Improving Felippa Bergan Triangular element by using UI approach for analysis of isotropic and FGM sandwich plates

This work presents the enhancement of Felippa Bergan Triangular (FBT) element from thin (Kirchhoff-Love plate theory) to thick plate (Reissner-Mindlin plate theory) using the unified and integrated approach. In FBT, the total transverse displacement w is used as a single independent variable; meanwhile, in the new triangular plate UI-T3 element, the single independent variable is the bending displacement (w_b). The difference between the two approaches lies in the transverse displacement w. In the UI approach, the transverse displacement w is expressed as the sum of the transverse bending displacement w_b and transverse shear displacements w_s. The first and second derivatives of the bending displacement w_b are the rotations and curvatures. The free formulation concept allows for non-conforming displacement functions that cover the lower and higher modes and are linearly independent. Rigid body mode and constant strain mode should be obtained by the lower mode displacement function. These lower and higher modes must create orthogonal bending energies to pass the patch test. The proposed element called UI-T3 is locking-free, has a proper rank, and gives satisfying results in the standard benchmark problems for isotropic plates and Functional Graded Material (FGM) sandwich plates.