scholarly journals On shallow shell equations

2009 ◽  
Vol 2 (3) ◽  
pp. 697-722 ◽  
Author(s):  
Peng-Fei Yao ◽  
Keyword(s):  
Shallow Shell ◽  
Shell Equations

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.

An Efficient Computational Approach for a Large Opening in a Cylindrical Vessel

1986 ◽  
Vol 108 (4) ◽  
pp. 436-442 ◽  
Author(s):  
C. R. Steele ◽  
M. L. Steele ◽  
A. Khathlan
Keyword(s):  
Shallow Shell ◽  
Computer Calculation ◽  
Computational Approach ◽  
Cylindrical Vessel ◽  
Intersection Curve ◽  
High Harmonics ◽  
Large Opening ◽  
Shell Equations ◽  
Present Effort ◽  
Good Agreement

In our previous work, solutions of the shallow shell equations have provided the basis for efficient computer calculation for a reinforced opening in a cylindrical vessel. However, solutions are restricted to smaller nozzles and openings (d/D≤0.5). In the present effort, an approach for the large opening has been developed which retains computational efficiency and minimum user time. The total solution can be divided into “high” harmonics around the intersection curve, which are obtained from asymptotic analysis, and particular solutions and low harmonics of self-equilibrating loads, which are obtained as “cut” solutions. By this, the vessel is considered to be cut along the portion of the circumference inside the intersection curve. Appropriate discontinuities of stress and displacement on the cut provide the necessary solutions. Results for a rigid nozzle with external loadings show good agreement with the previous shallow shell calculations for d/D≤0.5 with a substantial divergence for larger values of d/D. The behavior at the limit of d/D = 1 remains to be clarified.

Annular Dome Subjected to Uniform Load Over an Eccentric Circular Area

1978 ◽  
Vol 45 (4) ◽  
pp. 845-851
Author(s):  
H. Ainso
Keyword(s):  
General Solution ◽  
Shallow Shell ◽  
Outer Boundary ◽  
Uniform Load ◽  
Circular Area ◽  
Distributed Load ◽  
Load Effects ◽  
Particular Solution ◽  
Shell Equations ◽  
General Method

A general method is presented for solving shallow shell problems with finite boundaries and with an arbitrarily placed load that is uniformly distributed over a circular area of radius r0. A known solution for the distributed load on an unbounded shell is used to describe the load effects, and this particular solution is combined with Reissner’s general solution of the shallow shell equations in such a manner that all the boundary conditions are satisfied. Numerical results have been obtained for a shallow shell, clamped at the outer boundary and having a circular polar aperture free of tractions and support.

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.

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