The Elasticity Solution of a Long Circular-Cylindrical Shell Subjected to a Uniform, Circumferential, Radial Line Load

1962 ◽  
Vol 29 (7) ◽  
pp. 834-841 ◽  
Author(s):  
JEROME M. KLOSNER
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Elasticity Solution ◽  
Radial Line ◽  
Line Load

Bending of a Thin Cylindrical Shell Subjected to a Line Load Around a Circumference

1961 ◽  
Vol 28 (3) ◽  
pp. 427-433 ◽  
Author(s):  
H. R. Meck
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Thin Cylindrical Shell ◽  
Radial Line ◽  
Eighth Order ◽  
Line Load ◽  
Bending Stresses ◽  
Center Section ◽  
Fourth Order Equations ◽  
Thin Shell Theory

An analysis is developed for bending of a thin circular cylindrical shell under a varying radial line load distributed around the circumference at the center section. The problem is solved by reducing the eighth-order differential equation of thin-shell theory to two approximate fourth-order equations. Deflections, bending stresses, and membrane stresses are evaluated. Both simply supported and clamped ends are considered.

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.

Closed-End Cylindrical Shell Under Line Load Along a Generator

1980 ◽  
Vol 102 (1) ◽  
pp. 90-97 ◽  
Author(s):  
U. S. Chawla
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference ◽  
Discrete Element Method ◽  
Computer Program ◽  
Circular Cylindrical Shell ◽  
Numerical Technique ◽  
Elastic Analysis ◽  
Line Load ◽  
Shell Plate ◽  
Free Body

This paper presents a numerical technique for elastic analysis of a thin circular cylindrical shell with end plates under uniform line load along a generator. This technique is based upon the discrete element method. An accurate set of the governing differential equations due to Vlasov is used. The derivatives with respect to the circumferential coordinate are replaced by finite difference relationships. The end plate is analyzed as a free body under unit concentrated edge loads and the resulting coefficients are used to satisfy continuity conditions at the shell-plate junction. A computer program to implement this technique is developed and results are compared with those published in the literature. A number of new results are presented.

Stresses in Eccentric Stepwise Discontinuous Rings With Transition Section

1968 ◽  
Vol 12 (04) ◽  
pp. 269-278
Author(s):  
Arnold Allentuch ◽  
Joseph Kempner
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Maximum Stress ◽  
Circular Cylindrical Shell ◽  
Radial Line ◽  
Cross Sectional ◽  
Line Load ◽  
Transition Section ◽  
Parameter Values ◽  
Interaction Problem

The stress distribution in a ring of nonuniform cross section under the action of a uniform radial line load is obtained. The solution is an approximation to the exact interaction problem of a reinforced circular cylindrical shell under hydrostatic pressure. The ring is fabricated in three segments; one segment, whose cross-sectional area varies according to a power function, connects two uniform segments. By a proper choice of parameter values the ring geometry can be reduced to two segments, one of uniform depth, the other of continuously varying depth. Several sets of parameters are chosen for numerical calculations. Within these sets only the length of the transition section changes. Thus an appraisal of the importance of the transition section in reducing the maximum stress is made. The stress distribution in a frame with different lengths of transition section is obtained.

Elasticity Solution for a Multilayered Transversely Isotropic Circular Cylindrical Shell

1982 ◽  
Vol 49 (1) ◽  
pp. 108-114 ◽  
Author(s):  
K. Chandrashekhara ◽  
P. Gopalakrishnan
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Transversely Isotropic ◽  
Outer Radius ◽  
Elasticity Solution ◽  
Layered Shell ◽  
Load Following ◽  
Stress Function Method ◽  
Moduli Of Elasticity

An elasticity solution has been obtained for a long multilayered cylindrical shell of transversely isotropic layers subjected to axisymmetric radial load following Lekhnitskii’s stress function method. Numerical results are presented for a two layered shell for different ratios of thickness-to-outer radius and for different ratios of the moduli of elasticity in the radial direction of the layers. The results obtained from this analysis have been compared with those obtained from the multilayered shell theory of Ambartsumian.

SUPERSONIC FLUTTER CONTROL OF AN ELECTRORHEOLOGICAL FLUID-BASED SMART CIRCULAR CYLINDRICAL SHELL

2014 ◽  
Vol 14 (02) ◽  
pp. 1350064 ◽  
Author(s):  
SEYYED M. HASHEMINEJAD ◽  
M. AGHAYI MOTAALEGHI
Keyword(s):  
Cylindrical Shell ◽  
Gas Flow ◽  
Sliding Mode ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Electrorheological Fluid ◽  
Open Loop ◽  
Point Load ◽  
Integration Algorithm ◽  
Line Load

In this paper, active flutter suppression of a simply supported circular sandwich cylindrical shell with a tunable electrorheological fluid (ERF) core, under axial supersonic gas flow, is studied. The structural analysis is based on the classical thin shell theory, the ERF core is modeled as a first-order Kelvin–Voigt material, and the Krumhaar's modified supersonic piston theory is utilized to model the aerodynamic loading. Hamilton's principle is used to formulate the dynamic equations of motion together with the relevant boundary conditions. The generalized Fourier expansions in the circumferential and axial directions in conjunction with the classical Galerkin method are employed to set up the governing equations in the state-space domain. The critical free stream static pressures at which unstable oscillations arise are calculated for selected applied electric field strengths and cylinder length ratios. The Runge–Kutta time integration algorithm is used to determine the open-loop aeroelastic response of the system in two basic loading configurations, namely, a concentrated impulse point load and a sonic boom line load. Subsequently, a sliding mode control (SMC) strategy is adopted to actively suppress the closed loop system dynamic response in supersonic flight condition. Simulation results demonstrate performance and effectiveness of the adopted ERF-based SMC scheme. Limiting cases are considered and good agreements with the data available in the literature are obtained.

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