TY - JOUR

T1 - The least-squares collocation method in the mechanics of deformable solids

AU - Golushko, Sergey

AU - Shapeev, Vasily

AU - Belyaev, Vasily

AU - Bryndin, Luka

AU - Boltaev, Artem

AU - Gorynin, Arseniy

N1 - Funding Information: The research was partly carried out within the framework of the Program of Fundamental Scientific Research of the state academies of sciences in 2013-2020 (projects Nos. AAAA-A17-117030610136-3 and AAAA-A19-119051590004-5), was supported by the Russian Foundation for Basic Research (project no. 18-29-18029) and was carried out within the framework of the grant from the Russian Science Foundation (project no. 18-13-00392). Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved.

PY - 2021/1/4

Y1 - 2021/1/4

N2 - The paper is devoted to the application of the least-squares collocation method for solving the two- and one-dimensional problems in the mechanics of deformable solids. Calculation results of the deflections of isotropic and orthotropic elastic plates within the framework of various theories are presented. This paper shows that approximate solutions obtained by the hp-version of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy. Numerical and mathematical modeling of three-point bending of composite beams was carried out taking into account nonlinear stress-strain relationships, multi-modulus behavior, and incipient fracture. It was found that the simulation results are in good agreement with the results of mechanical tests of three-point bending of composite beams.

AB - The paper is devoted to the application of the least-squares collocation method for solving the two- and one-dimensional problems in the mechanics of deformable solids. Calculation results of the deflections of isotropic and orthotropic elastic plates within the framework of various theories are presented. This paper shows that approximate solutions obtained by the hp-version of the least-squares collocation method converge with a high order and agree with analytical solutions of test problems with a high degree of accuracy. Numerical and mathematical modeling of three-point bending of composite beams was carried out taking into account nonlinear stress-strain relationships, multi-modulus behavior, and incipient fracture. It was found that the simulation results are in good agreement with the results of mechanical tests of three-point bending of composite beams.

UR - http://www.scopus.com/inward/record.url?scp=85100703525&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1715/1/012029

DO - 10.1088/1742-6596/1715/1/012029

M3 - Conference article

AN - SCOPUS:85100703525

VL - 1715

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012029

T2 - International Conference on Marchuk Scientific Readings 2020, MSR 2020

Y2 - 19 October 2020 through 23 October 2020

ER -