Isogeometric Collocation Method to solve the strong form equation of UI-RM Plate Theory

Abstract

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.