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

Static Convergence Behaviour of Discrete Kirchhoff-Mindlin Triangular Element on Rectangular Functionally Graded Material Plates

“…The reference solutions are given in [1, 17,18]. The result on mesh index 64x128 becomes the reference solution for no reference in the literature.…”

An efficient shear and bending‐locking‐free quadrilateral plate element using a modified Hellinger‐Reissner functional and the Bergan free formulation

“…• imposition of the energy-orthogonality condition between the linear and quadratic bending modes (like in the 'Bergan free formulation'). [22][23][24][34][35][36] • the use of static condensation at the element level to eliminate the increments of rotations { Δβ n } and the tangential shear strain…”

“…The main theoretical aspects of the formulation are: the use of a modified Hellinger‐Reissner functional where the transverse shear strains are the mixed independent variables. the enhancement of the rotation field using incomplete quadratic approximations of β x and β y (as for DKQ 18 and DKMQ 20 ) the representation of the mixed shear strains $$$ {\underset{\_}{\upgamma}}_x $$$ and $$$ {\underset{\_}{\upgamma}}_y $$$ as in MITC4 21 (linear in ξ and η) with constant tangential components on the four sides (also used in DKMQ 20 ). the kinematical shear strains (in terms of w , β x , β y ) are approximated consistently with the mixed shear strain components. imposition of the energy‐orthogonality condition between the linear and quadratic bending modes (like in the ‘Bergan free formulation’) 22–24,34–36 the use of static condensation at the element level to eliminate the increments of rotations $$$ \left\{\Delta {\upbeta}_n\right\} $$$ and the tangential shear strain $$$ \left\{{\underset{\_}{\upgamma}}_{s_n}\right\} $$$ components. all matrices are evaluated using a 2 × 2 Gauss integration scheme. …”