PSI - Issue 33

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

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

Procedia Structural Integrity 33 (2021) 385–390

IGF26 - 26th International Conference on Fracture and Structural Integrity Stress state of an elastic rectangular domain under steady load IGF26 - 26th International Conference on Fracture and Structural Integrity Stress state of an elastic rectangular domain under steady load

O. Pozhylenkov*, N. Vaysfeld, Y. Protserov Odesa Mechnikov University, , Dvoryanskaya str. 2, Odesa 65082, Ukraine O. Pozhylenkov*, N. Vaysfeld, Y. Protserov Odesa Mechnikov University, , Dvoryanskaya str. 2, Odesa 65082, Ukraine

© 2021 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 scientific committee of the IGF ExCo Abstract The dynamic elasticity problem for rectangular domain is presented at this paper. The conditions of ideal contact are given at the lateral sides and bottom edge of the domain; the upper edge is loaded by normal stress. Problem is formulated as the boundary value problem in steady-state case. It was necessary to find the wave field of the rectangular domain. The Fourier transform was applied to formulated problem and reduced it to one dimensional vector boundary problem. The last one was solved with the method based on matrix differential calculations which was successfully applied earlier to solve the analogous static problem Pozhylenkov O. V. (2019). According to this procedure of the solving the exact solution of the vector boundary problem was constructed in transform domain in the explicit form. Application of the inverse Fourier transform finalized the deriving of the stated problem solution. The analyses of wave field of rectangular domain depending on different load types, frequency values and domain size was done. © 2021 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 Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo Keywords: Verctor boundary problem, Rectangular domain, Dynamic load 1. Introduction The problem of the rectangular domain stress estimation is not a new one, nevertheless a lot of unsolved issues remain. This problem was considered and solved in the different statements important to the engineering applications as with the help of analytical methods so and numerical ones. To the last direction one can reference the papers, where the boundary element-free method (BEFM) was applied to two dimensional problems of elasticity. This method is a numerical method which combines the boundary integral equation method and an improved moving least-square approximation. This, method as it was stated Liew K. M., Yuming Cheng, Kitipornchai S. (2005), gives the higher Abstract The dynamic elasticity problem for rectangular domain is presented at this paper. The conditions of ideal contact are given at the lat ral sides and bottom edg of the domain; the upper edg is loaded by normal str ss. Problem is formulated as the boundary value problem in steady-stat case. It was necessary to find the wave field of the rectangular do a n. The Fourier transf rm was applied to formulat d probl m and reduced it to one d mension l vector boundary problem. The last one was solved with the metho based on matrix differential cal ulat ons which was successfully applied earlier to solv the a alogous static problem Poz ylenkov O. V. (2019). According to this procedure of the solving the exact solution f the vector boundary problem was c nstructed in transform domain in the expl cit f rm. Application of the inv rse F urier transform finalized the deriving of the stated problem soluti n. The analyses of wave field of rectangular d main dep nding on different load types, frequency alues and domain size wa done. © 2021 Th 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 Statem nt: Peer-revi w under responsibility of the scientifi committee of the IGF ExCo Keywords: Verctor boundary problem, Rectangular domain, Dynamic load 1. Introduction The problem of the rectangular domain stress estimation is not a new one, nevertheless a lot of unsolved issues remain. This problem was conside ed and solv d in he different statem nts importan to the engineeri g application as with the help of analytical methods so and numerical ones. To the last direction one can r f renc the p ers, where the boundary eleme t-free method (BEFM) was applied to tw dimensional problems of elasticity. This m thod is a numerical method which combines the boundary int gral equat on method and an improved moving least-square approximation. This, method as it was stated Liew K. M., Yuming Ch ng, Kitipor chai S. (2005), gives the higher

* Corresponding author. E-mail address: leshiy12345678@gmail.com * Corresponding author. E-mail address: leshiy12345678@gmail.com

2452-3216 © 2021 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 Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo 2452-3216 © 2021 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 Statement: Peer-review under responsibility of the scientific committee of the IGF ExCo

2452-3216 © 2021 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 scientific committee of the IGF ExCo 10.1016/j.prostr.2021.10.046