Stress State Around an Elliptic Hole in a Conical Shell Under Tension

1973 ◽  
Vol 95 (1) ◽  
pp. 201-207 ◽  
Author(s):  
S. I. Chou
Keyword(s):  
Stress State ◽  
Conical Shell ◽  
Elliptic Hole ◽  
Cone Angle ◽  
Major Axis ◽  
Membrane Stress ◽  
Arbitrary Angle ◽  
Crack Problems ◽  
Curvature Parameter ◽  
Square Root Singularity

Membrane stress state around an elliptic hole in a conical shell under tension is determined by perturbation in terms of a nondimensional cone angle ε and a nondimensional curvature parameter β. Stress state around the hole in terms of the eccentricity of the elliptic hole whose major axis makes an arbitrary angle with the axis of the shell is given. For a crack making an arbitrary angle with the axis of the shell, stress state in the vicinity of the crack tip is given and shows the inverse square root singularity peculiar to crack problems.

Stresses Around an Elliptic Hole in a Cylindrical Shell

1969 ◽  
Vol 36 (1) ◽  
pp. 39-46 ◽  
Author(s):  
M. V. V. Murthy
Keyword(s):  
Cylindrical Shell ◽  
Stress Distribution ◽  
Theoretical Analysis ◽  
Circular Cylindrical Shell ◽  
Elliptic Hole ◽  
Major Axis ◽  
Axial Tension ◽  
Method Of Solution ◽  
Bending Stresses ◽  
Curvature Parameter

A theoretical analysis is presented for the membrane and bending stresses around an elliptic hole in a long, thin, circular cylindrical shell with the major axis of the hole parallel to the axis of the shell. The analysis has been carried out for the case of axial tension. The method of solution involves a perturbation in a curvature parameter and the results obtained are valid, if the hole is small in size compared to the shell. Formulas, from which the complete stress distribution at the hole can be calculated, are presented.

Stresses Around a Rib-Reinforced Elliptic Hole in a Circular Cylindrical Shell Under Tension

1977 ◽  
Vol 99 (1) ◽  
pp. 12-16
Author(s):  
S. I. Chou ◽  
Om P. Chaudhary
Keyword(s):  
Cylindrical Shell ◽  
Stress State ◽  
Stress Concentration ◽  
Cross Section ◽  
Circular Cylindrical Shell ◽  
Elliptic Hole ◽  
Axial Tension ◽  
Bending Stresses ◽  
Curvature Parameter ◽  
Moduli Of Elasticity

The stress state around a rib reinforced elliptic hole in a circular cylindrical shell under axial tension at its ends is determined by perturbation in terms of a curvature parameter and the eccentricity of the elliptic hole. The reinforcing rib is assumed to be rectangular in cross section, and has extensional, flexural and torsional rigidities. Nondimensional membrane stresses and bending stresses around the hole are given for different values of E1/E1 where E1 and E are moduli of elasticity of the rib and the shell respectively. It is shown that the reinforcing rib substantially reduces the stress concentration around the hole.

Stability and vibration analysis of an axially moving thin walled conical shell

2021 ◽  
pp. 107754632199760
Author(s):  
Hossein Abolhassanpour ◽  
Faramarz Ashenai Ghasemi ◽  
Majid Shahgholi ◽  
Arash Mohamadi
Keyword(s):  
Natural Frequency ◽  
Conical Shell ◽  
Shell Theory ◽  
Cone Angle ◽  
Theory Of Elasticity ◽  
Lower Velocity ◽  
Motion Equations ◽  
Conical Shells ◽  
Divergence Instability ◽  
Axially Moving

This article deals with the analysis of free vibration of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell shell theory assumptions, Hamilton principle, and Galerkin method, the motion equations of axially moving truncated conical shells are derived. Then, the perturbation method is used to obtain the natural frequency of the system. One of the most important and controversial results in studies of axially moving structures is the velocity detection of critical points. Therefore, the effect of velocity on the creation of divergence instability is investigated. The other important goal in this study is to investigate the effect of the cone angle. As a novelty, our study found that increasing or decreasing the cone angle also affects the critical velocity of the structure in addition to changing the natural frequency, meaning that with increasing the cone angle, the instability occurs at a lower velocity. Also, the effect of other parameters such as aspect ratio and mechanical properties on the frequency and instability points is investigated.

