Efficient and accurate plate bending elements based on the hybrid-Trefftz variational formulation are developed. Hybrid-Trefftz variational formulation requires two independent fields of generalized displacements. One is internal displacement fields satisfying governing differential equations of the Reissner-Mindlin plate theory, the other is boundary displacement fields with nodal displacements. Hybrid-Trefftz plate bending elements are known to be robust and free of shear locking in the thin limit because of internal displacements fields and linked boundary displacements. Also, their finite element approximation is very simple regardless to boundary shape since all element matrices can be calculated using only boundary integrals.
In this study, new hybrid-Trefftz variational formulation which is based on the total potential energy principle of internal displacements and displacement consistency conditions at the boundary is derived. In order to simplify finite element approximation, line shape functions are used. Using them, quadrilateral elements and triangular elements are derived in the same way. Flat shell elements are derived by combining hybrid-Trefftz bending stiffness and plane stress stiffness with drilling dofs. With these hybrid-Trefftz elements and flat shell elements, a series of tests are performed. The proposed elements show good results in view of accuracy and convergency.
