PSI - Issue 28

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

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 28 (2020) 2277–2282

© 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 the European Structural Integrity Society (ESIS) ExCo Abstract The approximate solution to the problem for an infinite plate with the circular hole under creep regime is obtained by the quasilinearization method. Four 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. 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 quasilinearization method is the effective method for nonlinear problems. The model problem for steady state creep of a rotating disc is either considered. The high values of the creep exponent are analyzed and it is shown that the high values of the creep exponent require more iterations in the quasilinearization method. © 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 the European Structural Integrity Society (ESIS) ExCo Keywords: crack in perfect plastic materials; sectorial solution; statically determinate problem; power law hardening material; mixity parameter; analytical solution; asymptotic solution . 1. Introduction One of the most common techniques in steady state creep analysis is quasilinearization (Boyle and Spence (1983)) since the most obvious route for nonlinear problems is to linearize the equations around an initial estimate and then solve the linear problem iteratively until the process converges. As it is noted in Boyle and Spence (1983), surprisingly, 1st Virtual European Conference on Fracture Approximate Solutions to Nonlinear Problems of Solid Mechanics by Quasilinearization Method 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 the European Structural Integrity Society (ESIS) ExCo

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 the European Structural Integrity Society (ESIS) ExCo 10.1016/j.prostr.2020.11.073