scholarly journals Elastic-Plastic Problem for a Stringer Plate with a Circular Hole

2021 ◽  
Vol 24 (3) ◽  
pp. 61-69
Author(s):  
Minavar V. Mir-Salim-zade ◽  
Keyword(s):  
Plastic Zone ◽  
Least Squares ◽  
Circular Hole ◽  
Strain State ◽  
Least Squares Method ◽  
Plasticity Condition ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Stress Strain State ◽  
Plastic Zones

When calculating the strength of machines, structures and buildings with technological holes, it is important to take into account the plastic zones that emerge around the holes. However, the unknown shape and size of the plastic zone complicate the solution of elastic-plastic problems. This paper gives an approximate method and solution of the plane elastic-plastic problem of the distribution of stresses in a thin plate, reinforced with a regular system of stiffeners (stringers). The stringer plate under consideration has a circular hole, which is completely surrounded by the zone of plastic deformation. At infinity, the plate is subjected to a uniform tension along the stiffeners. A constant normal load is applied to the contour of the hole. The plate and stringer materials are assumed to be isotropic. The loading conditions are assumed to be quasi-static. It is assumed that the plate is in the plane-stressed state. Taken as the plasticity condition in the plastic zone is the Tresca-Saint-Venant plasticity condition. Methods of perturbation theory, analytic function theory, and the least squares method are used. The solution to the stated elastic-plastic problem consists of two stages. At the first stage, the stress-strain state for the elastic zone is found, and then the unknown interface between the elastic and plastic zones is determined using the least squares method. A closed system of algebraic equations has been constructed in each approximation, the numerical solution of which makes it possible to study the stress-strain state of a stringer plate, with the hole entirely surrounded by the plastic zone, as well as to determine the magnitudes of the concentrated forces that replace the action of the stringers. The interface between the elastic and plastic deformations has been found. The presented solution technique can be developed to solve other elastic-plastic problems. The solution obtained in this paper makes it possible to consider elastic-plastic problems for a stringer plate with other plasticity criteria.

Stress-strain state of a flexible spherical shell with an eccentric circular hole

2007 ◽  
Vol 43 (10) ◽  
pp. 1142-1148 ◽  
Author(s):  
I. S. Chernyshenko ◽  
E. A. Storozhuk ◽  
I. B. Rudenko
Keyword(s):  
Spherical Shell ◽  
Circular Hole ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State

scholarly journals Effect of the sector radius of a workpiece-deforming tool on the stress-strain state in the contact zone with a cylindrical surface

2022 ◽  
Vol 25 (6) ◽  
pp. 696-707
Author(s):  
S. A. Zaides ◽  
Quan Minh Ho ◽  
Nghia Duc Mai
Keyword(s):  
Surface Layer ◽  
Plastic Zone ◽  
Residual Stresses ◽  
Cylindrical Surface ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State ◽  
Cylindrical Workpiece ◽  
Zone Depth ◽  
Depth Ranges

This paper aims to determine the effect of the sector radius of a workpiece-deforming tool on the stress-strain state in the center of elastoplastic deformation and residual stresses in the hardened zone of the surface layer of cylindrical workpieces. A mathematical model of local loading was constructed using the finite element method and AN-SYS software. This model was used to determine the values of temporary and residual stresses and deformations, as well as the depth of plastic zone, depending on the sector radius of the working tool. The simulation results showed that, under the same loading of a cylindrical surface, working tools with different sector radii create different maximum tempo-rary and residual stresses. An assessment of the stress state was carried out for situations when the surface layer of a product is treated by workpiece-deforming tools with a different shape of the working edge. It was shown that, compared to a flat tool, a decrease in the radius of the working sector from 125 to 25 mm leads to an increase in the maximum temporary and residual stresses by 1.2–1.5 times, while the plastic zone depth increases by 1.5–2.4 times. The use of a working tool with a flat surface for hardening a cylindrical workpiece ensures minimal temporary residual stresses, com-pared to those produced by a working tool with a curved surface. A decrease in the radius of the working sector leads to an increase in temporary residual stresses by 2–7%. The plastic zone depth ranges from 1.65 to 2.55 mm when chang-ing the sector radius of the working tool.

scholarly journals Finite element analysis of elastic-plastic state of crack at the interface between infinite plane and circular inclusion

2019 ◽  
pp. 20-23
Author(s):  
V. J. Adlucky ◽  
A. Yu. Hodes ◽  
V. V. Loboda
Keyword(s):  
Strain State ◽  
Circular Inclusion ◽  
Plastic State ◽  
Isotropic Hardening ◽  
Infinite Plane ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Stress Strain State ◽  
Crack Faces ◽  
Plastic Stress

The problem on determining of elastic-plastic stress-strain state of infinite plane with a circular inclusion made from another material and an arc crack at the interface under action of arbitrary mechanical loadings applied at infinity is considered using the FEM approach. The problem is resolved within the framework of contact model for which the possibility of appearance of contact macrozones between crack faces is assumed. The isotropic hardening of materials with bilinear approximation of stress-strain curves is considered. The infinite plane is modeled by square domain whose size is of an order of magnitude greater than inclusion diameter. Contact interaction of crack faces is simulated using gap elements. To obtain the energy release rate the J-integrals are calculated along several closed contours around the crack tips. The comparison of obtained results with available analytical solutions for linear elasticity shows that insignificant differences take place during transformation from pure elastic to elastic-plastic stress-strain state.

scholarly journals Influence of the form of axisymmetric load on the stress-strain state of an elastoplastic half-space

2019 ◽  
Vol 298 ◽  
pp. 00094
Author(s):  
Peter Ogar ◽  
Denis Gorokhov ◽  
Leonid Mamaev ◽  
Vladislav Kushnarev
Keyword(s):  
Plastic Deformation ◽  
Surface Layer ◽  
Half Space ◽  
Strain State ◽  
Stress Strain ◽  
Near Surface ◽  
Axisymmetric Load ◽  
Elastic Plastic ◽  
Stress Strain State

The problems of elastic sinking of materials and elastic restoration of an imprint under loading of an elastic-plastic half-space with an axisymmetric load of the form,P(r)=P0(1-r2/a2)β where 0<β<0.5 are considered. Expressions are obtained that describing the stress-strain state of an elastoplastic half-space. The conditions of the onset of plastic deformation in the near-surface layer and on the half-space of surface are considered depending on the parameter β.

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