S. K. Golushko, L. S. Bryndin, V. A. Belyaev, A. G. Gorynin
{"title":"A Cubic Version of the Least-Squares Collocation Method and\u0000Its Application to the Calculation\u0000of Plate Bending","authors":"S. K. Golushko, L. S. Bryndin, V. A. Belyaev, A. G. Gorynin","doi":"10.1134/S1990478924030074","DOIUrl":"10.1134/S1990478924030074","url":null,"abstract":"<p> A new cubic version of the least-squares collocation method based on adaptive grids is\u0000developed. Approximate values of the solution and its first derivatives at the vertices of\u0000quadrangular cells are the unknowns. This approach has made it possible to eliminate the\u0000matching conditions from the global overdetermined system of linear algebraic equations\u0000consisting of collocation equations and boundary conditions. The preconditioned system is solved\u0000using the <span>SuiteSparse</span> library by the\u0000orthogonal method with the CUDA parallel programming technology. We consider the\u0000Reissner–Mindlin plate problem in a mixed formulation. A higher accuracy of deflections and\u0000rotations of the transverse normal in comparison with the isogeometric collocation method as well\u0000as the uniform convergence of shear forces in the case of a thin plate are shown in the proposed\u0000method. Bending of an annular plate and round plates with an off-center hole is analyzed. An\u0000increase in the shear force gradient in the vicinity of the hole is shown both with a decrease in the\u0000plate thickness and with an increase in the eccentricity. The second order of convergence of the\u0000developed method is shown numerically. The results obtained using the Reissner–Mindlin theory\u0000are compared with the ones in the Kirchhoff–Love theory and three-dimensional finite element\u0000simulation.\u0000</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"448 - 464"},"PeriodicalIF":0.58,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142757922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}