An Object-Oriented Class Organization for Global-Local Generalized Finite Element Method

Abstract

This paper shows and discusses a generic implementation of the global-local analysis toward generalized finite element method (GFEM gl ). This implementation, performed into an academic computational platform, follows the object-oriented approach presented by the authors in a previous work for the standard version of GFEM in which the shape functions of finite elements are hierarchically enriched by analytical functions, according to the problem behavior. In global-local GFEM, however, the enrichment functions are constructed numerically from the solution of a local problem. This strategy allows the use of a coarse mesh even when the problem produces complex stress distributions. On the other hand, a local problem is defined where the stress field presents high gradients and it is discretized using a large number of elements. The results of the local problem are used to enrich the global problem which improves the approximate solution. The great advantage is allowing a well-refined description of the local problem, when necessary, avoiding an overburden for the computation of the global solution. Details of the implementation are presented and important aspects of using this strategy are highlighted in the numerical examples.

A computational framework for a two-scale generalized/extended finite element method

“…This computational framework, so called IN-SANE (Interactive Structural Analysis Environment) is an open source software available at http://www.insane.dees.ufmg.br. In the present paper, a new expansion that includes the G/XFEM gl is presented, extending the ideas firstly discussed in (Alves et al, 2013b, Malekan et al, 2016. The implementation, conducted through the development of comprehensive objectoriented design, allows generalization of the global-local approach in such way that any types of partition of unity methods, analysis model and enrichment strategy can be combined.…”

“…Actually, information of each local element will be used to enrich corresponding global element based on relationship between second and third steps of the global-local strategy. Further information on preliminary global-local implementation can be found in (Malekan et al, 2016). Figure 6 shows the relationship between the types of objects found in the package Value, which is used to define a generic boundary condition of the problem (e.g., conditions of Dirichlet, Neumann or Cauchy required by Eq.…”

A computational framework for the constitutive modeling of nonlinear micropolar media

“…The INSANE system [35] is an open-source software for computational mechanics based on the language Java, with an object-oriented structure. Since the structure of the software have been widely discussed in a number of previous publications (a selection of references on this topic from the same research group of the authors is, e.g., [34,54,55]), this section will deal only with the modules that are related to the implementation of the models described in Sect. 3.…”

Analysis of a main fatigue crack interaction with multiple micro-cracks/voids in a compact tension specimen repaired by stop-hole technique

“…The XFEM was introduced to overcome FEM issues with the discontinuity problems. [48][49][50][51][52] This is a partition of unity-based method that uses enrichment functions to represent phenomena of the problem and also to guarantee inter-element continuity. 53 The enrichment function allows the insertion of a crack inside the elements.…”