Buckling of Multiple-Bay Ring-Reinforced Cylindrical Shells Subject to Hydrostatic Pressure

1953 ◽  
Vol 20 (4) ◽  
pp. 469-474
Author(s):  
W. A. Nash
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Middle Surface ◽  
Elastic Buckling ◽  
Elastic Instability ◽  
Total Potential ◽  
External Forces ◽  
Work Done

Abstract An analytical solution is presented for the problem of the elastic instability of a multiple-bay ring-reinforced cylindrical shell subject to hydrostatic pressure applied in both the radial and axial directions. The method used is that of minimization of the total potential. Expressions for the elastic strain energy in the shell and also in the rings are written in terms of displacement components of a point in the middle surface of the shell. Expressions for the work done by the external forces acting on the cylinder likewise are written in terms of these displacement components. A displacement configuration for the buckled shell is introduced which is in agreement with experimental evidence, in contrast to the arbitrary patterns assumed by previous investigators. The total potential is expressed in terms of these displacement components and is then minimized. As a result of this minimization a set of linear homogeneous equations is obtained. In order that a nontrivial solution to this system of equations exists, it is necessary that the determinant of the coefficients vanish. This condition determines the critical pressure at which elastic buckling of the cylindrical shell will occur.

On the elastic buckling of cross-ply composite closed cylindrical shell under hydrostatic pressure

2021 ◽  
Vol 227 ◽  
pp. 108633
Author(s):  
Muhammad Imran ◽  
Dongyan Shi ◽  
Lili Tong ◽  
Ahsan Elahi ◽  
Muqeem Uddin
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Elastic Buckling ◽  
Closed Cylindrical Shell

scholarly journals The Interaction of Frictional Slip and Adhesion for a Stiff Sphere on a Compliant Substrate

2020 ◽  
Vol 87 (3) ◽  
Author(s):  
R. M. McMeeking ◽  
M. Ciavarella ◽  
G. Cricrì ◽  
K.-S. Kim
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Frictional Resistance ◽  
Linear Elastic ◽  
Adhesion Behavior ◽  
Stiff Material ◽  
Surface Microstructures ◽  
Work Done ◽  
Frictional Slip ◽  
Good Agreement

Abstract How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson–Kendall–Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A simple model for the interaction of friction and adhesion is utilized, in which some of the work done against frictional resistance is assumed to be stored reversibly. This behavior is considered to arise from surface microstructures associated with frictional slip such as interface dislocations, where these microstructures store some elastic strain energy in a reversible manner. When it is assumed that a fixed fraction of the work done against friction is stored reversibly, we obtain good agreement with data.

An experimental examination of the dynamical behaviour of a strut in a rigidly jointed truss framework

1963 ◽  
Vol 274 (1357) ◽  
pp. 225-238 ◽  
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Maximum Load ◽  
Dynamical Behaviour ◽  
Strain Rates ◽  
Axial Deformation ◽  
Jump Phenomenon ◽  
Tension Members ◽  
Work Done ◽  
Kinetic And Potential Energies

The relation between axial load and axial deformation for a strut generally involves an increase of deformation with decreasing load after the maximum load is reached. When a truss containing one or more struts is subjected to dead load, it is possible that equilibrium may be lost temporarily while the structure undergoes a ‘dynamic jump’ to a new position of equilibrium. The dynamic jump phenomenon was analyzed theoretically for a simple truss by Davies & Neal (1959). It was shown that the motion is governed by interchanges between the elastic strain energy stored in the tension members, the work done on the strut, and the kinetic and potential energies of the applied load. The present paper describes an experimental investigation into the dynamic jump phenomenon for the same simple truss system. Predictions concerning the collapse load at which the dynamic jump would occur, and the magnitude of the jump, were made using the energy method together with strut characteristics obtained previously under quasistatic conditions. It was found that the collapse loads could be predicted accurately with the aid of these characteristics. However, in order to determine the magnitude of each jump it was necessary to modify the strut characteristics markedly to allow for the effect of high strain rates during the jump in increasing the load sustained by the struts.

Latent Elastic Strain Energy Due to the Residual Stresses in a Plastically Deformed Polycrystal

1967 ◽  
Vol 34 (3) ◽  
pp. 606-611 ◽  
Author(s):  
T. H. Lin ◽  
Marvin Ito
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Residual Stress Field ◽  
Latent Energy ◽  
Energy Part ◽  
Crystallographic Slip ◽  
Work Done

A part of the work done on a plastically deformed metal reappears in the form of heat and the remaining part remains latent in the metal, known as latent energy. Part of this latent energy is the elastic strain energy of the residual stresses of the plastically deformed metal. In this paper, this strain energy in a polycrystal is calculated from the crystallographic slip properties of single crystals. The polycrystalline aggregate is composed of differently oriented cube-shaped crystals, each with one slip plane on which there are three slip directions. Neglecting the inhomogeneity and anisotropy of elastic constants, the polycrystal is taken to be elastically homogeneous and isotropic. The analogy between plastic strain gradient and body force in an infinite elastic medium is used to calculate the residual stress field. The residual stress calculation satisfies the condition of continuity, the equilibrium condition, and the single crystal stress-strain relationship throughout the aggregate. The variation of the latent elastic strain energy with the aggregate stress is shown. A similar method may be used to calculate the latent elastic strain energy of f.c.c. and b.c.c. polycrystals.

