Artur Portela - Profile on Academia.edu (original) (raw)
Papers by Artur Portela
Boundary Elements and other Mesh Reduction Methods XLI, Sep 11, 2018
The Meshfree Method with reduced integration (ILMF) is derived through the work theorem of struct... more The Meshfree Method with reduced integration (ILMF) is derived through the work theorem of structures theory. In the formulation of the ILMF, the kinematically-admissible strain field is an arbitrary rigid-body displacement; as a consequence, the domain term is canceled out and the work theorem is reduced to regular local boundary terms only. The moving least squares (MLS) approximation of the elastic field is used to construct the trial function in this local meshfree formulation. ILMF has a high performance in problems with irregular nodal arrangement leading to accurate numerical results. This paper presents the size effect of the irregularity nodal arrangement parameter (cn) on three different nodal discretization to solve the Timoshenko cantilever beam using values fixed for the local support domain (αs) and the local quadrature domain (αq). Results obtained are optimal for 2D plane stress problems when compared with the exact solution.
Brazilian Journal of Development, 2021
This paper is concerned with new formulations of local meshfree numerical method, for the solutio... more This paper is concerned with new formulations of local meshfree numerical method, for the solution of dynamic problems in linear elasticity, Integrated Local Mesh Free (ILMF) method. The key attribute of local numerical methods is the use of a modeling paradigm based on a node-by-node calculation, to generate the rows of the global system of equations of the body discretization. In the local domain, assigned to each node of a discretization, the work theorem is kinematically formulated, leading thus to an equation of mechanical equilibrium of the local node, that is used by local meshfree method as the starting point of the formulation. The main feature of this paper is the use of a linearly integrated local form of the work theorem. The linear reduced integration plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy. As a consequence, the derived meshfree and fin...
Approximation Methods
Finite Elements Using Maple, 2002
Introduction to Maple
Finite Elements Using Maple, 2002
Maple is a symbolic computational system. This means that it does not require numerical values fo... more Maple is a symbolic computational system. This means that it does not require numerical values for all variables, as numerical systems do, but manipulates information in a symbolic or algebraic manner, maintaining and evaluating the underlying symbols, like words and sentence-like objects, as well as evaluates numerical expressions. As a complement to symbolic operations, Maple provides the user with a large set of graphic routines, numerical algorithms and a comprehensive programming language.
Shape optimal design of structures with dual boundary elements
This paper is concerned with the numerical implementation of the dual boundary element method for... more This paper is concerned with the numerical implementation of the dual boundary element method for shape optimal design of two-dimensional linear elastic structures. The design objective is to minimize the structural compliance, subject to an area constraint. Sensitivities of objective and constraint functions, derived by means of Lagrangean approach and the material derivative concept with an adjoint variable technique, are computed through analytical expressions that arise from optimality conditions. The dual boundary element method, used for the discretization of the state problem, applies the stress equation for collocation on the design boundary and the displacement equation for collocation on other boundaries. The use of the stress boundary integral equation, discretized with discontinuous quadratic elements, allows an efficient and accurate computation of stresses on the design boundary. The perturbation field is described with linear continuous elements, in which the position of each node is defined by a design variable. Continuity along the design boundary is assured by forcing the end points of each discontinuous boundary element to be coincident with a design node. The optimization problem is solved by the modified method of feasible directions available in the program ADS. Examples of a plate with a hole are analyzed with the present method, for different loading conditions. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of shape optimal design of structures.
Fundamental Concepts and Models for the Direct Problem
This chapter presents the most recent developments on mesh free numerical methods at the Departme... more This chapter presents the most recent developments on mesh free numerical methods at the Department of Civil Engineering and Environment of the University of Brasília. Therefore, the concern of this chapter is a local mesh free method for solving linear elastic and fracture mechanics two-dimensional problems. For a nodal discretization of the problem domain, based in the work theorem from the theory of structures, the global system of equilibrium equations is constructed using a nodeby-node process, performed in the local domain of each node. The reduced numerical integration is implemented to improves the model accuracy. Both regular and irregular nodal distributions can be considered, which makes it a reliable model. Local mesh free numerical methods depends on two arbitrary parameters for the analysis: the size of the compact support, which control the accuracy; and the local domain of integration, which control the efficiency. Both parameters are automatically defined by means of a multi-objective optimization process, based on genetic algorithms and symbiotic organism search algorithm, which makes it a robust model. Linear elastic fracture mechanics applications of local mesh free are performed through the singularity subtraction technique (SST), which regularizes the elastic field, before the numerical solution, thus introducing the stress intensity factors (SIF) as additional primary unknowns of the problem. Hence, the numerical model performs a direct computation of the SIF and does not require a refined discretization to obtain accurate results which, therefore, is an efficient model strategy. On all this cases, benchmark problems were solved for an assessment of the accuracy and efficiency of these techniques.
