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

Abstract

This study introduces a new mixed finite element formulation for the analysis of elastic thin plates, incorporating inter-element interpolation points for enhanced performance and implementation simplicity. The method utilizes a regular rectangular mesh, where the displacement field is interpolated using bi-quadratic functions, and the stress field is approximated through bi-linear interpolation. The quadratic interpolation for displacements is flexibly defined by adjusting the positions of control points, which can be located within, on the boundaries, or outside, of the mesh elements. This approach ensures continuity across mesh elements while reducing the degrees of freedom in the discretized system of equations.The governing equations are derived by enforcing the stationary of the mixed Hellinger–Reissner functional. Numerical applications are conducted for isotropic, linearly elastic thin plates subjected to different loading conditions and boundary conditions. The numerical results demonstrate the high accuracy of the proposed method in reproducing displacement and stress fields, showing excellent agreement with analytical solutions and validating its effectiveness.