FLAT-TOP PARTITION OF UNIT IN THE GENERALIZED FINITE ELEMENT METHOD APPLIED TO DYNAMIC ANALYSIS

Resumo

The Generalized Finite Element Method (GFEM) has presented excellent results in the
dynamic analysis, especially in the obtaining of higher frequencies, one advantage compared to the
standard Finite Element Method (FEM). An important feature of GFEM is the possibility of expanding
the approximation space through the inclusion of non-polynomial enrichment functions, which usually
contain a-priori knowledge about the solution of the problem. However, this enrichment process may
lead a problem considerably ill-conditioned, limiting its applicability. This paper proposes the use of
flat-top functions as a Partition of Unit (PU) for the construction of approximation spaces enriched
with non-polynomial functions, aiming to improve the conditioning of the problem by reducing the

condition number of stiffness and mass matrices. Results are presented for one-dimensional and two-
dimensional problems, such as bars and membranes modal analysis, respectively. The condition

number of stiffness and mass matrices are evaluated and compared with results obtained by GFEM
with approximation spaces constructed with PU linear. Results obtained with the PU flat-top shown
improvement in the conditioning of the problems, with the reduction of the condition number of
stiffness and mass matrices, however with influences in the accuracy of responses.