Roque Luiz da Silva Pitangueira

An object-oriented approach to the Generalized Finite Element Method

The Generalized Finite Element Method (GFEM) is a meshbased approach that can be considered as one instance of the Partition of Unity Method (PUM). The partition of unity is provided by conventional interpolations used in the Finite Element Method (FEM) which are extrinsically enriched by other functions specially chosen for the analyzed problem. The similarities and differences between GFEM and FEM are pointed out here to expand a FEM computational environment. Such environment is an object-oriented system that allows linear and non-linear, static and dynamic structural analysis and has an extense finite element library. The aiming is to enclose the GFEM formulation with a minimum impact in the code structure and meet requirements for extensibility and robustness. The implementation proposed here make it possible to combine different kinds of elements and analysis models with the GFEM enrichment strategies. Numerical examples, for linear analysis, are presented in order to demonstrate the code expansion and to illustrate some of the above mentioned combinations.

AN OBJECT-ORIENTED CLASS ORGANIZATION FOR GLOBAL-LOCAL GENERALIZED FINITE ELEMENT METHOD

THIS PAPER SHOWS AND DISCUSSES A GENERIC IMPLEMENTATION OF THE GLOBAL-LOCAL ANALYSIS TOWARD GENERALIZED FINITE ELEMENT METHOD (GFEMGL). THIS IMPLEMENTATION, PERFORMED INTO AN ACADEMIC COMPU-TATIONAL 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: Generic imposition of boundary conditions

Purpose n n n n nThis paper aims to present a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon/phenomena. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having global- and local-scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately by using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution. n n n n nDesign/methodology/approach n n n n nThe implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analyses models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global–local strategy, the imposition of different boundary conditions is also generalized. n n n n nFindings n n n n nThe generalization done for boundary conditions is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are used, and the accuracy, robustness and computational efficiency are demonstrated. n n n n nOriginality/value n n n n nThis work shows a generalize imposition of different boundary conditions for global–local G/XFEM analysis through an object-oriented implementation. This generalization is very important, as the global–local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problems simultaneously and solving plate problems using global–local G/XFEM are other contributions of this work.

A Generalized Elasto-Plastic Micro-Polar Constitutive Model

This paper summarizes the implementation of an elasto-plastic constitutive model for a micro-polar continuum in the constitutive models framework of the software INSANE (INteractive Structural ANalysis Environment). Such an implementation is based on the tensorial format of a unified constitutive models formulation, that allows to implement different constitutive models independently on the peculiar numerical method adopted for the solution of the problem. The basic characteristics of the micro-polar continuum model and of the unified formulation of constitutive models are briefly recalled. A generalization of the micro-polar model is then introduced in order to include this model in the existent tensor-based formulation. Finally, an enhanced version of the general closest-point algorithm, ables to manage the generalized micro-polar formulation, is derived. A strain localization problem modeling illustrates the implementation.

A computational framework for G/XFEM material nonlinear analysis

Abstract The Generalized/eXtended Finite Element Method (G/XFEM) has been developed with the purpose of overcoming some limitations inherent to the Finite Element Method (FEM). Different kinds of functions can be used to enrich the original FEM approximation, building a solution specially tailored to problem. Certain obstacles related to the nonlinear analysis can be mitigated with the use of such strategy and the damage and plasticity fronts can be precisely represented. A FEM computational environment has been previously enclosed the G/XFEM formulation to linear analysis with minimum impact in the code structure and with requirements for extensibility and robustness. An expansion of the G/XFEM implementation to physically nonlinear analysis under the approach of an Unified Framework for constitutive models based on elastic degradation is firstly presented here. The flexibility of the proposed framework is illustrated by several examples with different constitutive models, enrichment functions and analysis models.

Discontinuous failure in micropolar elastic-degrading models

The present paper investigates the phenomenon of discontinuous failure (or localization) in elastic-degrading micropolar media. A recently proposed unified formulation for elastic degradation in micropolar media, defined in terms of secant tensors, loading functions and degradation rules, is used as a starting point for the localization analysis. Well-known concepts on acceleration waves propagation, such as the Maxwell compatibility condition and the Fresnel–Hadamard propagation condition, are derived for the considered material model in order to obtain a proper failure indicator. Peculiar problems are investigated analytically in details, in order to evaluate the effects on the onset of localization of two of the additional material parameters of the micropolar continuum, the Cosserat’s shear modulus and the internal bending length. Numerical simulations with a finite element model are also presented, in order to show the regularization behaviour of the micropolar formulation on the pathological effects due to the localization phenomenon.

Elementos finitos de casca do sistema computacional INSANE

This paper presents the shell finite elements of the computer system INSANE (INteractive Structural ANalysis Environment): four-node rectangular and threenode triangular, obtained by combining membrane and bending efforts, based on the Theory of Kirchhoff; a quadrilateral of four, eight and nine nodes that combines membrane, bending and shear efforts, according to the Reissner-Mindlin Theory. After summarizing the characteristics of the elements, the paper presents results of three convergence studies and two practical applications: an arch dam and a conicalcylindrical reservoir. The results are compared with analytical solutions and those obtained with the shell finite element of SAP2000.

Numerical Characterization of Concrete Heterogeneity

In this paper, a finite element model including both material heterogeneity and size effects is presented. The concrete is considered as a statistical combination of constituent phase with different properties (aggregate, mortar and interface material). The material point response is based on a combination of the random occurrence of the solid phases in the structural volume as well as on the differences of structural response due to the size effect. Such combination allows for higher or lower heterogeneity corresponding to smaller or larger structural size. Simulations of the material heterogeneity and associated size effect in a computationally efficient and simple manner show good qualitative agreement with available experimental results for the three-point bending and Brazilian split tests.