scholarly journals Application of Uniformly Valid Shell Theory

2021 ◽  
Author(s):  
Samuel W Chung ◽  
Hyun-ho Ju

For the purpose of demonstrating the applicability of the previously derived theories, the problem of a laminated circular cylindrical shell under internal pressure and edge loadings will be examined. The cylinder is assumed to consist of boron/epoxy composite layers. Each layer is taken to be homogeneous but anisotropic with an arbitrary orientation of the elastic axes. We need not consider the restriction of the symmetry of the layering due to the non-homogeneity considered in the original development of the theory expressed by the constitutive equations. Thus, each layer can possess a different thickness.

2021 ◽  
Author(s):  
Samuel W Chung ◽  
Hyun-ho Ju

For the purpose of demonstrating the applicability of the previously derived theories, the problem of a laminated circular cylindrical shell under internal pressure and edge loadings will be examined. The cylinder is assumed to consist of boron/epoxy composite layers. Each layer is taken to be homogeneous but anisotropic with an arbitrary orientation of the elastic axes. We need not consider the restriction of the symmetry of the layering due to the non-homogeneity considered in the original development of the theory expressed by the constitutive equations. Thus, each layer can possess a different thickness.


Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.


Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.


2012 ◽  
Vol 226-228 ◽  
pp. 262-266 ◽  
Author(s):  
Yan Qi Liu ◽  
Fu Lei Chu

In this paper, the vibration characteristics of the rotating thin circular cylindrical shell subjected to the radial excitation are presented. Based on the Love’s shell theory, the governing equation of the rotating thin circular cylindrical shell is derived by using the Hamilton’s principle. Then, the amplitude-frequency responses for traveling wave vibration of the circular cylindrical shell are investigated. The results indicate that there exists the traveling wave vibration for the rotating thin circular cylindrical shell, namely: the forward wave and the backward wave. The effects of the damping and excitation on the amplitude-frequency response are analyzed.


1972 ◽  
Vol 39 (1) ◽  
pp. 124-128 ◽  
Author(s):  
M. J. Forrestal ◽  
G. E. Sliter ◽  
M. J. Sagartz

A semi-infinite, elastic, circular cylindrical shell is subjected to two uniform, radial pressure pulses, one a step pulse and the other a short-duration, rectangular pulse. Solutions for the stresses emanating from both a clamped support and a simple support are presented for a Timoshenko-type shell theory and a shell bending theory. Results from the Timoshenko-type theory are obtained using the method of characteristics, and results from the shell bending theory are obtained using integral transform techniques. Numerical results from both shell theories are presented for the bending stress and the shear stress resultant. Results show that the effects of rotary inertia and shear deformation are important only in the vicinity of the wave fronts. However, if the duration of the pressure pulse is short, maximum stresses can occur in the vicinity of the wave fronts where a Timoshenko-type shell theory is required for realistic response predictions.


1973 ◽  
Vol 40 (3) ◽  
pp. 725-730 ◽  
Author(s):  
P. S. Pawlik ◽  
H. Reismann

A radially directed load is suddenly applied to a portion of the outer surface of a circular cylindrical shell which responds in a state of plane strain. An analytical solution for the resulting dynamic response is obtained within the context of linear elasticity theory, Flu¨gge shell theory, and an “improved” shell theory. A comparison of results for specific loading conditions indicates that the improved theory is far superior to the Flu¨gge theory in terms of predicting both the magnitude and characteristics of the response. However, as expected, neither shell theory satisfactorily predicts the wave character of the initial response.


2007 ◽  
Vol 51 (02) ◽  
pp. 94-103
Author(s):  
Li Xuebin

Following Flu¨ gge's exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of a circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion. The responses of displacements, strain, and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.


2002 ◽  
Vol 46 (03) ◽  
pp. 201-207
Author(s):  
Li Xuebin ◽  
Chen Yaju

An analysis is presented for the free vibration of an orthotropic circular cylindrical shell subjected to hydrostatic pressure. Based on Flügge shell theory, the equations of free vibrations of an orthotropic circular cylindrical shell under hydrostatic pressure are obtained. For shear diaphragms at both ends, the resulting characteristic equations about pressure and frequency are given. These two parameters are calculated exactly. The effect of the shell's parameters (L/R, h/R) and material properties on the free vibration characteristics are studied in detail. Differences between Love-Timoshenko, Donnell equations and that of the Flügge theory are examined as well.


1982 ◽  
Vol 49 (1) ◽  
pp. 108-114 ◽  
Author(s):  
K. Chandrashekhara ◽  
P. Gopalakrishnan

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.


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