Papers by Gabriel Ribeiro
Applied Mathematical Modelling, May 1, 2019
The conventional (local) constitutive modelling of materials exhibiting strain softening behaviou... more The conventional (local) constitutive modelling of materials exhibiting strain softening behaviour is susceptive to a spurious mesh dependence caused by numerically induced strain localization. Also, for refined meshes, numerical instabilities may be verified, mainly if the simulations are performed by the boundary element method. An alternative to overcome such difficulties is the adoption of the so called non-local constitutive models. In these approaches, some internal variables of the constitutive model in a single point are averaged considering its values of the neighbouring points. In this paper, the implicit formulation of the boundary element method for physically non-linear problems in solid mechanics is used with a non-local isotropic damage model and a very simple averaging scheme, over internal cells, is introduced. It is shown that the analysis become more stable in comparison to the case of a local application of the same model and that the results recover the desired objectiveness to mesh refinement.
Size effect is an important issue in concrete structures bearing in mind that it can influence ma... more Size effect is an important issue in concrete structures bearing in mind that it can influence many aspects of analysis such as strength, brittleness and structural ductility, fracture toughness and fracture energy, among others. Further this, ever more new methods are being developed to evaluate displacement fields in structures. In this paper an experimental evaluation of the size effect is performed applying Digital Image Correlation (DIC) technique to measure displacements on the surface of beams. Three point bending tests were performed on three different size concrete beams with a notch at the midspan. The results allow a better understanding of the size effect and demonstrate the efficiency of Digital Image Correlation to obtain measures of displacements.
Engineering Analysis With Boundary Elements, Oct 1, 2013
Abstract The object-oriented design used to implement a self-regular formulation of the boundary ... more Abstract 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.
Engineering Analysis With Boundary Elements, Jul 1, 2017
The Implicit Formulation of the Boundary Element Method (BEM) is used to deal with physically non... more The Implicit Formulation of the Boundary Element Method (BEM) is used to deal with physically non-linear 2D-problems in solids. An isotropic damage constitutive model, equipped with a strain softening rule, is applied to increasingly narrow bandwidths, determined by mesh refinement, showing the typical post-peak meshdependence behaviour. The Continuum Strong Discontinuity Approach (CSDA), characterized by the introduction of discontinuous jumps in the displacement field together with an equilibrium verification (using continuous constitutive models) on the discontinuity line, is also applied to the implicit formulation of the BEM. By a simple numerical example, it is shown that, beyond the mesh independence, the CSDA results represent the limit case of a zero localization bandwidth. Moreover, to demonstrate the accuracy of the CSDA, other three examples involving concrete fracture are presented and the obtained results are compared with experimental or analytical data available in the literature.
ForScience, 2015
Este estudo aborda a técnica de modelagem da resposta acústica de um veículo automotor. Esta pesq... more Este estudo aborda a técnica de modelagem da resposta acústica de um veículo automotor. Esta pesquisa discorre sobre a construção de modelos numéricos em elementos finitos para investigar o efeito da utilização de componentes móveis (capô, portas laterais e tampa do porta malas) na resposta acústica de um veículo. Para tanto, foram construídos dois modelos: um que abrange a utilização de todos os componentes móveis, e outro, que substitui cada componente móvel por elementos unidimensionais (1D), contendo apenas a massa e a inércia que representa cada um destes componentes. A resposta obtida em cada uma das etapas da simulação numérica é comparada com os resultados experimentais, a fim de validar o procedimento e compreender a significância da utilização de um modelo numérico simplificado e assim, validar um modelo simplificado capaz de reproduzir computacionalmente e de forma satisfatória a resposta acústica de um veículo. A utilização do referido modelo simplificado possibilita a i...
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2018
A drawback of the boundary element method (BEM) to analyse solid non-linear problems is the neces... more A drawback of the boundary element method (BEM) to analyse solid non-linear problems is the necessity to discretize, not only the boundaries, but also the domain in internal cells. Such discretization is required to evaluate the domain integrals involving the inelastic (initial) fields and represents a loss of one of the most remarkable features of the BEM, which is the reduction of the problem's dimension by one order. However, only regions where the dissipative effects take place need to be divided in cells, allowing optimization of the non-linear solution algorithms. In this paper, one of these optimization attempts is present in which the cells are progressively activated, augmenting the corresponding matrices, as the inelastic region develop and grow. In addition, the implicit formulation of the BEM with a unified constitutive modelling framework is used in order that different material behaviours may be addressed by a single numerical structure. Three numerical examples are presented: two involving ductile material behaviour, modelled with the elastoplastic von Mises associative constitutive model, and another to simulate quasi-brittle behaviour by an isotropic damage constitutive model.
