Local loads on a toroidal shell

1992 ◽  
Vol 27 (2) ◽  
pp. 59-66 ◽  
Author(s):  
D Redekop ◽  
F Zhang
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Elastic Shell ◽  
Toroidal Shell ◽  
Pipe Bend ◽  
Local Loads ◽  
Simply Supported ◽  
Linear Elastic ◽  
Wide Range ◽  
Theory Solution

In this study the effect of local loads applied on a sectorial toroidal shell (pipe bend) is considered. A linear elastic shell theory solution for local loads is first outlined. The solution corresponds to the case of a shell simply supported at the two ends. Detailed displacement and stress results are then given for a specific shell with loadings centred at three positions; the crown circles, the extrados, and the intrados. These results are compared with results for a corresponding cylindrical shell. The paper concludes with a table summarizing results for characteristic displacements and stresses in a number of shells, covering a wide range of geometric parameters.

Pipe Bend Analysis by Thin Shell Theory

1986 ◽  
Vol 53 (1) ◽  
pp. 173-180 ◽  
Author(s):  
J. F. Whatham
Keyword(s):  
Computer Program ◽  
Thin Shell ◽  
Shell Theory ◽  
Factor Versus ◽  
Pipe Bend ◽  
Pipe Elbow ◽  
Wide Range ◽  
Out Of Plane ◽  
Plane Bending ◽  
Thin Shell Theory

Thin shell theory is applied to pipe bends terminated by flanges or flange-ended tangent pipes and subjected to any end loading, either in-plane or out-of-plane. Graphs of flexibility factor versus pipe bend characteristic are presented for in-plane bending of a wide range of pipe elbows terminated by flanges or short flange-ended tangents. Experimental results verify the thin shell solutions for in-plane and out-of-plane bending of a flanged pipe elbow. The capabilities of a computer program BENDPAC are also described.

Effect of Ring Support Position and Geometrical Dimension on the Free Vibration of Ring-Stiffened Cylindrical Shells

2014 ◽  
Vol 580-583 ◽  
pp. 2879-2882
Author(s):  
Xiao Wan Liu ◽  
Bin Liang
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Geometrical Dimension ◽  
Stiffened Cylindrical Shell ◽  
Simply Supported ◽  
Ring Support ◽  
Stiffened Cylindrical Shells

Effect of ring support position and geometrical dimension on the free vibration of ring-stiffened cylindrical shells is studied in this paper. The study is carried out by using Sanders shell theory. Based on the Rayleigh-Ritz method, the shell eigenvalue governing equation is derived. The present analysis is validated by comparing results with those in the literature. The vibration characteristics are obtained investigating two different boundary conditions with simply supported-simply supported and clamped-free as the examples. Key Words: Ring-stiffened cylindrical shell; Free vibration; Rayleigh-Ritz method.

scholarly journals DESIGN OF CONCRETE CHIMNEYS VIA BEAM THEORY AND NONLINEAR SHELL ANALYSIS

2016 ◽  
Vol 7 ◽  
pp. 79-84
Author(s):  
Franziska Wehr ◽  
Reinhard Harte
Keyword(s):  
Bearing Capacity ◽  
Shell Theory ◽  
Elastic Shell ◽  
Beam Theory ◽  
Nonlinear Material ◽  
Load Bearing Capacity ◽  
Load Bearing ◽  
Linear Elastic ◽  
Shell Analysis ◽  
Safe Side

This paper compares the load-bearing capacity of chimneys calculated via beam and shell theory. It becomes apparent that the design via beam theory is on the safe side for the vertical reinforcement of the chosen examples for h/d ratios larger than 30. For non-slender chimneys the design via beam theory overestimates the load distribution around the circumference and yields to wrong results. On the other hand a linear elastic shell calculation underestimates the load-bearing capacity of the chimney. However a realistic distribution of stresses in the cross section of a chimney can still be calculated using shell theory with nonlinear material properties.

The Application of Long and Short Cylindrical Shell Solutions for Stress and Flexibility Determination in a Single Mitred Bend

2016 ◽  
Author(s):  
Igor Orynyak ◽  
Andrii Bogdan ◽  
Iryna Selivestrova
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Bending Moment ◽  
Axial Direction ◽  
Piping System ◽  
Structural Elements ◽  
Thin Cylindrical Shell ◽  
Straight Pipe ◽  
Pipe Bend ◽  
Short Shell

