Artigos em revistas


A computational framework for a two-scale generalized/extended finite element method: generic imposition of boundary conditions

Mohammad Malekan, Felicio Barros, Roque Luiz da Silva Pitangueira, Phillipe Daniel Alves, Samuel Silva Penna

Engineering Computations , v. 34, Issue 3 , 2017

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Resumo (em inglês)

Purpose
This paper presents a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having a 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 using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution.

Design/methodology/approach
The 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 analysis 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.

Findings
The generalization done for boundary conditions is very important since 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 employed and the accuracy, robustness and computational efficiency are demonstrated.

Originality/value
This 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 since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. Also, solving multiple local problem simultaneously and solving plate problems using global-local G/XFEM is another contributions of this work.


A computational framework for constitutive modelling

Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira

Computers & Structures , v. 187 , p. 1-23 , 2017

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Resumo (em inglês)

The field of computational constitutive modelling for engineering applications is an active research tread in academia. New advanced models and formulations are constantly proposed. However, when dealing with implementation aspects, often the main concern is to provide a minimal environment to show a certain model and its applications, with implementations made from scratch. Though advanced, usually such implementations lack of generality and are well-suited for a certain numerical method while not compatible with other ones, making it difficult to reuse the code in other contexts. The Object-Oriented Paradigm (OOP) to programming have been widely applied in the last years for the realization of numerous academic numerical simulation softwares, due to its fundamental properties of abstraction, inheritance and polymorphism that allow the creation of programs well-suited for an easy collaboration between developers with expertise in different fields of engineering and mechanics. As showed in this paper, the same properties can be effectively extended also to the constitutive aspects of a model. The application of the OOP to the constitutive modelling of a wide range of materials of engineering interest is investigated, aiming to the creation of a computational framework for constitutive models that is fully independent on the other components of a code and easy to expand.


A computational framework for G/XFEM material nonlinear analysis

A.B. Monteiro, A.R.V. Wolenski, F.B. Barros, R.L.S. Pitangueira, S.S. Penna

Advances in Engineering Software , 2017

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Resumo (em inglês)

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.


An enhanced tensorial formulation for elastic degradation in micropolar continua

Lapo Gori, Samuel Silva Penna, Roque Luiz da Silva Pitangueira

Applied Mathematical Modelling , v. 41 , p. 299-315 , 2017

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Resumo (em inglês)

In the past, a lot of applications of the micropolar (or Cosserat) continuum theory have been proposed, especially in the field of granular materials analysis and for strain localization problems in elasto-plasticity, due to its regularization properties. In order to make possible the application of the micropolar theory to different constitutive models and to extend its regularization properties also to damage models, in this work a general formulation for elastic degradation based on the micropolar theory is proposed. Such formulation is presented in a unified format, able to enclose different kinds of elasto-plastic, elastic-degrading and damage constitutive models. A peculiar tensor-based representation is introduced, in order to guarantee the conformity with analogous theories based on the classic continuum, in such a way as to make possible the application to the micropolar theory of theoretical and numerical resources already defined for the classic theory. Peculiar micropolar scalar damage models are also proposed, and derived within the new general formulation.


High regularity partition of unity for structural physically non-linear analysis

D.C.C. Pinheiro, F.B. Barros, R.L.S. Pitangueira, S.S. Penna

Engineering Analysis with Boundary Elements , v. 83 , p. 43-54 , 2017

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Resumo (em inglês)

Meshfree techniques, such as hp-Clouds and Element Free Galerkin Methods, have been used as attractive alternatives to finite element method, due to the flexibility in constructing conforming approximations. These approximations can present high regularity, improving the description of the state variables used in physically non-linear problems. On the other hand, some drawbacks can be highlighted, as the lack of the Kronecker-delta property and numerical integration problems. These drawbacks can be overcome by using a Ck, k arbitrarily large, partition of unity (PoU) function, built over a finite element mesh, but with the approximate characteristic of the meshfree methods. Here, this procedure is for the first time investigated to simulate the non-linear behavior of structures with quasi-brittle materials. The smeared crack model is adopted and numerical results, obtained with different kinds of polynomial enrichments, are compared with the experimental results.


