A finite element method with inter-element interpolation points for thin plate. Part I: Compatible formulation

In this study, an inter-element point interpolation is introduced within a displacement-based formulation of the Finite Element Method (FEM) to analyze elastic thin plates. The problem domain is discretized using a mesh of rectangular elements, where the deflection field is the sole primary variable. The displacement field is interpolated using quadratic functions, with the flexibility to customize these functions by adjusting the positions of control points either within, along the borders, or outside the mesh elements. This approach ensures continuity between adjacent elements and reduces the overall degrees of freedom in the governing discretized equations. A weak formulation is employed to derive the system of discretized equations, incorporating both displacement and rotational boundary conditions. The FEM formulation is implemented in a computational framework to solve the static problem of an elastic thin plate under a specified load. Numerical applications are conducted to evaluate the performance of the proposed model on isotropic, linear elastic thin plates. The results indicate that the model can accurately reproduce both displacement and moment fields, demonstrating good agreement with corresponding analytical solutions.