Engineering Fracture Mechanics, 2018
The implicit formulation of the boundary element method is applied to bidimensional problems of m... more The implicit formulation of the boundary element method is applied to bidimensional problems of material failure involving, sequentially, inelastic dissipation with softening in continuous media, bifurcation and transition between weak and strong discontinuities. The bifurcation condition is defined by the singularity of the localization tensor. Weak discontinuities are related to strain localization bands of finite width, which become increasingly narrow until to collapse in a surface with discontinuous displacement field, called strong discontinuity surface. To associate such steps to the fracture process in quasi-brittle materials, an isotropic damage constitutive model is used to represent the behaviour in all of them, considering the adaptations that come from the strong discontinuity analysis for the post-bifurcation steps. The crack propagation across the domain is done by an automatic cells generation algorithm and, in this context, the fracture process zone in the crack tip became totally represented.
Engineering Analysis with Boundary Elements, 2016
A new solution strategy for the non-linear Implicit Formulation of the Boundary Element Method is... more 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.
Proceedings of the ... International Congress of Mechanical Engineering, 2015
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2009
Two non-singular boundary element method (BEM) algorithms for two-dimensional potential problems ... more Two non-singular boundary element method (BEM) algorithms for two-dimensional potential problems have been implemented using isoparametric quadratic, cubic and quartic elements. The first one is based on the self-regular potential boundary integral equation (BIE) and the second on the self-regular flux-BIE. The flux-BIE requires the C 1,α continuity of the density functions, which is not satisfied by the standard isoparametric elements. This requirement is remedied by adopting the relaxed continuity strategy. The self-regular flux-BIE has presented some poor and oscillatory results, mainly with continuous quadratic elements. This odd behavior has completely disappeared when discontinuous elements, which satisfy the continuity requirement, were applied, and this suggests that the 'relaxed continuity hypothesis' seems to be the main cause of numerical errors in the implementation of the self-regular flux-BIE. On the other side, the potential algorithm has shown very reliable solutions.
This paper considers the practical application of nonlinear models in the analysis of reinforced ... more This paper considers the practical application of nonlinear models in the analysis of reinforced concrete structures. The results of some analyses performed using the reinforced concrete model of the general purpose finite element code Ansys are presented and discussed. The differences observed in the response of the same reinforced concrete beam as some variations are made in a material model that is always basically the same are emphasyzed. The consequences of small changes in modelling are discussed and it is shown that satisfactory results may be obtained from relatively simple and limited models.
International Journal for Numerical Methods in Engineering, 2003
This work presents two new error estimation approaches for the BEM applied to 2D potential proble... more This work presents two new error estimation approaches for the BEM applied to 2D potential problems. The ÿrst approach involves a local error estimator based on a gradient recovery procedure in which the error function is generated from di erences between smoothed and non-smoothed rates of change of boundary variables in the local tangential direction. The second approach involves the external problem formulation and gives both local and global measures of error, depending on a choice of the external evaluation point. These approaches are post-processing procedures. Both estimators show consistency with mesh reÿnement and give similar qualitative results. The error estimator using the gradient recovery approach is more general, as this formulation does not rely on an 'optimal' choice of an external parameter. This work presents also the use of a local error estimator in an adaptive mesh reÿnement procedure. This r-reÿnement approach is based on the minimization of the standard deviation of the local error estimate. A non-linear programming procedure using a feasible-point method is employed using Lagrange multipliers and a set of active constraints. The optimization procedure produces ÿner meshes close to a singularity and results that are consistent with the problem physics.
