Collapse loads for thin cantilevers with rectangular holes along the centre-line

1976 ◽  
Vol 11 (2) ◽  
pp. 84-96 ◽  
Author(s):  
A S Ranshi ◽  
W Johnson ◽  
N R Chitkara
Keyword(s):  
Lower Bound ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Slip Line ◽  
Rectangular Cross Section ◽  
Local Buckling ◽  
Experimental Results ◽  
Line Field ◽  
Theoretical Results

Plane stress slip-line field solutions, which provide the modes of yielding and the corresponding yield loads, are presented for the plastic bending of end-loaded thin cantilevers of rectangular cross-section containing rectangular holes. The theoretical results obtained from these solutions are compared with some experimental results and those obtained from plane strain slip-line fields and lower bound estimates, all presented previously by the authors (1)‡. It is observed that the correlation of the experimental results was much better with the plane stress solutions than with either the plane strain or lower bound results. The effect of adjacent holes and possible lateral or local buckling on the ultimate strength of the cantilevers is also examined.

Plane-Stress yielding of cantilevers in bending due to combined shear and axial load

1974 ◽  
Vol 9 (2) ◽  
pp. 67-77 ◽  
Author(s):  
W Johnson ◽  
N R Chitkara ◽  
A S Ranshi
Keyword(s):  
Lower Bound ◽  
Plane Stress ◽  
Slip Line ◽  
Axial Load ◽  
Rectangular Cross Section ◽  
Field Analysis ◽  
Collapse Load ◽  
Line Field ◽  
Deformation Patterns ◽  
Deformation Modes

A plane-stress slip-line field analysis has been made of the possible plastic deformation modes of a built-in cantilever beam of rectangular cross-section subjected to a shear force at the free end with or without an axial load. Plastic-collapse loads for the several types of deformation patterns suggested are computed and the results presented in detail in the form of curves. Some simple upper- and lower-bound estimates to the collapse load have also been determined and are compared with both the plane-stress slip-line results and those presented by Green (1), plane-strain conditions being assumed. The agreement between the plane-stress slip-line fields and the assumed lower-bound results is found to be excellent.

A Slip Line Field Solution of the Free Oblique Continuous Cutting Problem in Conditions of Light Friction at Chip-Tool Interface

1980 ◽  
Vol 102 (4) ◽  
pp. 310-314 ◽  
Author(s):  
W. A. Morcos
Keyword(s):  
Plane Strain ◽  
Slip Line ◽  
Metal Cutting ◽  
Orthogonal Cutting ◽  
Cutting Parameters ◽  
Experimental Results ◽  
Line Field ◽  
Slip Line Field ◽  
Field Solution ◽  
Cutting Problem

Lee and Shaffer’s slip line field solution [11] for orthogonal cutting is generalized to the free oblique continuous cutting problem in plane strain. Comparison of the results as predicted by this solution with those of the plane strain modified Merchant model [8] and experimental results is achieved for some key metal cutting parameters. It is shown that in some respect, the plane strain modified Merchant model [8] predicts values of parameters which are closer to experimental results.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

Slip Line Field Analysis of a Simple Plane Strain Closed-Die Forging

1989 ◽  
Vol 203 (2) ◽  
pp. 91-99
Author(s):  
M V Srinivas ◽  
P Alva ◽  
S K Biswas
Keyword(s):  
Velocity Field ◽  
Plane Strain ◽  
Slip Line ◽  
Field Analysis ◽  
Line Field ◽  
Slip Line Field ◽  
Die Forging ◽  
Closed Die Forging ◽  
Cavity Filling ◽  
Single Cavity

A slip line field is proposed for symmetrical single-cavity closed-die forging by rough dies. A compatible velocity field is shown to exist. Experiments were conducted using lead workpiece and rough dies. Experimentally observed flow and load were used to validate the proposed slip line field. The slip line field was used to simulate the process in the computer with the objective of studying the influence of flash geometry on cavity filling.

Damage and healing mechanics in plane stress, plane strain, and isotropic elasticity

2020 ◽  
Vol 29 (8) ◽  
pp. 1246-1270 ◽  
Author(s):  
George Z Voyiadjis ◽  
Chahmi Oucif ◽  
Peter I Kattan ◽  
Timon Rabczuk
Keyword(s):  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Elastic Energy ◽  
Elastic Stiffness ◽  
Self Healing ◽  
Theoretical Formulation ◽  
Stiffness Reduction ◽  
Energy Equivalence ◽  
Isotropic Elasticity

The present paper presents a theoretical formulation of different self-healing variables. Healing variables based on the recovery in elastic modulus, shear modulus, Poisson's ratio, and bulk modulus are defined. The formulation is presented in both scalar and tensorial cases. A new healing variable based on elastic stiffness recovery in proposed, which is consistent with the continuum damage-healing mechanics. The evolution of the healing variable calculated based on cross-section as function of the healing variable calculated based on elastic stiffness is presented in both hypotheses of elastic strain equivalence and elastic energy equivalence. The components of the fourth-rank healing tensor are also obtained in the case of isotropic elasticity, plane stress, and plane strain. It is found that the healing variable calculated based on elastic stiffness reduction is greater than the one calculated based on cross-section reduction in the case of the hypothesis of elastic energy equivalence. It is also shown that the healing tensor fits the boundary conditions of the healing variable in the case of scalar formulation.

The Investigation of the Kinetic Energy of Slug in a Horizontal Channel Using VOF Method

2018 ◽  
Author(s):  
Nariman Ashrafi ◽  
Mohammad Reza Ansari ◽  
Armin Chegini ◽  
Ali Sadeghi
Keyword(s):  
Kinetic Energy ◽  
Pressure Gradient ◽  
Cross Section ◽  
Volume Fraction ◽  
Rectangular Cross Section ◽  
Vof Method ◽  
Experimental Results ◽  
Two Phase ◽  
Trapped Air ◽  
Helmholtz Condition

In this article, two-phase slug regime in a duct with rectangular cross-section is investigated numerically, using the volume of fluid (VOF) method. Equations of mass, momentum and advection of volume fraction are solved accompanying k-∈ realizable turbulence equations. To ensure the creditability, numerical results have been compared with experimental results using same geometry. With occurrence of instability in the entrance of duct, Kelvin-Helmholtz condition satisfies and with increasing instability, slug phenomenon occurs. With closing the cross-section of duct, slug causes pressure gradient in it. Trapped air behind a slug transfers the momentum and increases the kinetic energy of slug. In this research the kinetic energy of a slug is investigated.

Condensation Phenomena in High Speed Flow of Steam—Experimental Apparatus

1973 ◽  
Vol 187 (1) ◽  
pp. 199-205 ◽  
Author(s):  
B. A. Campbell ◽  
F. Bakhtar
Keyword(s):  
Cross Section ◽  
Test Section ◽  
High Speed ◽  
Rectangular Cross Section ◽  
Experimental Results ◽  
Theoretical Treatment ◽  
Wet Steam ◽  
High Speed Flow ◽  
Speed Flow ◽  
Experimental Apparatus

The paper describes a steam circuit for studies of nucleation and behaviour of wet steam. The test section is a duct of rectangular cross-section in which particular geometries are produced by fitting shaped profiles to its sides. To deliver steam to the test section, at required conditions, a turbine, cooler and superheater are included in the circuit. The experimental results presented are concerned with the variations of Wilson point as a function of pressure. Comparisons are made with the results of a theoretical treatment already published (1)‡ and agreement is shown to be good.

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