Quadrilateral Finite Element for Thin and Thick Plates

The object of research is quadrilateral finite element based on linear approximations of moments for calculations thin and thick plates. Method. The additional energy functional, the virtual displacements principle and the moments approximations allows us to get analytically all necessary expressions of matrices elements. Using the virtual displacements principle, it is constructed the equilibrium equations, which are added to the additional energy functional. Results. The proposed method gives satisfactory results converging towards the reference solution as for the thin as thick plates. The locking effect for the thin plates is absent. It had been demonstrated the proposed finite element isn’t sensitive to the form distortions. The proposed method allows to calculate stiffness matrix of the finite element and to use it in the finite element method softs based on displacements approximations.