Hybrid-Trefftz formulation for analysis of anisotropic and symmetric laminated plates

In this paper, two novel and efficient elements are proposed for analysis of anisotropic and symmetric laminated thick plates based on hybrid-Trefftz formulation. In this approach, two independent displacement fields are defined for internal and boundary of the elements. The internal field is selected in such a manner that the governing equation of thick plates could be satisfied. At the first step, the governing differential equations of anisotropic and symmetric laminated thick plates are derived. Then, the analytical solution of these equations is considered. By using these analytical functions, the internal displacement field of proposed elements is achieved. Also, the boundary field is related to the nodal degrees of freedom by the boundary interpolation functions. For this aim, the interpolation functions of tow-node laminated Timoshenko beam element are calculated for boundary field. By utilizing these displacement fields and hybrid-Trefftz functional, a triangular element THT-7 and quadrilateral element QHT-11 are proposed. These elements have 9 and 12 degrees of freedom, respectively. The results of the numerical testes are proven the absence of the shear locking and high accuracy and efficiency of the proposed elements for analysis of anisotropic and symmetric laminated plates.