A solution strategy for non-linear implicit BEM formulation using a unified constitutive modelling framework

R.G. Peixoto, F.E.S. Anacleto, G.O. Ribeiro, R.L.S. Pitangueira, S.S. Penna

Engineering Analysis with Boundary Elements , v. 64 , p. 295-310 , 2016

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Resumo (em inglês)

A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is presented. Such strategy is based on a decomposition of the strain increment variation vector in two parts: one associated to the cumulative external loads and another associated to the current unbalanced vector, obtained from the difference of the first part and the calculated internal strain field distribution, during the iterative process. This approach makes the algorithm generic enough to deal with different control methods that governs the progression of the non-linear analysis. Also, a unified constitutive modelling framework for a single loading function is used to provide the material constitutive informations required by the solution strategy, which permits the implementation of a very comprehensive series of models in an independent way. However, only local models were treated. To demonstrate the efficiency and versatility of the methodology, some numerical examples are presented.


An object-oriented class organization for global-local Generalized Finite Element method

Malekan, Mohammad; Barros, Felício Bruzzi; Pitangueira, Roque Luiz da Silva; Alves, Phillipe D.

Latin American Journal of Solids and Structures , v. 13, No. 13 , p. 2529-2551 , Rio de Janeiro , 2016

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Resumo (em inglês)

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 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 generalized elasto-plastic micro-polar constitutive model

Lapo Gori, Roque Luiz da Silva Pitangueira, Samuel Silva Penna, Jamile Salim Fuina

Applied Mechanics and Materials , v. 798 , p. 505-509 , 2015

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Resumo (em inglês)

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.


Experimental and finite element analysis of bond-slip in reinforced concrete

Wolenski, Anderson Renato Vobornik, Castro, Saulo Silvestre, Penna, Samuel Silva, Pitangueira, R. L. S.

Revista IBRACON de Estruturas e Materiais , v. 8, N. 6 , p. 787-799 , São Paulo , 2015

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Resumo

A modelagem de estruturas de concreto armado tem tido um crescente progresso na Mecânica Computacional, de modo que os fenômenos complexos, tais como fissuração e esmagamento, fluência, escoamento da armadura, perda da aderência aço-concreto, podem ser modelados de forma razoavelmente realista, usando um conjunto apropriado de recursos numéricos e computacionais. Entre as diversas opções, os baseados no Método dos Elementos Finitos (MEF) permitem simulações complexas de análises de estruturas de concreto armado, incluindo a interação de diferentes efeitos não lineares. Este artigo lida com a análise não linear em elementos finitos, da perda de aderência entre a armadura de aço e o concreto, levando em consideração um estudo experimental anteriormente realizado. A análise via MEF apresentada usa uma combinação de recursos onde o comportamento do concreto é descrito pelo Modelo Constitutivo de Microplanos, e um Modelo de Armadura Embutida é usado para representar o aço inserido no concreto e levar em conta o efeito da perda de aderência. Os modelos do MEF foram criados usando o sistema computacional INSANE (Interactive Structural Analysis Environment), software de código aberto que possui um conjunto de ferramentas para análise não linear de estruturas em concreto armado. As correlações entre os resultados numérico-experimentais e os vários parâmetros validam a combinação de recursos proposta e identificam o significado de vários efeitos sobre a resposta.


An object-oriented approach to the Generalized Finite Element Method

Alves, Phillipe D., Barros, Felício Bruzzi, Pitangueira, Roque Luiz da Silva

Advances in Engineering Software , v. 59 , p. 1-18 , 2013

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Resumo (em inglês)

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 tridimensional self-regular boundary element method implementation

Anacleto, F.E.S., Ribeiro, T.S.A., Ribeiro, G.O., Pitangueira, R.L.S. ; Penna, S.S.

