TY - JOUR
T1 - Isogeometric collocation method to solve the strong form equation of UI-RM plate theory
AU - Katili, Irwan
AU - Aristio, Ricky
AU - Setyanto, Samuel Budhi
N1 - Funding Information:
The authors gratefully acknowledge financial support from Universitas Indonesia, Depok 16424, Indonesia, through the Publikasi Terindeks Internasional (PUTI) Q1 Program, Grant no. NKB-1410/UN2.RST/HKP.05.00/2020.
Publisher Copyright:
Copyright © 2020 Techno-Press, Ltd.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2020/11/25
Y1 - 2020/11/25
N2 - This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.
AB - This work presents the formulation of the isogeometric collocation method to solve the strong form equation of a unified and integrated approach of Reissner Mindlin plate theory (UI-RM). In this plate theory model, the total displacement is expressed in terms of bending and shear displacements. Rotations, curvatures, and shear strains are represented as the first, the second, and the third derivatives of the bending displacement, respectively. The proposed formulation is free from shear locking in the Kirchhoff limit and is equally applicable to thin and thick plates. The displacement field is approximated using the B-splines functions, and the strong form equation of the fourth-order is solved using the collocation approach. The convergence properties and accuracy are demonstrated with square plate problems of thin and thick plates with different boundary conditions. Two approaches are used for convergence tests, e.g., increasing the polynomial degree (NELT = 1×1 with p = 4, 5, 6, 7) and increasing the number of element (NELT = 1×1, 2×2, 3×3, 4×4 with p = 4) with the number of control variable (NCV) is used as a comparable equivalent variable. Compared with DKMQ element of a 64×64 mesh as the reference for all L/h, the problem analysis with isogeometric collocation on UI-RM plate theory exhibits satisfying results.
KW - B-spline
KW - Collocation method
KW - Isogeometric analysis
KW - Unified and integrated Reissner-Mindlin
UR - http://www.scopus.com/inward/record.url?scp=85102639064&partnerID=8YFLogxK
U2 - 10.12989/sem.2020.76.4.435
DO - 10.12989/sem.2020.76.4.435
M3 - Article
AN - SCOPUS:85102639064
SN - 1225-4568
VL - 76
SP - 435
EP - 449
JO - Structural Engineering and Mechanics
JF - Structural Engineering and Mechanics
IS - 4
ER -