Two higher order hybrid-Trefftz elements for thin plate bending analysis

• Two higher-order hybrid-Trefftz elements are proposed.
• To formulate these elements, the hybrid-Trefftz method is employed.
• In this study, two independent fields are introduced.
• The findings demonstrate the high accuracy of the proposed elements in analyzing the thin bending plates.

To analyze thin bending plates, a triangular and a quadrilateral element are presented in this paper. These suggested elements are formulated based on the hybrid-Trefftz method. The triangular element is named as THT-15, and it has 6 nodes and 18 degrees of freedom. The quadrilateral element is composed of 8 nodes and 24 degrees of freedom, and it is denoted as QHT-23. Two independent fields are introduced: one within the element and the other on the edges of the element. The internal field satisfies the governing equation of the thin plates. The boundary field is related to the nodal degrees of freedom by shape functions. For better capability, the shape functions of a 3 node Euler–Bernoulli beam are used for each edge of the element. The order of these functions for the deflection, rotation and torsion fields is equal to five, four and two, respectively. By depicting these fields in general coordinates, x–y, shape functions for the elements׳ edges are obtained. Several numerical tests are performed to assess the robustness of the suggested elements. The findings demonstrate the high accuracy of the proposed elements in analyzing the thin bending plates.