Analytical Approach to the Derivation of the Stress Field of a Cylindrical Shell with a Circular Hole Under Axial Tension

2021 ◽  
pp. 115-130
Author(s):  
Stanislava V. Kashtanova ◽  
Alexey V. Rzhonsnitskiy
Keyword(s):  
Cylindrical Shell ◽  
Stress Field ◽  
Circular Hole ◽  
Analytical Approach ◽  
Axial Tension

scholarly journals An Analytical Approach to Obtaining the Stress Field of a Cylindrical Shell with a Circular Hole under Tension

2021 ◽  
pp. 64-75
Author(s):  
S. V Kashtanova ◽  
A. V Rzhonsnitskiy
Keyword(s):  
Cylindrical Shell ◽  
Circular Hole ◽  
Main Parameter ◽  
Analytical Approach ◽  
Analytical Study ◽  
Infinite System ◽  
Basis Functions ◽  
Exact Equation ◽  
Algebraic Equations ◽  
Mechanical Nature

The problem of a cylindrical shell with a circular hole under uniaxial tension is considered. The main obstacle of solving this problem is the necessity to find such coefficients in the expansion of the solution into a sum of basis functions, for which this solution satisfies the boundary conditions. The study of the classical works led to understanding that none of the so far proposed approaches can be considered successfully, and the results of these approaches differ, so it is not clear, which results can be used as a basis. In the present paper, a new analytical approach to studying this issue is proposed. It allows expanding the range of applicability of the solution and gives the opportunity for the analytical study of the stress state. The idea consists in expanding each of the basis functions in a Fourier series by dividing the variables, which allows obtaining explicitly an infinite system of algebraic equations for finding coefficients. One of the important steps of this research is that the authors were able to prove which exact equation is a linear combination of the others and exclude, which made it possible to compose a reduced system for finding unknown coefficients. The proposed approach, in contrast to most classical works, does not impose mathematical restrictions on the values of the main parameter characterizing the cylindrical shell. The existing restrictions are of mechanical nature, as larger cutouts require another model. Moreover, the numerical results obtained by the new method are presented in a fairly complete manner and they are compared with the results of the classical works.

Stress Field Near a Nanosized Spheroidal Cavity under Bi-Axial Tension Perpendicular to the Revolution Axis

2008 ◽  
Vol 33-37 ◽  
pp. 1005-1010
Author(s):  
Zhi Ying Ou ◽  
Gang Feng Wang ◽  
Tie Jun Wang
Keyword(s):  
Surface Energy ◽  
Stress Field ◽  
Elasticity Theory ◽  
Surface Elasticity ◽  
Elastic Field ◽  
Classical Elasticity ◽  
Axial Tension ◽  
Spheroidal Cavity ◽  
Shape And Size ◽  
The Revolution

The elastic field around a nanosized spheroidal cavity is derived on the basis of surface elasticity theory. The effects of surface energy, shape and size of the cavity are discussed. It is seen that the stress field near the nanosized cavity depends on the shape and the size of the cavity as well as the properties of the surface. These new characteristics are different from those predicted by the classical elasticity and may illuminate some new mechanisms at nanoscale.

scholarly journals Analytical Approach to Compute the Internal Stress Field of NEMS Considering Casimir Forces

2011 ◽  
Vol 10 ◽  
pp. 3757-3763 ◽  
Author(s):  
Javab Abdi ◽  
Yaghoob Tadi Beni ◽  
Amin Reza Noghrehabadi ◽  
Ali Koochi ◽  
Asieh Sadat Kazemi ◽  
...  
Keyword(s):  
Stress Field ◽  
Internal Stress ◽  
Analytical Approach ◽  
Casimir Forces ◽  
Internal Stress Field

Influence of Material Orthotropy on the State of Stress Around a Circular Hole in a Cylindrical Shell

1977 ◽  
Vol 99 (3) ◽  
pp. 454-458 ◽  
Author(s):  
H. V. Lakshminarayana ◽  
S. Viswanath
Keyword(s):  
Cylindrical Shell ◽  
Circular Hole ◽  
Numerical Solutions ◽  
Laminated Composite ◽  
The State ◽  
Pressure Loading ◽  
State Of Stress ◽  
Loading Matrix ◽  
Shell Finite Element ◽  
Anisotropic Cylindrical Shell

Numerical solutions are obtained for stresses around a circular hole in laminated composite cylindrical shells subjected to uniform internal pressure loading. Matrix method of structural analysis using a high-precision triangular laminated anisotropic cylindrical shell finite element is employed. Results are presented to show significant influence of composite material systems, winding patterns and curvatures on the state of stress around the opening.

Stress Concentration in a Cylindrical Shell Containing a Circular Hole

1971 ◽  
Vol 93 (4) ◽  
pp. 953-961 ◽  
Author(s):  
N. J. I. Adams
Keyword(s):  
Cylindrical Shell ◽  
Stress Concentration ◽  
Hole Radius ◽  
Axial Tension ◽  
State Of Stress ◽  
Curvature Parameter ◽  
Circular Cutout ◽  
Shell Equations ◽  
Plate Solution ◽  
Limiting Value

The state of stress in a cylindrical shell containing a circular cutout was determined for axial tension, torsion, and internal pressure loading. The solution was obtained for the shallow shell equations by a variational method. The results were expressed in terms of a nondimensional curvature parameter which was a function of shell radius, shell thickness, and hole radius. The function chosen for the solution was such that when the radius of the cylindrical shell approaches infinity, the flat-plate solution was obtained. The results are compared with solutions obtained by more rigorous analytical methods, and with some experimental results. For small values of the curvature parameter, the agreement is good. For higher values of the curvature parameter, the present solutions indicate a limiting value of stress concentration, which is in contrast to previous results.

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.

Comments on "Stresses about a Circular Hole in a Cylindrical Shell"

AIAA Journal ◽  
1966 ◽  
Vol 4 (4) ◽  
pp. 0765a-0765a ◽  
Author(s):  
ALEKSANDER KORNECKI
Keyword(s):  
Cylindrical Shell ◽  
Circular Hole
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