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.

scholarly journals The thickness functions of the shells of revolution subjected to axisymmetrical loads

2005 ◽  
Vol 27 (2) ◽  
pp. 66-73
Author(s):  
Ngo Huong Nhu ◽  
Pham Hong Nga
Keyword(s):  
Differential Equations ◽  
Thin Shell ◽  
Numerical Solutions ◽  
External Pressure ◽  
Shells Of Revolution ◽  
Varying Thickness ◽  
Shell Design ◽  
Mathematical Difficulties ◽  
Thickness Function

The inverse problems for determining the meridian shape or varying thickness function of momentless shells of revolution under given loads were concerned in many works [2, 3, 4]. However, for the complexity of loads or configuration of a shell these problems haven' t bee.n solved perfectly because of its mathematical difficulties. In this paper, the problem for determining the thickness function of shells of revolution such as a parabola, sphere arc! under axisymmetrical loads is considered. The general integro-differential equations for determination of the meridian form and shell thickness are obtained. A solution of differential equations by semi-analytical and numerical methods for the thickness is presented. The numerical solutions are given for the parabola under external pressure, the sphere immerged in the fluid and the sphere arc. Obtained results may be used in the thin shell design.

On the Accuracy of Some Shell Solutions

1959 ◽  
Vol 26 (4) ◽  
pp. 577-583
Author(s):  
G. D. Galletly ◽  
J. R. M. Radok
Keyword(s):  
Negative Curvature ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Equilibrium Equations ◽  
Influence Coefficients ◽  
Bending Loads ◽  
Edge Influence

Abstract R. B. Dingle’s method [1] for finding asymptotic solutions of ordinary differential equations of a type such as occur in the bending theory of thin shells of revolution is presented in outline. This method leads to the same results as R. E. Langer’s method [2], recently used for problems of this kind, and permits a simple analytical and less formal interpretation of the asymptotic treatment of such equations. A comparison is given of edge influence coefficients due to bending loads, obtained by use of these asymptotic solutions and numerical integration of the equilibrium equations, respectively. The particular shells investigated are of the open-crown, ellipsoidal, and negative-curvature toroidal types. The results indicate that the agreement between these solutions is satisfactory. In the presence of uniform pressure, the use of the membrane solutions for the determination of the particular integrals appears to lead to acceptable results in the case of ellipsoidal shells. However, in the case of toroidal shells, the membrane and the numerical solutions disagree significantly.

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.

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.

Maysel's formula generalized for piezoelectric vibrations - Application to thin shells of revolution

1996 ◽  
Author(s):  
Hans Irschik ◽  
Franz Ziegler ◽  
Hans Irschik ◽  
Franz Ziegler
Keyword(s):  
Thin Shells ◽  
Shells Of Revolution

DETERMINING THE DESALINATION UNIT COMPOSITION FOR COSTAL AREAS AND SMALL ISLANDS USE ANALYTIC HIERARCHY PROCESS

2017 ◽  
Vol 9 (1) ◽  
Author(s):  
Imam Setiadi ◽  
Dinda Rita K. Hartaja
Keyword(s):  
Analytic Hierarchy Process ◽  
Energy Demand ◽  
Pairwise Comparison ◽  
Small Islands ◽  
Ahp Method ◽  
Analytic Hierarchy ◽  
Comparison Research ◽  
Hierarchy Process ◽  
Selection Of

Selection of the appropriate composition desalination units can be done with a variety of method approaches, one of the method is the Analytic Hierarchy Process. In determining the desalination unit with AHP method to consider is setting a goal, an alternative criteria and pairwise comparison. Research for the determination of the exact composition of the desalination unit in order to achieve sustainable drinking water suppy in coastal areas and small islands has been conducted. The results of the study are as follows, the energy demand of 50.83%, operator costs of 26.64%, maintenance costs of 14.13% and chemical requirement 8.4%. For an alternative composition desalination unit of RO 10 m3 / day is the best alternative composition with value of 59.61%, the composition of the next alternative is RO 20 m3/ day of 30.40% and the last alternative of the desalination unit composition is RO 120 m3/ day of 09.99%.Key words : Desalination, Mukti Stage Flash Composition, AHP

Optimization of the selection of analysis methods for the determination of naturally occurring radionuclides

Kerntechnik ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. 118-121
Author(s):  
T. Heinrich ◽  
L. Funke ◽  
M. Köhler ◽  
U.-K. Schkade ◽  
F. Ullrich ◽  
...  
Keyword(s):  
Naturally Occurring ◽  
Analysis Methods ◽  
Naturally Occurring Radionuclides ◽  
Selection Of
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