TY - JOUR

T1 - A Cubic Version of the Least-Squares Collocation Method and Its Application to the Calculation of Plate Bending

AU - Golushko, S. K.

AU - Bryndin, L. S.

AU - Belyaev, V. A.

AU - Gorynin, A. G.

N1 - The work was carried out within the framework of the implementation of the Program of the Center of the National Technological Initiative on the topic “Technologies for Modeling and Developing New Functional Materials with Specified Properties” on the basis of Novosibirsk State University, project 4.1. A Cubic Version of the Least-Squares Collocation Method and Its Application to the Calculation of Plate Bending / S. K. Golushko, L. S. Bryndin, V. A. Belyaev, A. G. Gorynin // Journal of Applied and Industrial Mathematics. – 2024. – Vol. 18, No. 3. – P. 448-464. – DOI 10.1134/S1990478924030074.

PY - 2024/12/1

Y1 - 2024/12/1

N2 - Abstract: A new cubic version of the least-squares collocation method based on adaptive grids isdeveloped. Approximate values of the solution and its first derivatives at the vertices ofquadrangular cells are the unknowns. This approach has made it possible to eliminate thematching conditions from the global overdetermined system of linear algebraic equationsconsisting of collocation equations and boundary conditions. The preconditioned system is solvedusing the SuiteSparse library by theorthogonal method with the CUDA parallel programming technology. We consider theReissner–Mindlin plate problem in a mixed formulation. A higher accuracy of deflections androtations of the transverse normal in comparison with the isogeometric collocation method as wellas the uniform convergence of shear forces in the case of a thin plate are shown in the proposedmethod. Bending of an annular plate and round plates with an off-center hole is analyzed. Anincrease in the shear force gradient in the vicinity of the hole is shown both with a decrease in theplate thickness and with an increase in the eccentricity. The second order of convergence of thedeveloped method is shown numerically. The results obtained using the Reissner–Mindlin theoryare compared with the ones in the Kirchhoff–Love theory and three-dimensional finite elementsimulation.

AB - Abstract: A new cubic version of the least-squares collocation method based on adaptive grids isdeveloped. Approximate values of the solution and its first derivatives at the vertices ofquadrangular cells are the unknowns. This approach has made it possible to eliminate thematching conditions from the global overdetermined system of linear algebraic equationsconsisting of collocation equations and boundary conditions. The preconditioned system is solvedusing the SuiteSparse library by theorthogonal method with the CUDA parallel programming technology. We consider theReissner–Mindlin plate problem in a mixed formulation. A higher accuracy of deflections androtations of the transverse normal in comparison with the isogeometric collocation method as wellas the uniform convergence of shear forces in the case of a thin plate are shown in the proposedmethod. Bending of an annular plate and round plates with an off-center hole is analyzed. Anincrease in the shear force gradient in the vicinity of the hole is shown both with a decrease in theplate thickness and with an increase in the eccentricity. The second order of convergence of thedeveloped method is shown numerically. The results obtained using the Reissner–Mindlin theoryare compared with the ones in the Kirchhoff–Love theory and three-dimensional finite elementsimulation.

KW - Reissner–Mindlin plate theory

KW - adaptive grid

KW - automatic solution continuity

KW - least-squares collocation method

KW - off-center hole

UR - https://www.mendeley.com/catalogue/090e2511-649a-3747-bb59-f1b905ec96f9/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105008190127&origin=inward&txGid=7e5e251caa3b351ead8dbea9829ffb02

UR - https://www.elibrary.ru/item.asp?id=75143767

U2 - 10.1134/S1990478924030074

DO - 10.1134/S1990478924030074

M3 - Article

VL - 18

SP - 448

EP - 464

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -