Classical Solution and Edge Effect in the Problem of Stability of an Axially Compressed Cylindrical Shell

2020 ◽  
Vol 22 (1) ◽  
pp. 48-54
Author(s):  
Guyk A. Manuylov ◽  
Sergey B. Kosytsyn ◽  
Maksim M. Begichev
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Critical Load ◽  
Classical Solution ◽  
Edge Effect ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Critical Stresses ◽  
Membrane Deformations ◽  
Initial Arrangement

The classical solution for critical stresses in the problem of stability of a circular longitudinally compressed cylindrical shell consists of two terms, reflecting the ability of the shell to resist buckling due to bending and membrane deformations. However, with usual boundary conditions the classical solution appears only with the absence of the Poisson expansion of a shell. With a non-zero Poisson's ratio, an axisymmetric edge effect presents. It reduces the critical load and causes the initial arrangement of its own forms to change as the load increases.

Evaluation of Effective Elastic Mechanical Properties of Graphene Sheets

2012 ◽  
Author(s):  
Khalid I. Alzebdeh
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Graphene Sheet ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Graphene Sheets ◽  
Numerical Predictions

The mechanical behaviour of a single-layer nanostructured graphene sheet is investigated using an atomistic-based continuum model. This is achieved by equating the stored energy in a representative unit cell for a graphene sheet at atomistic scale to the strain energy of an equivalent continuum medium under prescribed boundary conditions. Proper displacement-controlled (essential) boundary conditions which generate a uniform strain field in the unit cell model are applied to calculate one elastic modulus at a time. Three atomistic finite element models are adopted with an assumption that force interactions among carbon atoms can be modeled by either spring-like or beam elements. Thus, elastic moduli for graphene structure are determined based on the proposed modeling approach. Then, effective Young’s modulus and Poisson’s ratio are extracted from the set of calculated elastic moduli. Results of Young’s modulus obtained by employing the different atomistic models show a good agreement with the published theoretical and numerical predictions. However, Poisson’s ratio exhibits sensitivity to the considered atomistic model. This observation is supported by a significant variation in estimates as can be found in the literature. Furthermore, isotropic behaviour of in-plane graphene sheets was validated based on current modeling.

scholarly journals Nonlinear analysis of buckling and postbuckling for axially compressed functionally graded cylindrical panels with the Poisson's ratio varying smoothly along the thickness

2012 ◽  
Vol 34 (1) ◽  
pp. 27-44 ◽  
Author(s):  
Dao Van Dung ◽  
Le Kha Hoa
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Compressive Load ◽  
Cylindrical Panel ◽  
Functionally Graded ◽  
Poisson's Ratio ◽  
Postbuckling Behavior ◽  
Nonlinear Buckling ◽  
Dimensional Parameter ◽  
Classical Shell Theory

In this paper an approximate analytical solution to analyze the nonlinear buckling and postbuckling behavior of imperfect functionally graded panels with the Poisson's ratio also varying smoothly along the thickness is investigated. Based on the classical shell theory and von Karman's assumption of kinematic nonlinearity and applying Galerkin procedure, the equations for finding critical loads and load-deflection curves of cylindrical panel subjected to axial compressive load with two types boundary conditions, are given. Especially, the stiffness coefficients are analyzed in explicit form. Numerical results show various effects of the inhomogeneous parameter, dimensional parameter, boundary conditions on nonlinear stability of panel. An accuracy of present theoretical results is verified by the previous well-known results.

scholarly journals Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension

1952 ◽  
Vol 19 (4) ◽  
pp. 526-528
Author(s):  
M. L. Williams
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Poisson's Ratio ◽  
Vertex Angle ◽  
Stress Singularities ◽  
Stress Concentrations ◽  
Various Boundary Conditions ◽  
Free Case

Abstract As an analog to the bending case published in an earlier paper, the stress singularities in plates subjected to extension in their plane are discussed. Three sets of boundary conditions on the radial edges are investigated: free-free, clamped-clamped, and clamped-free. Providing the vertex angle is less than 180 degrees, it is found that unbounded stresses occur at the vertex only in the case of the mixed boundary condition with the strength of the singularity being somewhat stronger than for the similar bending case. For vertex angles between 180 and 360 degrees, all the cases considered may have stress singularities. In amplification of some work of Southwell, it is shown that there are certain analogies between the characteristic equations governing the stresses in extension and bending, respectively, if ν, Poisson’s ratio, is replaced by −ν. Finally, the free-free extensional plate behaves locally at the origin exactly the same as a clamped-clamped plate in bending, independent of Poisson’s ratio. In conclusion, it is noted that the free-free case analysis may be applied to stress concentrations in V-shaped notches.

scholarly journals FREE OSCILLATIONS OF PIPELINES LIKE THIN CYLINDRICAL SHELLS WITH REGARDS TO INTERNAL PRESSURE

2019 ◽  
Vol 3 (1) ◽  
pp. 46-52
Author(s):  
Nuriddin Kurbonovich Esanov ◽  
Keyword(s):  
Cylindrical Shell ◽  
Internal Pressure ◽  
Cross Section ◽  
Modulus Of Elasticity ◽  
Poisson’S Ratio ◽  
Cylindrical Shells ◽  
Poisson's Ratio ◽  
Free Oscillations ◽  
Closed Cylindrical Shell ◽  
The Cross

The paper deals with the free oscillations of pipelines as thin cylindrical shells with regard to internal pressure. The pipeline is presented in the form of a closed cylindrical shell with a radius of the midline of the cross section. The material is considered isotropic with density, modulus of elasticity, and Poisson’s ratio

PROPAGATION AND RESONANCE OF LONGITUDINAL WAVES IN PRISMATIC RODS

1936 ◽  
Vol 14a (2) ◽  
pp. 48-55
Author(s):  
R. Ruedy
Keyword(s):  
Boundary Conditions ◽  
Poisson’S Ratio ◽  
Equations Of Motion ◽  
Poisson's Ratio ◽  
Longitudinal Waves ◽  
Fundamental Frequencies ◽  
Cubic Equation ◽  
Resonance Frequencies ◽  
Fourth Series ◽  
Shearing Motion

For vibrations involving shearing and rotation, and for those involving both distortion and dilatation, the equations of motion combined with the boundary conditions yield in the simplest case a cubic equation for the resonance frequencies; its solution depends on Poisson's ratio and on the resonance frequencies fx, fy, fz, which the rod possesses when in pure shearing motion in the direction of its three axes. Three series of resonance frequencies are obtained when fy and fz are constant and the frequencies of the overtones are inserted for fx. A fourth series of resonance frequencies begins above the highest of the fundamental frequencies fx, fy, fz.

The Center of Shear Again

1943 ◽  
Vol 10 (2) ◽  
pp. A62-A64
Author(s):  
W. R. Osgood
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Unique Point ◽  
Usual Definition ◽  
Different Boundary Conditions ◽  
Definition Of

Abstract There is disagreement in the literature as to the location of the center of shear. Timoshenko, for example, states that the position of this point depends upon Poisson’s ratio, whereas Trefftz says that it does not. Both Timoshenko’s and Trefftz’ solutions are compatible with the usual definition of the center of shear. The disagreement may be attributed to the assumptions of different boundary conditions. In this paper the boundary conditions are examined, and a definition of the center of shear is proposed that leads to a unique point for any cross section.

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