PSI - Issue 37

Available online at www.sciencedirect.com Structural Integrity Procedia 00 (2019) 000 – 000 Available online at www.sciencedirect.com ScienceDirect

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Procedia Structural Integrity 37 (2022) 920–925

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira Abstract The approximate analytical solution to the problem for an infinite plate with the central circular hole subjected to uniaxial tension under creep regime is obtained by the quasilinearisation method. Three approximations of the solution for the nonlinear creep problem are found. It is shown that with increasing the number of approximations the solution converges to the limit numerical solution. Using SUMULIA Abaqus soft-package several numerical solutions for various creep exponent values are obtained It is worth to note that the tangential stress reaches its maximum value not at the circular hole but at the internal point of the plate. It is shown that quasilinearisation method is the effective method for nonlinear problems. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira Keywords: power law creep material; quasilinearisation method; analytical solution; approximate solution, partial differential equations . 1. Introduction Despite the possibilities of modern computer technologies that allow us to obtain numerical solutions of systems of nonlinear partial differential equations, obtaining analytical exact solutions is an important problem today. At present the problem of obtaining analytical solutions of nonlinear differential equations is a subject of numerous i ICSI 2021 The 4th International Conference on Structural Integrity An effective scheme for solving a class of nonlinear boundary value problems of stress concentration through quasilinearisation approach L.V. Stepanova a , R.M. Zhabbarov a * a Department of Mathematical Modelling in Mechanics, Samara National Research University, Moskovskoye shosse, 34, 443086, Samara, Russia

* Corresponding author. Tel.: +7 9277522102; fax: +0-000-000-0000 . E-mail address: Stepanova.lv@ssau.ru

2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of Pedro Miguel Guimaraes Pires Moreira 10.1016/j.prostr.2022.02.026