Engineering Analysis with Boundary Elements , v. 37, Issue 10 , p. 1276-1284 , 2013

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Resumo (em inglês)

The object-oriented design used to implement a self-regular formulation of the boundary element method is presented. The self-regular formulation is implemented to four integral equations: the displacement boundary integral equation, and the Somigliana’s integral identities for displacement, stress and strain. The boundary-layer effect that arises in the classical BEM on the transition from interior to boundary points is eliminated and thus special integration schemes to treat nearly singular integrals become unnecessary. The self-regular formulations lead to very accurate results. Comparisons of displacements, stress and strain obtained from analytical solutions and the numerical results for bidimensional and tridimensional elastostatics problems are presented, and the self-regular formulation shows strong stability. The implemented code is open-source and is available under the GNU General Public License.


Estudo comparativo de modelos de fissuração distribuída para estruturas de concreto

Samuel Silva Penna, Roque Luiz da Silva Pitangueira, Jamile Salim Fuina

Semina: Ciências Exatas e Tecnológicas , v. 34, N. 2 , p. 211-228 , Londrina , 2013

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Resumo

O artigo mostra como a modelagem constitutiva do concreto evoluiu, desde as tentativas iniciais de caracterizar o meio fissurado como contínuo, passando-se pelos modelos de fissuras distribuídas, de dano e de microplanos, até a tendência atual de conceber diferentes modelos segundo um único arcabouço teórico. Uma formulação genérica para os modelos de fissuração distribuída, que inclui os modelos de direção fixa e rotacional, bem como a degradação em tração e em compressão, é apresentada. Usando esta formulação, três modelos são gerados, especificando as leis de degradação. Um estudo comparativo dos modelos, baseado em simulações computacionais de uma viga submetida a cisalhamento em quatro pontos, é apresentado. Os resultados são comparados, entre si e com resultados experimentais, permitindo uma análise critica dos modelos.


A comparison of two microplane constitutive models for quasi-brittle materials

Fuina, J.S., Pitangueira, R.L.S., Penna, S.S.

Applied Mathematical Modelling , v. 35, Issue 11 , p. 5326-5337 , 2011

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Resumo (em inglês)

This article presents a comparison of two microplane constitutive models. The basis of the microplane constitutive models are described and the adopted assumptions for the conception of these models are discussed, with regard to: decomposition of the macroscopic strains into the microplanes, definition of the microplane material laws, including the choice of variables that control the material degradation, and homogenization process to obtain the macroscopic quantities. The differences between the two models, with respect to the employed assumptions, are emphasized and expressions to calculate the macroscopic stresses are presented. The models are then used to describe the behavior of quasi-brittle materials by finite element simulations of uniaxial tension and compression and pure share stress tests. The results of the simulations permit to compare the capability of the models in describing the post critical strain-softening behavior, without numerically induced strain localization.


Abordagem orientada a objetos para implementação computacional de elementos finitos de placa

Samir Silva Saliba, Samuel Silva Penna, Roque Luiz Pitangueira

Cadernos de Engenharia de Estruturas (Online) , v. 13, N. 60 , p. 37-54 , São Carlos , 2011

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Resumo

Este artigo apresenta um programa computacional para análise estrutural de placas que disponibiliza vários elementos finitos, baseados nas teorias de Kirchhoff e de Reissner-Mindlin. Essas teorias são discutidas brevemente, destacando-se diferenças e particularidades relevantes para o projeto do software. A implementação do sistema, realizada segundo o paradigma de programação orientada a objetos, é então apresentada através de diagramas Unified Modelling Language (UML) que descrevem as principais classes e interfaces utilizadas. Para fins de ilustração e validação dos recursos disponibilizados, algumas simulações numéricas são apresentadas. Por fim, a importância do sistema para apoiar o estudo do tema e as possibilidades de expansão do mesmo são discutidas.


