Comparison of the stress and strain intensity factors for the corner area of the structure boundary

Lyudmila Frishter,A Mottaeva,B Melović

doi:10.1051/matecconf/201819303029

Lyudmila Frishter, A Mottaeva + Show 1 more

Open Access

https://doi.org/10.1051/matecconf/201819303029

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Abstract

The stress-strain state of structures in areas with corner cut-outs and cuts of boundaries features the occurrence of areas of stress concentration and requires assessment of strength and reliability of facilities, which is a relevant task in engineering practice. Theoretical analysis of stress-strain state (SSS) of corner cut-outs zones of the area boundary is reduced to the study of singular solutions of the elasticity theory problem with exponential features. At that, the concept of stress or strain concentration in an irregular point of the area boundary is meaningless. This paper considers the stress-strain state in the vicinity of the top of the corner cut-out of the flat area boundary, which is recorded using the intensity factors as limit values of stresses and strains. We give two approaches for obtaining the limit values for stress and strain in the vicinity of an irregular point of the plane area boundary using the stress intensity factors and the strain intensity factors. The stress-strain state in the corner cut-outs zone of structures and buildings boundary recorded in the form of limit values of stresses and strains may further be used to determine and record the influence of changing the factors of intensity of stresses and strains on SSS of structures, which is a separate task of solid mechanics. The difference in the expressions of stresses and displacements obtained for limit values of stresses and strains determines practical significance of the work when carrying out experiments and at determination of critical values of stresses and strains.

Highlights

The stress-strain state (SSS) of composite structures in zones of connection of elements under the action of forced strains being ruptural along the line of the elements contact is characterized by exponential feature
The exponential feature of the SSS depends on the shape of the area boundary - a cutout, a cut, the order of which depends on the eigenvalues of the homogeneous elastic problem [4,5,6]
For a perfect mathematical cut, singular stresses are characterized by the stress intensity factors [3,5,7,8,11,12,13,14,15,16,17,18]

Summary

Introduction

The stress-strain state (SSS) of composite structures in zones of connection of elements under the action of forced strains being ruptural along the line (surface) of the elements contact is characterized by exponential feature. The stress-strain state in the irregular point zone of the area boundary under the action of forced strains, in particular temperature ones, is determined by solution of the homogeneous boundary value problem of elasticity theory. The exponential feature of the SSS depends on the shape of the area boundary - a cutout, a cut, the order of which depends on the eigenvalues of the homogeneous elastic problem [4,5,6]. The purpose of this work is to determine the stress-strain state in the zone of corner cut-out of arbitrary opening of the area boundary using factors of intensity of stresses and strains as the limit values of stresses and strains

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