A new hybrid-Trefftz triangular and quadrilateral plate elements

We develop 9 DOF triangular and 12 DOF quadrilateral plate bending elements based on the hybrid-Trefftz method. Among the two independent displacement fields, i.e. the internal and the boundary displacements, we use the Mindlin–Reissner’s thick plate solution with a particular solution under pressure load as the internal displacement field. For the boundary displacement field, we approximate transverse displacement w˜ and rotations β˜x and β˜y by cubic and quadratic hierarchical shape functions, respectively. We derive the transverse shear strains from constitutive equations and equilibrium equations, respectively, and then, remove additional degrees of freedom of hierarchical shape functions using the relations between these two shear strains. Results of numerical tests reveal that the new triangular (T32-7T32-7) and quadrilateral (Q32-11Q32-11) elements are robust, accurate and free of shear locking in the thin limit.