Global journal of research in engineering, Jan 11, 2022
In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since t... more In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since the representation of this singularity in a numerical model raises considerable numerical difficulties, the paper uses a strategy that regularizes the elastic field, subtracting the singularity from the stress field, known as the singularity subtraction technique (SST). In this paper, the SST is implemented in a local mesh-free numerical model, coupled with modern optimization schemes, used for solving twodimensional problems of the linear elastic fracture mechanics. The mesh-free numerical model (ILMF) considers the approximation of the elastic field with moving least squares (MLS) and implements a reduced numerical integration. Since the ILMF model implements the singularity subtraction technique that performs a regularization of the stress field, the mesh-free analysis does not require a refined discretization to obtain accurate results and therefore, is a very efficient numerical analysis.
Método Sem Malha Local Com Integração Reduzida Para Configuração Nodal Com Grande Irregularidade
Tópicos em ciências exatas e da Terra, 2021
Generalized-strain mesh-free method (GSMF) for two-dimensional elasticity problems
Comparative Study of the Weak-Form Collocation Meshless Formulation and Other Meshless Methods
Abstract. This paper is concerned with the numerical comparison of the weak-form collocation, a n... more Abstract. This paper is concerned with the numerical comparison of the weak-form collocation, a new local meshless method, and other meshless methods, for the solution of two-dimensional problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain Mesh-free (GSMF) formulation, the Rigid-body Displacement Mesh-free (RBDMF) formulation, the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume Method (MLPG FVM). While the RBDMF, EFG and MLPG FVM rely on integration and quadrature process to obtain the stiffness matrix, the GSMF is completely integration free, working as a weighted-residual weak-form collocation. This weak-form collocation readily overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and instability of the solution. A numerical example was analyzed with these methods, in order to assess the accuracy and the computational effort. The results obtained are in agreement with those of...
Finite Elements Using Maple, 2002
I hereby declare that all information in this document has been obtained and presented in accorda... more I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.
Local Meshfree Method Optimization with Genetic Algorithms
Coleção desafios das engenharias: Engenharia de computação 3
Trefftz boundary element method applied to fracture mechanics
The linear elastic problem is solved by means of Trefftz functions which automatically satisfy th... more The linear elastic problem is solved by means of Trefftz functions which automatically satisfy the elasticity equations in a 2D domain. Using Kolosov–Muskhelishvili's complex variable representation, complex potentials are expanded in power series. Trial elementary elastic ...
The present paper further develops the boundary element singularity subtraction technique, to pro... more The present paper further develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed-mode deformation of two-dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. Extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the Williams solution; the procedure can take into account any number of terms of the series expansion. The standard boundary element method is modified to handle additional unknowns and extra boundary conditions. Analysis of plates with symmetry boundary conditions is shown to be straightforward, with the modified boundary element method. In the case of non-symmetrical plates, the singular tip-tractions are not primary boundary element unknowns. The boundary element method must be further modified to introduce the boundary integral stress equations of an internal point, approaching the notch-tip, as primary unknowns in the formulation. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed-mode problems. New results are presented for the mixed-mode analysis of a non-symmetrical configuration of a single edge notched plate.
This paper describes an application of the dual boundary element method to the analysis of mixed-... more This paper describes an application of the dual boundary element method to the analysis of mixed-mode crack growth in linear elastic fracture mechanics. Crack-growth processes are simulated with an incremental crack-extension analysis based on the maximum principal stress criterion which is expressed in terms of the stress intensity factors. For each increment of the crack extension, the dual boundary element method is applied to perform a single-region stress analysis of the cracked structure and the J-integral technique is used to compute the stress intensity factors. When the crack extension is modelled with new boundary elements, remeshing is not required because of the single-region analysis, an intrinsic feature of the dual boundary element method. Results of this incremental crack-extension analysis are presented for several geometries. The analysis of fatigue crack-growth is introduced as a post-processing procedure on the crack-extension results and an example is presented.
Boundary solutions for the linear theory of structures and the generalization of the work theorem
Formulation of local numerical methods in linear elasticity
Multidiscipline Modeling in Materials and Structures
PurposeThis paper is concerned with new formulations of local meshfree and finite element numeric... more PurposeThis paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.Design/methodology/approachIn the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.FindingsThe reduced integration, performed by this linearly integrated formulation, play...
Performance of the Weak-form Collocation Meshless Formulation
Proceedings of the 6th International Symposium on Solid Mechanics
Cracked plate analysis with the dual boundary element method and Williams׳ eigenexpansion
Engineering Analysis with Boundary Elements
ABSTRACT This paper provides a numerical verification that the singular term of Williams׳ series ... more ABSTRACT This paper provides a numerical verification that the singular term of Williams׳ series eigenexpansion can be used as a singular solution, valid in the neighborhood of each crack tip, in a single-region dual boundary element analysis of two-dimensional piece-wise flat multi-cracked plates, either with edge or internal cracks, in mixed-mode deformation, as an intermediate and necessary research step towards the implementation of the singularity subtraction technique.
