Sergio Persival Baroncini Proença

An Object-Oriented class design for the Generalized Finite Element Method programming

The Generalized Finite Element Method (GFEM) is a numerical method based on the Finite Element Method (FEM), presenting as its main feature the possibility of improving the solution by means of local enrichment functions. In spite of its advantages, the method demands a complex data structure, which can be especially benefited by the Object-Oriented Programming (OOP). Even though the OOP for the traditional FEM has been extensively described in the technical literature, specific design issues related to the GFEM are yet little discussed and not clearly defined. In the present article it is described an Object-Oriented (OO) class design for the GFEM, aiming to achieve a computational code that presents a flexible class structure, circumventing the difficulties associated to the method characteristics. The proposed design is evaluated by means of some numerical examples, computed using a code implemented in Python programming language.

THE SPLITTING METHOD AND THE GFEMIN THE TWO-DIMENSIONAL ANALYSIS OF LINEAR ELASTIC DOMAINS WITH MULTIPLE CRACKS

THE AIM OF THIS PAPER IS TO ANALYSE TWO-DIMENSIONAL LINEAR ELASTIC CONTINUUM CONTAINING MULTIPLE INTERACTING CRACKS. BOTH THE MECHANI-CAL MODEL AND THE NUMERICAL APPROACH ARE ADDRESSED THROUGHOUT THE TEXT AS KEY CONCEPTS FOR THE COMPUTATIONAL FRAMEWORK, WHOSE MAIN CHARACTERISTICS WILL BE DESCRIBED. THE SPLITTING METHOD IS A DECOMPO-SITION METHOD CONSIDERED FOR MECHANICAL MODELING OF MULTIPLE INTER-ACTING CRACKS. ACCORDINGLY, THE ORIGINAL PROBLEM IS DIVIDED INTO A SET OF GLOBAL AND LOCAL SUB-PROBLEMS. THE GENERALIZED FINITE ELEMENT METHOD (GFEM) IS ADOPTED AIMING AT FINDING ACCURATE NUMERICAL SOLUTIONS FOR LOCAL SUB-PROBLEMS. SUCH PROBLEMS ARE CONCEIVED SO AS TO CONSIDER THE STRESS CONCENTRATION AND THE EFFECTS OF INTERACTION ON THE CRACKS. THE MAIN FINDINGS ARE RELATED TO THE EFFECTIVENESS OF THE PROPOSED COMBINATION BETWEEN THE SPLITTING METHOD AND THE GFEM TO PROVIDE ACCURATE RESULTS, AS WELL AS THE VERSATILITY OF THE CONCEIVED COMPUTATIONAL FRAMEWORK FOR ANALYZING DIFFERENT SCENARIOS, INCLUDING CRACKS OF MULTILINEAR SHAPES AND MIXED MODE FRACTURES.

Modelagem simplificada do processo de fissuração e colapso em pórticos e arcos de concreto armado

The consistent simulation of progressive failure and structural collapse processes still is a problem of great interest for the engineering. Among theories which are somehow capable of model such class of problems, the continuum damage mechanics is the latest. However, one of the issues that still persist is when in the numerical simulations the structure begins to present the strain localisation phenomenon, with consequent dependence of the results on the mesh used. To solve this problem several so-called regularisation methods were developed. Nevertheless, despite effectiveness these methods can insert a significant degree of complexity on the numerical approaches. In this paper is proposed a simplified methodology to nonlinear structural analysis of frames and arches by means of the previous localisation of inelastic phenomena on hinges, located on the edges of the finite elements of frame and arch. Therefore it is possible to circumvent the mesh dependency and to reproduce satisfactorily real problems, as the examples of reinforced concrete structures gathered at the end of this article.