Closure to “Discussion of ‘Analyses of Axisymmetric Upsetting and Plane-Strain Side-Pressing of Solid Cylinders by the Finite Element Method’” (1971, ASME J. Eng. Ind., 93, p. 454)

1971 ◽  
Vol 93 (2) ◽  
pp. 454-454
Author(s):  
C. H. Lee ◽  
Shiro Kobayashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Strain ◽  
The Finite Element Method ◽  
Element Method

Analyses of Axisymmetric Upsetting and Plane-Strain Side-Pressing of Solid Cylinders by the Finite Element Method

1971 ◽  
Vol 93 (2) ◽  
pp. 445-454 ◽  
Author(s):  
C. H. Lee ◽  
Shiro Kobayashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plastic Zone ◽  
Plane Strain ◽  
Deformation Characteristics ◽  
Stress Distributions ◽  
The Finite Element Method ◽  
Percent Reduction ◽  
Zone Development ◽  
Element Method

Detailed studies of the deformation characteristics in axisymmetric upsetting and plane-strain side-pressing were attempted by the finite element method. Solutions were obtained up to a 33 percent reduction in height in axisymmetric upsetting and up to a 19 percent reduction in height in side-pressing, under conditions of complete sticking at the tool-workpiece interface. Load-displacement curves, plastic zone development, and strain and stress distributions were presented, and some of the computed solutions were compared with those found experimentally.

scholarly journals Voids Nucleation at Inclusions of Various Shapes in Front of the Crack in Plane Strain

2016 ◽  
Vol 61 (3) ◽  
pp. 1587-1592 ◽  
Author(s):  
A. Neimitz ◽  
U. Janus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Distribution ◽  
Stress Field ◽  
Plane Strain ◽  
Crack Front ◽  
The Finite Element Method ◽  
Element Method

Abstract An analysis is presented of the stress field in and around inclusions of various shapes. Results were obtained by the finite element method. Inclusions were located within elementary cells located at the centre of the specimen next to the crack front. The influence of an in-plane constraint on the stress distribution was tested.

Plane strain sliding contact of multilayer magnetic storage thin-films using the finite element method

2009 ◽  
Vol 15 (7) ◽  
pp. 1097-1110 ◽  
Author(s):  
Raja R. Katta ◽  
Emerson Escobar Nunez ◽  
Andreas A. Polycarpou ◽  
Sung-Chang Lee
Keyword(s):  
Thin Films ◽  
Finite Element Method ◽  
Finite Element ◽  
Plane Strain ◽  
Sliding Contact ◽  
Magnetic Storage ◽  
The Finite Element Method ◽  
Element Method

Analysis of Hydrostatic Extrusion by the Finite Element Method

1972 ◽  
Vol 94 (2) ◽  
pp. 697-703 ◽  
Author(s):  
K. Iwata ◽  
K. Osakada ◽  
S. Fujino
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Strain ◽  
Frictional Coefficient ◽  
Hydrostatic Extrusion ◽  
Displacement Curve ◽  
Element Solution ◽  
The Finite Element Method ◽  
Entry And Exit ◽  
Element Method

An elastoplastic analysis of hydrostatic extrusion is made using the finite element method. The effect of frictional coefficient on the spread of plastic zone, the pressure-displacement curve, and the stress and the strain distributions are studied for the non-steady state in plane-strain and axisymmetric extrusions. Comparisons of results between the finite element solution and slip-line solution and between plane-strain and axisymmetric extrusions are presented. Tensile stresses on the surface of the extruded part behind the die are found to exist. It is also found that the die pressure is high near the die entry and exit and that the surface of the billet in front of the die entry tends to contract.

scholarly journals Finite element method with account of singularity for mixed mode cracks

2020 ◽  
pp. 220-236
Author(s):  
A. M Tartygasheva ◽  
V. N Shlyannikov ◽  
A. V Tumanov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Mixed Mode ◽  
Singular Boundary ◽  
The Finite Element Method ◽  
Central Crack ◽  
Distribution Features ◽  
Element Method

The paper deals with obtaining an analytical solution for stiffness matrix coefficients at a crack tip area for mixed mode cracks in plane strain conditions. The numerical study is focused on an infinite plate with a straight-through central crack under mixed loading. Analytical solutions are obtained as kinematic boundary conditions for plane strain. We analyzed distribution features of the stress-strain state fields and stress intensity coefficients at the top of the crack area, determined using the finite element method taking into account the singularity. The analytical formulas are obtained which set the kinematic conditions for a general and special case of loading a plate with a defect in the elastic setting for the case of plane deformation. The comparative analysis of the numerical results is presented for two cases of forming the design diagram of the top of the crack: the traditional method of creating a mathematical cut and the finite element method taking into account the singularity. The advantage of using the finite element method considering the singularity is found. We used an example of a plate with a through straight rectilinear central crack with the equal biaxial tension to show that setting the boundary conditions at the top of the crack taking into account the singularity allows one to significantly reduce dimensions of a calculation scheme of the finite element method and keep the calculation accuracy. It is concluded that such a formulation can be applied in an elastic-plastic formulation. The comparison between the classical finite element solution and finite element with singularity is presented. The convenience of the finite element method with singular boundary conditions is demonstrated.

Finite Plane Strain of Incompressible Elastic Solids by the Finite Element Method

1968 ◽  
Vol 19 (3) ◽  
pp. 254-264 ◽  
Author(s):  
J. Tinsley Oden
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Plane Strain ◽  
Simple Shear ◽  
Finite Elasticity ◽  
The Finite Element Method ◽  
Finite Plane ◽  
Elastic Solids ◽  
Non Linear ◽  
Element Method

SummaryThe finite element method is extended to the problem of finite plane strain of elastic solids. A highly elastic body subjected to two-dimensional deformations is represented by an assembly of triangular elements of finite dimension. The displacement fields within each element are approximated by linear functions of the local coordinates. Non-linear stiffness relations involving generalised node forces and displacements are derived from energy considerations. For demonstration purposes, the non-linear stiffness equations are applied to the problems of finite simple shear and generalised shear. For finite simple shear, it is shown that these relations are in exact agreement with finite elasticity theory. Convergence rates of finite element representations of these problems are briefly examined.

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