An adaptive and selective generalized finite element method for free vibration of trusses

Resumo

The ability to support large loads over a great span makes trusses structural systems with a variety of
applications in engineering. In regards to dynamic analysis, such structures do have few known analytical solutions
and, thus, are usually analyzed through approximated methods such as the Generalized Finite Element Method
(GFEM). The GFEM is based on the Partition of Unity Method and uses previous knowledge of the problem’s
solution to expand the traditional Finite Element Method (FEM) approximation space. In previous literature an
adaptive GFEM has been proposed for the free vibration problem of bars and trusses and has led to excellent
results. This method consists of an iterative process that incorporates in the enrichment an approximated natural
frequency result in each step. On the other hand, another technique found in literature is the use of the Friberg
error indicator to identify which elements of a mesh have greater impact on the solution in an enrichment process.
The indicator has already been shown to be applicable in GFEM analysis. The selective technique aims to reduce
the number of degrees of freedom necessary in obtaining good approximations of a determined natural frequency.
In this paper a selective adaptive technique is proposed. The Friberg indicator is used to define which bars of the
truss will be enriched and the adaptive process is used to improve the accuracy of the solution. Thus, combining
the advantages of both methods leads to results with low error and reduced number of degrees of freedom when
compared to the traditional GFEM approach. The results obtained by the proposed technique are compared with
reference solutions found in literature.