An optimum triangular plate element based on DSPM with incomplete quadratic functions and an assumed orthogonality condition

This paper focuses on the formulation and evaluation of a triangular bending plate element, taking into account the shear effect, with 3 DOFs at each corner node. The new element, called DSPM3, is developed from T3γ_r element by increasing the linear (lower order) rotation function β_x and β_y with incomplete quadratic functions (higher-order). An assumed orthogonality condition between lower and higher bending energies is applied using a free formulation approach to pass the bending moment patch test. A discrete shear constraint is applied on each element side to provide a constant shear strain along the side and simultaneously avoid the shear-locking problem. The constant transverse shear strain on each side of the element is then projected to the corner nodes using the Discrete Shear Projection Method (DSPM). The values ​​at each node are then averaged to represent the constant shear strain in the element domain. The element application on static and free vibration analysis of isotropic plates demonstrates excellent convergence behaviour, superiority, and precision compared to the T3γ_r element on which the development was based.