Issue 38

N. Vaysfeld et alii, Frattura ed Integrità Strutturale, 38 (2016) 1-11; DOI: 10.3221/IGF-ESIS.38.01 1 Focussed on Multiaxial Fatigue and Fracture On the stress investigation at the edges of the fixed elastic semi-strip N. Vaysfeld Odessa Mechnikov University, Institute of Mathematics, Economics and Mechanics vaysfeld@onu.edu.ua O. Kryvyi National University «Odessa Maritime Academy» (NU «OMA») krivoy-odessa@ukr.net, kryvyi-od@math.onma.edu.ua Z. Zhuravlova Odessa Mechnikov University, Institute of Mathematics, Economics and Mechanics zhuravleva@te.net.ua A BSTRACT . The stress state of the elastic fixed semi-strip with the regarding of the singularities at its edge is investigated in the article. The initial boundary problem is reduced to a vector boundary problem in the transformation’s domain by the use of integral Fourier transformation. The one-dimensional vector boundary problem is solved exactly with the help of matrix differential calculations and Green’s matrix apparatus. The problem’s solving was focused at the solving of the singular integral equation (SIE) with the two fixed singularities at the ends of the integration’s interval. The symbol of SIE was constructed and the generalized method of the SIE solving was applied. The stress’ distributions of the semi-strip are investigated. K EYWORDS . Semi-strip; Vector boundary problem; Singular integral equation; Fixed singularity. Citation: Vaysfeld, N., Kryvyi, O., Zhuravlova, Z., On the stress investigation at the edges of the fixed elastic semi-strip, Frattura ed Integrità Strutturale, 38 (2016) 1- 11. Received: 14.04.2016 Accepted: 09.06.2016 Published: 01.10.2016 Copyright: © 2016 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he plain elasticity problems for a semi-strip are important as the model examples for the different engineering applications. So many authors have examined these problems in their works. A short review of the different approaches to the solving of the plane elasticity problems for an elastic semi-strip is given below. The reducing of the problem to the Fredholm's integral equation of the first kind was used in [1] for estimation of the symmetrically loaded semi-strip fixed by the short edge. Another approach based on the construction of the stress function as the combination of the Fourier’s integrals and the series was used in [2, 3]. The problems for a semi-strip considered in [4, 5] were reduced to the singular integral equations which were solved numerically, it leaded to the solving