Limit Analysis of Symmetrically Loaded Thin Shells of Revolution

1959 ◽  
Vol 26 (1) ◽  
pp. 61-68
Author(s):  
D. C. Drucker ◽  
R. T. Shield
Keyword(s):  
Cylindrical Shell ◽  
Lower Bounds ◽  
Yield Surface ◽  
Limit Analysis ◽  
Thin Shell ◽  
Upper And Lower Bounds ◽  
Thin Shells ◽  
Hexagonal Prism ◽  
Shells Of Revolution ◽  
Thin Cylindrical Shell

Abstract The yield surface for a thin cylindrical shell is shown to be a very good approximation to the yield surface for any symmetrically loaded thin shell of revolution. Hexagonal prism approximations to this yield surface, appropriate for pressure vessel analysis, are described and discussed in terms of limit analysis. Procedures suitable for finding upper and lower bounds on the limit pressure for the complete vessel are developed and evaluated. They are applied for illustration to a portion of a toroidal zone or knuckle held rigidly at the two bounding planes. The combined end force and moment which can be carried by an unflanged cylinder also is discussed.

The Preferred Mode Shape in the Linear Buckling of Circular Cylindrical Shells Under Axial Compression

1965 ◽  
Vol 32 (4) ◽  
pp. 793-802 ◽  
Author(s):  
P. Mann-Nachbar ◽  
W. Nachbar
Keyword(s):  
Cylindrical Shell ◽  
Aspect Ratio ◽  
Axial Compression ◽  
Probability Distributions ◽  
Thin Shells ◽  
Thin Cylindrical Shell ◽  
Linear Buckling ◽  
Manufacturing Tolerances ◽  
Circular Cylindrical Shells ◽  
Circumferential Waves

The chessboard buckle pattern in the solution of the linearized Donnell equations for buckling of a thin, cylindrical shell under axial compression is so sensitive to uncertainties in shell dimensions that the number of circumferential waves and the aspect ratio of the buckles is indeterminate. This problem is treated statistically. Shell dimensions are treated as random variables with probability distributions dependent on nominal values and manufacturing tolerances. Distributions for aspect ratio and number of circumferential waves are found by a Monte-Carlo technique. It is found that the linear theory does contain a mechanism for distinguishing among buckle modes. There is always a preferred buckle mode. For thin shells and attainable manufacturing tolerances, the aspect ratio of the preferred mode is closer to one than that of any other possible mode, and the corresponding number of buckles is large.

Full-Strength Reinforcement of a Cutout in a Cylindrical Shell

1964 ◽  
Vol 31 (4) ◽  
pp. 667-675 ◽  
Author(s):  
Philip G. Hodge
Keyword(s):  
Cylindrical Shell ◽  
Lower Bounds ◽  
Upper Bound ◽  
Circular Cylindrical Shell ◽  
Minimum Weight ◽  
Upper And Lower Bounds ◽  
Minimum Weight Design ◽  
Initial Strength ◽  
Weight Design ◽  
Circular Cutout

A long circular cylindrical shell is to be pierced with a circular cutout, and it is desired to design a plane annular reinforcing ring which will restore the shell to its initial strength. Upper and lower bounds on the design of the reinforcement are obtained. Although these bounds are far a part, it is conjectured that the upper bound, in addition to being safe, is reasonably close to the minimum weight design. Some suggestions for further work on the problem are advanced.

scholarly journals Bounds for the Collapse Load of a Beam Compressed by Three Dies

1956 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
W Freiberger
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Plastic Yielding ◽  
Plane Plastic

This paper deals with the problem of the plastic deformation of a beam under the action of three perfectly rough rigid dies, two dies applied to one side, one die to the other side of the beam, the single die being situated between the two others. It is treated as a problem of plane plastic flow. Discontinuous stress and velocity fields are assumed and upper and lower bounds for the pressure sufficient to cause pronounced plastic yielding determined by limit analysis.

Limit Analysis of Nonsymmetrically Loaded Spherical Shells

1972 ◽  
Vol 39 (2) ◽  
pp. 422-430 ◽  
Author(s):  
S. Palusamy ◽  
N. C. Lind
Keyword(s):  
Lower Bounds ◽  
Limit Analysis ◽  
Upper And Lower Bounds ◽  
Spherical Shells ◽  
Limit Loads ◽  
Analytical Results

Upper and lower bounds are found for limit loads on nonsymmetrically loaded spherical shells. The influence of geometrical and load parameters are discussed. The analytical results are compared with the results of tests on four steel models.

A Digital Computer Program for the General Axially Symmetric Thin-Shell Problem

1962 ◽  
Vol 29 (4) ◽  
pp. 655-661 ◽  
Author(s):  
W. K. Sepetoski ◽  
C. E. Pearson ◽  
I. W. Dingwell ◽  
A. W. Adkins
Keyword(s):  
Computer Program ◽  
Thin Shell ◽  
Thin Shells ◽  
Axially Symmetric ◽  
Shells Of Revolution ◽  
Computational Accuracy ◽  
Symmetric Loading ◽  
Shell Geometry ◽  
General Computer Program ◽  
General Computer

This paper describes the development of a general computer program to handle arbitrary thin shells of revolution subject to radially symmetric loading or temperature variation. An elimination method is used to solve the set of difference equations obtained from the basic differential equations; a feature of the method is that “edge effect” difficulties that can arise with conventional differential-equation routines are avoided. The program is quite flexible and permits discontinuities in shell geometry or loading. The results of applying the program to several classical problems of known solution are given. These results permit the examination of computational accuracy for varying boundary conditions and mesh sizes. Finally, some program solutions of unconventional problems are presented.

Alternative lower bounds analysis of elastic thin shells of revolution

1996 ◽  
Vol 13 (2/3/4) ◽  
pp. 41-75 ◽  
Author(s):  
Itaru Mutoh ◽  
Shiro Kato ◽  
Y. Chiba
Keyword(s):  
Lower Bounds ◽  
Thin Shells ◽  
Shells Of Revolution

Numerical Methods for the Limit Analysis of Plates

1968 ◽  
Vol 35 (4) ◽  
pp. 796-802 ◽  
Author(s):  
P. G. Hodge ◽  
T. Belytschko
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Mathematical Programming ◽  
Rectangular Plate ◽  
Yield Point ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Upper And Lower Bounds ◽  
Mathematical Programming Problems

The determination of upper and lower bounds on the yield-point loads of plates are formulated as mathematical programming problems by using finite element representations for the velocity and moment fields. Results are presented for a variety of square and rectangular plate problems and are compared to other available solutions.

An Approach to Optimum Shape Determination for a Class of Thin Shells of Revolution

1968 ◽  
Vol 35 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Han-Chung Wang ◽  
Will J. Worley
Keyword(s):  
Thin Shell ◽  
Failure Criteria ◽  
Optimum Shape ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Numerical Iteration ◽  
Shape Determination ◽  
Selection Of ◽  
Convex Shell

A method is presented for the determination of an optimum shape of a convex shell of revolution with respect to volume and weight. The technique depends on selecting a multiparameter equation and varying the parameters to achieve a near optimum shape for prescribed failure criteria. As an illustration of the method, the first quadrant of the meridian (x/a)α + (y/b)β = 1 is selected. Here a, b, α, and β are positive constants not necessarily integers, with α and β equal to or greater than unity. Variations in shape are expressed in terms of the parameters b/a, α and β. The procedure is applied to the selection of a thin shell which will fit within the space defined by a circular cylinder of radius b and length 2a. The shell is optimized, in terms of α and β, with respect to volume and weight. The numerical iteration was performed by means of a digital computer.

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