitions. This is motivated by the authors’ desire to unify the apparent differences among the API 2A, ISO 19902 and NORSOK design standards. It will be shown that the NORSOK provisions are equivalent to the Tresca yield criterion as derived from shell plasticity theory. API 2A provisions are demonstrated to piecewise-linearly approximate this Tresca yield surface with reasonable consistency. The 2007 edition of ISO 19902 will be shown to be too conservative when compared to these other two design standards.

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