PSI - Issue 30

Available online at www.sciencedirect.com Available online at www.sciencedirect.com Sci nceD rect Structural Integrity Procedia 00 (2020) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2020) 000–000

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 30 (2020) 113–119

© 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 EURASTRENCOLD - 2020 guest editors The paper considers an example of mathematical modeling of the process of deformation of a structure made of fiber-composite material. Timoshenko's theory of thin beams is used to describe the reinforcing fiber model. The paper concerns a numerical solving of the equilibrium problem for a two-dimensional elastic body with a thin Timoshenko elastic inclusion and a thin semirigid inclusion. Both inclusions are of a rectilinear shape and delaminate from the elastic matrix. Therefore, the problem is posed in the domain with a cut and conditions of the form of inequalities are specified at the edges of the crack, as on a part of the boundary. These conditions exclude mutual penetration of the crack edges into each other. At the same time, such a formulation leads to the nonlinearity of the problem and the need to use additional mathematical methods to construct an algorithm for the numerical solution of the problem. The inclusions have a joint point at which junction conditions are written out. For the numerical solving of the problem in a domain with a cut, a variational formulation is used using the domain decomposition method and the Uzawa algorithm. To obtain an approximate solution that satisfies the conditions of semirigid inclusion, an additional algorithm is built using methods of mathematical analysis, an example with calculations is given. © 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 EURASTRENCOLD - 2020 guest editors Keywords: Uzawa algorithm; thin inclusion; semirigid inclusion; Timoshenko inclusion; crack; nonlinear boundary condition; junction conditions. IX Eurasian Symposium on the problems of strength and resource in low climatic temperatures (EURASTRENCOLD-2020) On numerical solving of junction problem for semirigid and Timoshenko inclusions in elastic body Tatiana S. Popova* North-Eastern Federal University, Yakutsk, 677000, Russia Abstract The paper considers an example of mathematical modeling of the process of deformation of a structure made of fiber-composite materi l. Timosh nko's theory of thin b a s is use to describ the reinforcing fiber m del. The paper concerns a nu erical solving of the equilibrium problem for two-dimensional elastic body with a thin Timoshenko el stic inclusion a d a thin em ri id inclusion. Both inclusions are of a rect linear sh p nd delaminate from the elastic matrix. Therefore, the problem s posed in the domain wi a t and conditions of th form of inequalities r specified at the edges of t crack as on a part of the boundary. These conditions ex lude mutual p net ati n of the crack edg s nto each oth r. A the same time, such a formulation leads to the nonlinearity of the probl m and the need to use additio al mat ematical methods to construct an algorithm for the numerical solution of the problem. The inclusions have a joint p i t at w ich junction con iti ns are writte out. For the numerical solving of the problem in a domain with a cut, a variatio al formulatio is used us ng the domai decompositio thod and the Uzawa algorithm. To obtain an approximate solu that satisfies the con itio s of semirig d in lusion, an additional lgorithm is built using eth ds of mathematical analy is, an example with calculations is given. © 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 EURASTRENCOLD - 2020 guest editors K ywords: Uzawa algorithm; thin inclusion; semirigid inclusion; Timoshenko inclusion; crack; nonlinear boundary condition; junction conditions. IX Eurasian Symposium on the problems of strength and resource in low climatic temperatures (EURASTRENCOLD-2020) On numerical solving of junction problem for semirigid and Timoshenko inclusions in elastic body Tatiana S. Popova* North-Eastern Federal University, Yakutsk, 677000, Russia Abstract

* Corresponding author. Tel.: +7-411-235-2090; fax: +7-411-232-1314. E-mail address: ts.popova@s-vfu.ru * Corresponding author. Tel.: +7-411-235-2090; fax: +7-411-232-1314. E-mail address: ts.p pova@s-vfu.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 the responsibility of the EURASTRENCOLD - 2020 guest editors 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 u der the responsibility of the EURASTRENCOLD - 2020 gu st editors

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 EURASTRENCOLD - 2020 guest editors 10.1016/j.prostr.2020.12.019