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On the Use of a Plane-Strain Model to Solve Generalized Plane-Strain Problems
Journal of Applied Mechanics, 1997Many composite problems are generalized plane strain in nature. They are often solved using three-dimensional finite element analyses. We propose a technique to solve these problems with a plane-strain model, which is achieved by introducing some artificial out-of-plane thermal strains in a two-dimensional finite element analysis.
Hu, Shoufeng, Pagano, N. J.
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On uniqueness and strain localization in plane strain and plane stress elastoplasticity
Mechanics Research Communications, 1990Etude de la plasticite associee, avec une surface de plasticite rendant compte du durcissement et de l'adoucissement mecanique sous l'hypothese d'un petit gradient de deplacement.
Bigoni, Davide, T. Hueckel
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Materials Science Forum, 2019
In this paper, we obtained analytical solutions of the fields of strain tensors under uniaxial tension of a rigidplasticstrip underthe conditions of a plane stress state.The topicalityof the construction of these solutions is connected with significant difficulties in determining the strain fields by numerical methods (for example, the finite element ...
A.L. Grigorieva +2 more
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In this paper, we obtained analytical solutions of the fields of strain tensors under uniaxial tension of a rigidplasticstrip underthe conditions of a plane stress state.The topicalityof the construction of these solutions is connected with significant difficulties in determining the strain fields by numerical methods (for example, the finite element ...
A.L. Grigorieva +2 more
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Curvature and Out-of-Plane-Strain for Generalized Plane Strain
Journal of Applied Mechanics, 1972Out-of-plane strains and stresses are determined using reciprocity for the central region of very long bars (approaching infinite length) of uniform transverse cross section subjected to the same in-plane loads on every cross section. The loading explicitly specifies no end loads on the bars.
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2020
Finding the slip intensity when setting the shear resistance in a general form leads to rather complex integration–differential equations. Therefore, the determination of strains is associated with big mathematical difficulties. This chapter studies a partial case when only two addends are preserved in the shear resistance operator, which contain the ...
Valentin Molotnikov +1 more
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Finding the slip intensity when setting the shear resistance in a general form leads to rather complex integration–differential equations. Therefore, the determination of strains is associated with big mathematical difficulties. This chapter studies a partial case when only two addends are preserved in the shear resistance operator, which contain the ...
Valentin Molotnikov +1 more
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A characterization of plane strain
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1991Abstract A new characterization of plane strain is given that holds even under weak regularity hypotheses on the deformation.
John Macleod Ball, R. D. James
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1979
The plane problems to be discussed in this chapter occur as exact or approximate solutions of certain three-dimensional problems in the theory of elasticity. For isotropic materials these solutions may be expressed in terms of biharmonic functions of two variables. The use of functions of the corresponding complex variable is clearly indicated, because
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The plane problems to be discussed in this chapter occur as exact or approximate solutions of certain three-dimensional problems in the theory of elasticity. For isotropic materials these solutions may be expressed in terms of biharmonic functions of two variables. The use of functions of the corresponding complex variable is clearly indicated, because
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Plane Stress and Plane Strain Problems
2019Many structural members can be analyzed applying simplifying assumptions of plane stress or plane strain state. Examples include plates under in-plane loading, thick pipes under internal pressure, rotating discs, etc. Although many problems of this type can be solved in a closed analytical form assuming linear-elastic material behavior (Altenbach et al,
Konstantin Naumenko, Holm Altenbach
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Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1953
Abstract A general theory of plane strain, valid for large elastic deformations of isotropic materials, is developed using a general system of co-ordinates. No restriction is imposed upon the form of the strain-energy function in the formulation of the basic theory, apart from that arising naturally from the assumption of plane strain.
Adkins, J. E. +2 more
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Abstract A general theory of plane strain, valid for large elastic deformations of isotropic materials, is developed using a general system of co-ordinates. No restriction is imposed upon the form of the strain-energy function in the formulation of the basic theory, apart from that arising naturally from the assumption of plane strain.
Adkins, J. E. +2 more
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Metals Technology, 1984
AbstractThe forces and stresses associated with the final stages of die-corner fillout during a closed-die forging operation are difficult to predict. This problem was investigated for the forging of high-conductivity copper under plane-strain conditions, using an upper-bound method.
J. M. Monaghan, A. A. Torrance
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AbstractThe forces and stresses associated with the final stages of die-corner fillout during a closed-die forging operation are difficult to predict. This problem was investigated for the forging of high-conductivity copper under plane-strain conditions, using an upper-bound method.
J. M. Monaghan, A. A. Torrance
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