Study on Bi-Stable Behaviors of Double-Layered Cylindrical Shell

2011 ◽  
Vol 243-249 ◽  
pp. 5981-5984
Author(s):  
Yao Peng Wu
Keyword(s):  
Cylindrical Shell ◽  
Shell Model ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Stable Structure ◽  
Total Strain ◽  
Total Strain Energy ◽  
Broad Application ◽  
Layered Cylindrical Shell ◽  
External Forces

Bi-stable structure can be stable in both its extended and coiled forms. As a novel deployable structure, it shows a broad application prospect in the field of aeronautics and civil engineering, etc. Considered two cylindrical shells having the same flattening configurations, they can be closely bound together by applying external forces. And the corresponding double-layered cylindrical shell model is proposed. Expressions for the bending and stretching strain energies of the cylindrical shells are presented. Calculations show that total strain energy has two local minimal values, which reveals that the double-layered cylindrical shell has its bi-stability. The corresponding rolled-up radii are thus determined.

An isotropic elasto-damage-plastic micromechanical framework of innovative pothole patching materials featuring high-toughness, low-viscosity nanomolecular resin

2021 ◽  
pp. 105678952110286
Author(s):  
H Zhang ◽  
J Woody Ju ◽  
WL Zhu ◽  
KY Yuan
Keyword(s):  
Strain Energy ◽  
Three Dimensional ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Computational Algorithms ◽  
Mechanical Behaviors ◽  
High Toughness ◽  
Low Viscosity ◽  
Innovative Materials ◽  
Continuum Thermodynamic

In a recent companion paper, a three-dimensional isotropic elastic micromechanical framework was developed to predict the mechanical behaviors of the innovative asphalt patching materials reinforced with a high-toughness, low-viscosity nanomolecular resin, dicyclopentadiene (DCPD), under the splitting tension test (ASTM D6931). By taking advantage of the previously proposed isotropic elastic-damage framework and considering the plastic behaviors of asphalt mastic, a class of elasto-damage-plastic model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation to predict the behaviors of the innovative materials more accurately. Specifically, the governing damage evolution is characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence; the plastic flow is introduced by means of an additive split of the stress tensor. Corresponding computational algorithms are implemented into three-dimensional finite elements numerical simulations, and the outcomes are systemically compared with suitably designed experimental results.

Analysis of Energy Balance When Using Cohesive Zone Models to Simulate Fracture Processes

2002 ◽  
Vol 124 (4) ◽  
pp. 440-450 ◽  
Author(s):  
C. Shet ◽  
N. Chandra
Keyword(s):  
Cohesive Energy ◽  
Cohesive Zone ◽  
Strain Energy ◽  
Fracture Process ◽  
Fracture Process Zone ◽  
Process Zone ◽  
Elastic Strain Energy ◽  
Inelastic Strain ◽  
External Work ◽  
Cohesive Zone Models

Cohesive Zone Models (CZMs) are being increasingly used to simulate fracture and fragmentation processes in metallic, polymeric, and ceramic materials and their composites. Instead of an infinitely sharp crack envisaged in fracture mechanics, CZM presupposes the presence of a fracture process zone where the energy is transferred from external work both in the forward and the wake regions of the propagating crack. In this paper, we examine how the external work flows as recoverable elastic strain energy, inelastic strain energy, and cohesive energy, the latter encompassing the work of fracture and other energy consuming mechanisms within the fracture process zone. It is clearly shown that the plastic energy in the material surrounding the crack is not accounted in the cohesive energy. Thus cohesive zone energy encompasses all the inelastic energy e.g., energy required for grainbridging, cavitation, internal sliding, surface energy but excludes any form of inelastic strain energy in the bounding material.

Finite Element Analysis of the Hydro-Mechanical Punching Process

2006 ◽  
Vol 505-507 ◽  
pp. 871-876
Author(s):  
Jong Hun Yoon ◽  
Hoon Huh ◽  
Yong Sin Lee ◽  
Seung Soo Kim ◽  
E.J. Kim ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Ductile Fracture ◽  
Sheet Material ◽  
Middle Surface ◽  
Initial Crack ◽  
Fracture Criteria ◽  
Element Analysis ◽  
Final Fracture ◽  
Ductile Fracture Criteria ◽  
Punching Process

This paper investigates the characteristics of a hydro-mechanical punching process. The hydro-mechanical punching process is divided into two stages: the first stage is the mechanical half piercing in which an upper punch goes down before the initial crack is occurred; the second stage is the hydro punching in which a lower punch goes up until the final fracture is occurred. Ductile fracture criteria such as the Cockcroft et al., Brozzo et al. and Oyane et al. are adopted to predict the fracture of a sheet material. The index value of ductile fracture criteria is calculated with a user material subroutine, VUMAT in the ABAQUS Explicit. The hydrostatic pressure retards the initiation of a crack in the upper region of the blank and induces another crack in the lower region of the blank during the punching process. The final fracture zone is placed at the middle surface of the blank to the thickness direction. The result demonstrates that the hydro-mechanical punching process makes a finer shearing surface than the conventional one as hydrostatic pressure increases.

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