Elementos finitos de casca do sistema computacional INSANE

Flávio Henrique Ajeje, Samuel Silva Penna, Roque Luiz da Silva Pitangueira

Rem: Revista Escola de Minas , v. 64, N. 4 , p. 399-405 , Ouro Preto , 2011

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Resumo

Esse artigo apresenta os elementos finitos de casca do sistema computacional INSANE (INteractive Structural ANalysis Environment): retangular de quatro nós e triangular de três nós, obtidos por combinações de esforços de membrana e flexão, baseadas na Teoria de Kirchhoff; quadrilaterias de quatro, oito e nove nós, que combinam esforços de membrana, flexão e cisalhamento, conforme a Teoria de Reissner-Mindlin. Após resumir as características dos elementos, o artigo apresenta resultados de três estudos de convergência e de duas aplicações práticas: uma barragem em arco e um reservatório cônico-cilíndrico. Os resultados são comparados com soluções analíticas e com aqueles obtidos com o elemento finito de casca do SAP2000.


Contínuos Generalizados: de Voigt à modelagem de materiais parcialmente frágeis

Jamile Salim Fuina, Roque Luiz da Silva Pitangueira, Samuel Silva Penna

Semina: Ciências Exatas e Tecnológicas , v. 31 , p. 119-130 , Londrina , 2010

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Resumo

Este artigo discute a utilização das teorias de contínuos generalizados para incorporar os efeitos da microestrutura na análise não linear, via Método dos Elementos Finitos, de materiais parcialmente frágeis e, assim, sanar problemas de dependência de malha. Inicia-se com uma descrição do problema denominado localização de deformações numericamente induzida, frequentemente encontrado em análises numéricas fisicamente não lineares via Método dos Elementos Finitos. A seguir, apresenta-se um breve histórico sobre os modelos baseados na Mecânica do Contínuo Generalizado, desde o trabalho inicial de Voigt (1887) até estudos mais recentes. Analisando esses modelos, observa-se que o contínuo de Cosserat e o contínuo com microexpansão são casos particulares de uma formulação geral que descreve o contínuo micromórfico. Após relatar tentativas de incorporação dos efeitos da microestrutura do material em modelos baseados na Mecânica do Contínuo Clássico, o artigo mostra a recente tendência de fazê-la segundo as premissas da Mecânica do Contínuo Generalizado. Por fim, apresentam-se resultados numéricos que permitem caracterizar esta tendência como um promissor caminho para solucionar o problema.


Um modelo para propagaςão de fissuras no concreto baseado no Método dos Elementos Finitos Estendido

Kelson Pothin Wolff, Roque Luiz Pitangueira, Samuel Silva Penna

Mecánica Computacional , v. XXIX , p. 10131-10153 , 2010

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Resumo

O artigo trata da implementação computacional de um modelo capaz de descrever o comportamento do concreto sujeito à fissuração. Utilizam-se relações constitutivas baseadas no modelo de fissuras coesivas para representar a região fissurada do concreto, enquanto o restante do volume nãofissurado é representado como linearmente elástico. Tais relações constitutivas são, então, combinadas com as hipóteses do Método dos Elementos Finitos Estendido, formando um modelo que, introduzindo um salto no campo de deslocamentos do Método dos Elementos Finitos Padrão, para representar a descontinuidade provocada neste campo pela fissura, é capaz de descrever a propagação da mesma. O critério de propagação é baseado no limite de resistência à tração do material e a geometria da fissura é definida por um conjunto de segmentos lineares. O modelo assim concebido permite que a fissura se propague livremente pela malha convencional, atravessando o domínio e a interface dos elementos finitos. O modelo foi implementado no núcleo numérico do sistema computacional INSANE (Interactive Structural Analysis Environment), permitindo simular problemas de propagação de fissuras em peças de concreto submetidas a tração axial, flexão e compressão diametral. Os resultados são obtidos dentro da faixa de resposta esperada. A principal dificuldade encontrada relaciona-se com o critério de propagação escolhido, que não se mostra adequado para predição da direção correta de propagação da fissura quando a análise alcança níveis elevados de tensão.