Study of stress–strain state of elastic body with hyperbolic notch

Zirakashvili, Natela

doi:10.1007/s00033-019-1131-1

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…So we have the following: Proposal 1. The functional series corresponding to (11) and (13) are absolute and uniform by convergent series on the area…”

Section: It Is Clear Thatmentioning

confidence: 99%

“…In order to solve boundary value and boundary-contact problems in the areas with curvilinear border, it is purposeful to examine such problems in the relevant curvilinear coordinate system. Namely, the problems for the regions bounded by a circle or its parts are considered in the polar coordinate system [1][2][3][4], while the problems for the regions bounded by an ellipse or its parts or hyperbola are considered in the elliptic coordinate system [5][6][7][8][9][10][11][12][13], and the problems for the regions with parabolic boundaries are considered in the parabolic coordinate system [14][15][16]. The problems for the regions bounded by the circles with different centers and radiuses are considered in the bipolar coordinate system [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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2D Elastostatic Problems in Parabolic Coordinates

Zirakashvili¹

2020

Solid State Physics [Working Title]

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In the present chapter, the boundary value problems are considered in a parabolic coordinate system. In terms of parabolic coordinates, the equilibrium equation system and Hooke's law are written, and analytical (exact) solutions of 2D problems of elasticity are constructed in the homogeneous isotropic body bounded by coordinate lines of the parabolic coordinate system. Analytical solutions are obtained using the method of separation of variables. The solution is constructed using its general representation by two harmonic functions. Using the MATLAB software, numerical results and constructed graphs of the some boundary value problems are obtained.

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“…So we have the following: Proposal 1. The functional series corresponding to (11) and (13) are absolute and uniform by convergent series on the area…”

Section: It Is Clear Thatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

2D Elastostatic Problems in Parabolic Coordinates

Zirakashvili¹

2020

Solid State Physics [Working Title]

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Applied Systems Theory: Mathematical and Numerical Simulation of Strength of Thick-wall Pipe by Using Static Elastic Problems

Zirakashvili

2021

International Journal of Circuits, Systems and Signal Processing

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In Systems Theory, the Mathematical and numerical simulation of strength of thick-wall pipe by using static elastic problems is an important problem and has attracted the attention of many researches, academicians and practitioners. the The present work studies the change in the strength of a quite long isotropic thick-wall pipe (circular cylinder) for the varying pipe diameter, wall thickness and material. The pipe is in the plane deformed state, i.e. plane deformation is considered. Based on the problems of statics of the theory of elasticity, a mathematical model to calculate the strength of the thick-wall pipe was developed and the problems of statics of the theory of elasticity were set and solved analytically in the polar coordinate system. The analytical solution was obtained by the method of separation of variables, which is presented by two harmonious functions. The dependence of the pipe strength on the thickness and material of the pipe wall, when (a) normal stress is applied to the internal boundary (internal pressure) and external boundary is free from stresses and (b) normal stress is applied to the external boundary (external pressure) and the internal boundary is free from stresses, is studied. In particular, the minimum thicknesses of the walls of homogeneous isotropic circular cylinders of different materials and diameters with a plane deformed mode when the pressures in the cylinders do not exceed the admissible values were identified. Some numerical results are presented as tables, graphs and relevant consideration.

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Study of stress–strain state of elastic body with hyperbolic notch

Cited by 2 publications

References 17 publications

2D Elastostatic Problems in Parabolic Coordinates

2D Elastostatic Problems in Parabolic Coordinates

Applied Systems Theory: Mathematical and Numerical Simulation of Strength of Thick-wall Pipe by Using Static Elastic Problems

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