Isogeometric Galerkin in rectangular plate bending problem based on UI approach

- Unified and integrated (UI) approach is a modification of Reissner-Mindlin plate theory.
- In UI approach total displacement is divided into bending and shear displacement.
- UI approach is used to define curvature and shear deformation as second and third derivative of bending displacement.
- With UI approach no shear locking problem occurs due to strong interdependence between bending displacement and rotation.
- In UI approach bending and shear displacement can be defined, while these are unrecognizable in Reissner-Mindlin theory.
- Numerical tests were done to see the performance of IGA Galerkin based on UI approach for thin to thick rectangular plate.

This paper presents the development of Isogeometric Analysis for plate bending problems based on unified and integrated (UI) approach, which is a modification of Reissner-Mindlin plate theory for solving thick to thin plate problems. In Reissner-Mindlin, the total displacement and two rotations are independent of each other, while in this UI approach the total displacement is split into bending displacement and shear displacement which causes the rotations, curvatures and shear deformations can be defined as first, second and third derivatives of bending displacement, respectively. The virtual work of Galerkin Method is used to define bending stiffness and shear stiffness of the element. Several convergence tests were conducted to observe the performance of unified and integrated approach in rectangular plate of different types of boundaries conditions. The result of thick and thin plate showed good results despite of low number of element with fourth degree of polynomial or increasing degree of polynomial with only one element.