The Hierarchical Finite Element Method applied to dynamics analysis of Kirchhoff-Love plates

Resumo

The theoretical model proposed by Kirchhoff-Love, also referred to as the thin plate model, once applied
to the dynamic analysis, is useful on several problems in Engineering, such as seismic effects on slabs, dynamic
impacts of aircraft on airport runways and industrial floor structures subject to machinery activities. There is a lot
of numerical methods that intend to provide an approximate solution for this problem, for an example the
conventional Finite Element Method (FEM), the p-Fourier Method and the Hierarchical Finite Element Method
(HFEM). The aim of this paper is to evaluate the efficiency of the HFEM applied to free vibration analysis of thin
plates. The HFEM improves the accuracy of the solution by adding hierarchical shape functions of higher order.
This does not require a change in the mesh and in the number of element nodes, which would be necessary in the
conventional FEM. The results obtained by HFEM are compared to reference analytical solutions found in
literature and to other numerical methods, such as the conventional FEM and the p-Fourier Method.