Stress State of Thin Spherical Shells with an Off-Center Elliptic Hole

2003 ◽  
Vol 39 (5) ◽  
pp. 595-598 ◽  
Author(s):  
Vladimir Maksimyuk ◽  
V. P. Mulyar ◽  
Ivan Chernyshenko
Keyword(s):  
Stress State ◽  
Elliptic Hole ◽  
Spherical Shells

Bifurcation buckling from a membrane stress state

2012 ◽  
Vol 90 (7) ◽  
pp. 867-881 ◽  
Author(s):  
Herbert A. Mang ◽  
Gerhard Höfinger
Keyword(s):  
Stress State ◽  
Membrane Stress ◽  
Bifurcation Buckling

Evaluating actuator distributions in simply supported truncated thin conical shell with embedded piezoelectric layers

2018 ◽  
Vol 29 (12) ◽  
pp. 2641-2659 ◽  
Author(s):  
Rasa Jamshidi ◽  
Ali A Jafari
Keyword(s):  
Conical Shell ◽  
Piezoelectric Layer ◽  
Cone Angle ◽  
Expansion Method ◽  
Longitudinal Direction ◽  
Modal Expansion ◽  
Simply Supported ◽  
Modal Expansion Method ◽  
Layer Segmentation ◽  
Distributed Actuator

In this investigation, distributed modal actuator forces of simply supported truncated conical shell embedded by a piezoelectric layer are studied. Piezoelectric layer is distributed on the conical shell surface as actuators. Three types of distributions are considered: longitudinal, circumferential, and diagonal distributions. First, electromechanical equations of the conical shell with embedded piezoelectric actuator layer are extracted. Then modal expansion method is used to define independent modal characteristics of the conical shell. For each kind of distribution, three case studies are considered and evaluated. Results showed that in the longitudinal and diagonal distributed actuator, membrane force in the longitudinal direction is the dominant force and in the circumferential distributed actuator, the membrane force in the circumferential direction is the dominant force. The effects of cone angle, piezoelectric thickness, and piezoelectric layer segmentation on modal forces of each distributed actuator are also studied. In circumferential distributed actuator, modal forces increase as the cone angle increases. This phenomenon in the longitudinal and diagonal distributed actuator is almost reversed. The piezoelectric layer segmentation effect on the modal forces distribution is also evaluated, and it showed that this phenomenon has a critical effect on the modal forces distribution.

scholarly journals Determination of the Stress State of a Piecewise Homogeneous Elastic Body with a Row of Cracks on an Interface Surface Subject to Antiplane Strains with Inclusions at the Tips

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Ali Golsoorat Pahlaviani ◽  
Suren Mkhitaryan
Keyword(s):  
Stress State ◽  
Elastic Body ◽  
Linear Equations ◽  
The Body ◽  
Shear Stresses ◽  
Interface Surface ◽  
Special Cases ◽  
Crack Problems ◽  
Fourier Sine Series

The stress state of a bimaterial elastic body that has a row of cracks on an interface surface is considered. It is subjected to antiplane deformations by uniformly distributed shear forces acting on the horizontal sides of the body. The governing equations of the problem, the stress intensity factors, the deformation of the crack edges, and the shear stresses are derived. The solution of the problem via the Fourier sine series is reduced to the determination of a singular integral equation (SIE) and consequently to a system of linear equations. In the end, the problem is solved in special cases with inclusions. The results of this paper and the previously published results show that the used approach based on the Gauss-Chebyshev quadrature method can be considered as a generalized procedure to solve the collinear crack problems in mode I, II, or III loadings.

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