This work deals with the implementation of the boundary element method (BEM) for multiregion doma... more This work deals with the implementation of the boundary element method (BEM) for multiregion domain problems, under the hypothesis that the domain is composed of elasto/viscoplastic materials. The Perzyna’s flow rule is adopted in order to achieve viscoplastic responses. The technique adopted to solve the multi-region problem consists of applying the classical BEM to solve separately each region with interfacial nodes restrained against displacements and the other nodes with the specified boundary conditions. Following this, a stiffness matrix is evaluated for each subregion by successively applying the BEM with a unit displacement value prescribed to each degree of freedom correspondent to each interfacial node and direction. By enforcing the compatibility and equilibrium conditions at the interfacial nodes and assembling a global stiffness matrix one can evaluate the displacements at the interfaces, and after this, the remaining unknowns can be obtained. This technique can also be u...
The solution of linear problems of plates must be satisfied within the context of the respective ... more The solution of linear problems of plates must be satisfied within the context of the respective governing differential equations. This work deals with the formulation of the boundary integral equation of the bending plate problem taking into account the Reissner’s Theory and the numerical solution by means of boundary element method. The Reissner’s Theory considers the strain energy not only from bending deformation but also from transversal shear deformation, which leads to a partial differential equation of sixth order. It results in a more consistent numerical procedure in which three physical conditions along the boundary plate can be enforced. The implementation has been performed as an extension of a computational system based on object-oriented programming in Java called INSANE, developed at the Structural Engineering Department of UFMG. The current applications are focused in the analysis of flat plate slabs with supports inside the domain. The results obtained from several...
Computer Modeling in Engineering and Sciences
This work deals with a numerical solution technique for the self-regular gradient form of Green’s... more This work deals with a numerical solution technique for the self-regular gradient form of Green’s identity, the flux boundary integral equation (flux-BIE). The required C 1,α inter-element continuity conditions for the potential derivatives are imposed in the boundary element method (BEM) code through a non-symmetric variational formulation. In spite of using Lagrangian C 0 elements, accurate numerical results were obtained when applied to heat transfer problems with singular or quasi-singular conditions, like boundary points and interior points which may be arbitrarily close to the boundary. The numerical examples proposed show that the developed algorithm based on the self-regular flux-BIE are highly efficient, and quite straightforward in that no integral transformations are necessary to compute the singular integrals and even a small number of integration Gauss points gives very accurate results. The variational self-regular flux-BIE formulation has improved the results for quad...
Advances in Computational Mechanics with High Performance Computing, 1998
This paper considers the practical application of nonlinear models in the analysis of reinforced ... more This paper considers the practical application of nonlinear models in the analysis of reinforced concrete structures. The results of some analyses performed using the reinforced concrete model of the general purpose finite element code Ansys are presented and discussed. The differences observed in the response of the same reinforced concrete beam as some variations are made in a material model that is always basically the same are emphasyzed. The consequences of small changes in modelling are discussed and it is shown that satisfactory results may be obtained from relatively simple and limited models.
The formulation of the Boundary Element Method applied to the plate bending problem using the Rei... more The formulation of the Boundary Element Method applied to the plate bending problem using the Reissner's hypothesis is developed. This hypothesis makes possible to achieve a more consistent numerical procedure in which three physical conditions along the plate boundary can be enforced. The boundary element approach using this theory is extended to consider initial stress fields over the plate domain, as well as to take into account several kinds of loads. The presence of initial stress fields enables one to analyze shrinkage and temperature effects, and to formulate procedures to deal with physical non-linearities. A procedure to consider elastoplastic behavior of RC plates is implemented using an incremental iterative algorithm based on the modified Newton-Raphson Method, where the plastic solution is obtained by applying initial stress fields. The elastoplastic concrete behavior is modeled based on the Willam-Warnke version of the five parameter failure surface. This surface is taken directly as a fixed yield surface in the stress space and the steel bars are regarded as unidimensional elements of elastic perfectly plastic material under the Von Mises yield criterion. The concrete behaves as a perfect plastic material after the maximum carrying capacity has been reached. An associated flow rule is adopted. There is no need to assume fictitious plate division into layers, in order to take into account of the through-thickness yielding, as usually made for this kind of problem. Stresses are computed at selected control Gauss points defined along the thickness and in each of these points a plane stress state is achieved and analyzed.
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Papers by Gabriel Ribeiro