The continuous pipe bend behavior is well elaborated in literature. It is characterized by local ovalization of each cross section during bending which results in enhanced flexibility of it as compared to straight pipe. When pipe bend approaches some other structural elements of a piping system the end effect take place which can be described by so called long shell solution. This long solution is, in fact, a semi-membrane Vlasov’s solution when the derivative of any geometrical or force function in axial direction is much smaller than in the circumferential one [1]. Mitred bend is formed by conjunction by welding of two oblique sections of initially straight pipes. Its behavior during loading by pressure or bending moment is not evident and poorly described in standards. The goal of this paper is to give a set of general functions within a thin cylindrical shell theory which will give the opportunity to consider the mitred bend as an element of a piping system. Here we additionally introduce the so called short solution when the derivative of any parameter in axial direction is much bigger than that in circumferential one. Its main goal is to give the local behavior of stress in the vicinity of the oblique weld. Each of these two solutions satisfy by differential equations of forth order. The complete theoretical solution for a particular mitred bend is compared with a) existing analytical solutions and formulas; b) numerical results obtained by FEM with distinction of the zones of influence of a long as well as short shell solution; c) experimental data on real mitred bends given in the literature.

Vibration analysis of porous metal foam shells rested on an elastic substrate

2019 ◽  
Vol 54 (3) ◽  
pp. 199-208 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Ali Dabbagh ◽  
Abbas Rastgoo
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Metal Foam ◽  
Porous Metal ◽  
Elastic Substrate ◽  
Porosity Distribution ◽  
Simply Supported ◽  
First Order ◽  
Porosity Coefficient

In this article, the vibration problem of an embedded cylindrical shell consisted of porous metal foam is solved via an analytical method with respect to the influences of various porosity distributions. Three types of porosity distribution across the thickness are covered, namely, uniform, symmetric, and asymmetric. The strain–displacement relations of the shell are assumed to be derived on the basis of the first-order shear deformation shell theory. Then, the achieved relations will be incorporated with the Hamilton’s principle in order to reach the Navier equations of the cylindrical shell. Next, the well-known Galerkin’s method is utilized to calculate the natural frequencies of the system. The influences of both simply supported and clamped boundary conditions are included. In order to show the accuracy of the presented method, the results of the present research are compared with those reported by former published papers. The reported results show that an increase in the porosity coefficient can decrease the frequency of the shell. Also, the stiffness of the system can be lesser decreased while symmetric porosity distribution is chosen.

Analysis of Spectral Characteristics of Sound Waves Scattered from a Cracked Cylindrical Elastic Shell Filled with a Viscous Fluid

2013 ◽  
Vol 38 (3) ◽  
pp. 335-350 ◽  
Author(s):  
Olexa Piddubniak ◽  
Nadia Piddubniak
Keyword(s):  
Viscous Fluid ◽  
Shell Theory ◽  
Elastic Shell ◽  
Spectral Characteristics ◽  
Steel Shell ◽  
Sound Waves ◽  
Thin Cylindrical Shell ◽  
Shell Surface ◽  
Theory Approximation ◽  
Directivity Patterns

Abstract The scattering of plane steady-state sound waves from a viscous fluid-filled thin cylindrical shell weak- ened by a long linear slit and submerged in an ideal fluid is studied. For the description of vibrations of elastic objects the Kirchhoff-Love shell-theory approximation is used. An exact solution of this problem is obtained in the form of series with cylindrical harmonics. The numerical analysis is carried out for a steel shell filled with oil and immersed in seawater. The modules and phases of the scattering amplitudes versus the dimensionless wavenumber of the incident sound wave as well as directivity patterns of the scattered field are investigated taking into consideration the orientation of the slit on the elastic shell surface. The plots obtained show a considerable influence of the slit and viscous fluid filler on the diffraction process.

Cylindrical Shells Under Line Load

1957 ◽  
Vol 24 (4) ◽  
pp. 553-558
Author(s):  
R. M. Cooper
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Transverse Shear Deformation ◽  
System Of Equations ◽  
Principle Of Superposition ◽  
Line Load ◽  
Simply Supported ◽  
Shell Equations ◽  
Shell Geometry

Abstract The problem of a line load along a segment of a generator of a simply supported circular cylindrical shell is treated using shallow cylindrical shell equations which include the effect of transverse-shear deformation. The line load is first treated as a sinusoidally-varying edge load over the length of the shell, with boundary conditions prescribed along the loaded generator such that the continuity of the shell is maintained. The solution for the problem of a uniform line load over a segment of a generator is obtained from the preceding solution, using the principle of superposition. By means of a numerical example it is shown that the results predicted by the Donnell equations for the stresses are in excellent agreement with those obtained from the system of equations employed here. However, the radial displacement predicted by the Donnell equations is in error by as much as 20 per cent in the range of shell geometry considered.

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