On the pure bending of an elastic, perfectly plastic curved bar in the state of plane strain

1960 ◽  
Vol 270 (4) ◽  
pp. 301-316
Author(s):  
S.A. Murch
1958 ◽  
Vol 25 (2) ◽  
pp. 239-242
Author(s):  
D. R. Bland ◽  
P. M. Naghdi

Abstract This paper is concerned with a compressible elastic-plastic wedge of an included angle β < π/2 in the state of plane strain. The solution, deduced for an isotropic nonwork-hardening material, employs Tresca’s yield criterion and the associated flow rules. By means of a numerical example the solution is compared with that of an incompressible elastic-plastic wedge in one case (β = π/4) for various positions of the elastic-plastic boundary.


Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.


1957 ◽  
Vol 24 (1) ◽  
pp. 98-104
Author(s):  
P. M. Naghdi

Abstract An elastic, perfectly plastic wedge of an incompressible isotropic material in the state of plane strain is considered, where the stress-strain relations of Prandtl-Reuss are employed in the plastic domain. For a wedge (with an included angle β) subjected to a uniform normal pressure on one boundary, the complete solution is obtained which is valid in the range 0 < β < π/2; this latter limitation is due to the character of the initial yield which depends on the magnitude of β. Numerical results for stresses and displacements are given in one case (β = π/4) for various positions of the elastic-plastic boundary.


1969 ◽  
Vol 91 (4) ◽  
pp. 816-821
Author(s):  
J. W. Wesner ◽  
A. S. Weinstein

A computer adaptation of Southwell’s Relaxation Method was developed for the solution of elastic-perfectly plastic stress distribution problems. This method was employed to study some aspects of the problem of the plane-strain indenter. For two ratios of strip thickness to indenter width, the load for, and location of, initial yielding and the load for the onset of indentation were found. The results are compared with slip-line solutions.


1987 ◽  
Vol 109 (3) ◽  
pp. 357-358
Author(s):  
Hui Fan ◽  
G. E. O. Widera

The analysis of elastic, perfectly plastic compressible materials under the assumption of plane strain is a statically indeterminate problem. In the present paper, by introducing a perturbation parameter ε = 1/2−ν, the problem can be changed into a series of statically determinate ones. The first-order approximation yields the solution for the incompressible material. In order to show the details of this method, the second-order approximation for the problem of the thick-walled cylinder under internal pressure is obtained.


1984 ◽  
Vol 21 (2) ◽  
pp. 338-348 ◽  
Author(s):  
A. M. Britto ◽  
O. Kusakabe

Unsupported plane strain trenches and axisymmetric shafts cannot be excavated to great depths in a purely cohesive soil. Therefore, it is standard practice to provide some form of support. Timber supports with struts are conventional and quite common. Bentonite slurry support has become more popular in recent years especially in the construction of diaphragm walls. In this paper the effect of rigid lateral support and slurry support on the stability (mode of failure) for both plane strain and axisymmetric excavations are investigated under undrained conditions. When immediate failure is of interest in saturated clays the changes in the water content can be neglected and the soil can be treated as a [Formula: see text] material. For the purposes of the analyses presented here the lateral support is assumed to be rigid and the soil is idealized as an elastic perfectly plastic material with cohesion Cu. The results from upper bound calculations, finite element collapse analyses, and centrifuge tests are presented. The analogy between deep footing failure and base failure of excavation allows the solutions for the footing problem to be interpreted for trench excavations. It is found that slurry support is more effective than rigid lateral support for axisymmetric excavations. The slurry support reduces the amount of surface settlement and also stabilises the trench against base failure. For excavations with rigid lateral support the possibility of base failure is greatly increased. The results are presented in the form of stability charts. Keywords: limit analysis, slurry support, stability number, supported excavation, upper bound solution.


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