Boundary Elements and other Mesh Reduction Methods XLI, Sep 11, 2018
The Meshfree Method with reduced integration (ILMF) is derived through the work theorem of struct... more The Meshfree Method with reduced integration (ILMF) is derived through the work theorem of structures theory. In the formulation of the ILMF, the kinematically-admissible strain field is an arbitrary rigid-body displacement; as a consequence, the domain term is canceled out and the work theorem is reduced to regular local boundary terms only. The moving least squares (MLS) approximation of the elastic field is used to construct the trial function in this local meshfree formulation. ILMF has a high performance in problems with irregular nodal arrangement leading to accurate numerical results. This paper presents the size effect of the irregularity nodal arrangement parameter (cn) on three different nodal discretization to solve the Timoshenko cantilever beam using values fixed for the local support domain (αs) and the local quadrature domain (αq). Results obtained are optimal for 2D plane stress problems when compared with the exact solution.
Brazilian Journal of Development, 2021
This paper is concerned with new formulations of local meshfree numerical method, for the solutio... more This paper is concerned with new formulations of local meshfree numerical method, for the solution of dynamic problems in linear elasticity, Integrated Local Mesh Free (ILMF) method. The key attribute of local numerical methods is the use of a modeling paradigm based on a node-by-node calculation, to generate the rows of the global system of equations of the body discretization. In the local domain, assigned to each node of a discretization, the work theorem is kinematically formulated, leading thus to an equation of mechanical equilibrium of the local node, that is used by local meshfree method as the starting point of the formulation. The main feature of this paper is the use of a linearly integrated local form of the work theorem. The linear reduced integration plays a key role in the behavior of local numerical methods, since it implies a reduction of the nodal stiffness which, in turn, leads to an increase of the solution accuracy. As a consequence, the derived meshfree and fin...
Approximation Methods
Finite Elements Using Maple, 2002
Introduction to Maple
Finite Elements Using Maple, 2002
Maple is a symbolic computational system. This means that it does not require numerical values fo... more Maple is a symbolic computational system. This means that it does not require numerical values for all variables, as numerical systems do, but manipulates information in a symbolic or algebraic manner, maintaining and evaluating the underlying symbols, like words and sentence-like objects, as well as evaluates numerical expressions. As a complement to symbolic operations, Maple provides the user with a large set of graphic routines, numerical algorithms and a comprehensive programming language.
Shape optimal design of structures with dual boundary elements
This paper is concerned with the numerical implementation of the dual boundary element method for... more This paper is concerned with the numerical implementation of the dual boundary element method for shape optimal design of two-dimensional linear elastic structures. The design objective is to minimize the structural compliance, subject to an area constraint. Sensitivities of objective and constraint functions, derived by means of Lagrangean approach and the material derivative concept with an adjoint variable technique, are computed through analytical expressions that arise from optimality conditions. The dual boundary element method, used for the discretization of the state problem, applies the stress equation for collocation on the design boundary and the displacement equation for collocation on other boundaries. The use of the stress boundary integral equation, discretized with discontinuous quadratic elements, allows an efficient and accurate computation of stresses on the design boundary. The perturbation field is described with linear continuous elements, in which the position of each node is defined by a design variable. Continuity along the design boundary is assured by forcing the end points of each discontinuous boundary element to be coincident with a design node. The optimization problem is solved by the modified method of feasible directions available in the program ADS. Examples of a plate with a hole are analyzed with the present method, for different loading conditions. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of shape optimal design of structures.
Fundamental Concepts and Models for the Direct Problem
This chapter presents the most recent developments on mesh free numerical methods at the Departme... more This chapter presents the most recent developments on mesh free numerical methods at the Department of Civil Engineering and Environment of the University of Brasília. Therefore, the concern of this chapter is a local mesh free method for solving linear elastic and fracture mechanics two-dimensional problems. For a nodal discretization of the problem domain, based in the work theorem from the theory of structures, the global system of equilibrium equations is constructed using a nodeby-node process, performed in the local domain of each node. The reduced numerical integration is implemented to improves the model accuracy. Both regular and irregular nodal distributions can be considered, which makes it a reliable model. Local mesh free numerical methods depends on two arbitrary parameters for the analysis: the size of the compact support, which control the accuracy; and the local domain of integration, which control the efficiency. Both parameters are automatically defined by means of a multi-objective optimization process, based on genetic algorithms and symbiotic organism search algorithm, which makes it a robust model. Linear elastic fracture mechanics applications of local mesh free are performed through the singularity subtraction technique (SST), which regularizes the elastic field, before the numerical solution, thus introducing the stress intensity factors (SIF) as additional primary unknowns of the problem. Hence, the numerical model performs a direct computation of the SIF and does not require a refined discretization to obtain accurate results which, therefore, is an efficient model strategy. On all this cases, benchmark problems were solved for an assessment of the accuracy and efficiency of these techniques.
Global journal of research in engineering, Jan 11, 2022
In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since t... more In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since the representation of this singularity in a numerical model raises considerable numerical difficulties, the paper uses a strategy that regularizes the elastic field, subtracting the singularity from the stress field, known as the singularity subtraction technique (SST). In this paper, the SST is implemented in a local mesh-free numerical model, coupled with modern optimization schemes, used for solving twodimensional problems of the linear elastic fracture mechanics. The mesh-free numerical model (ILMF) considers the approximation of the elastic field with moving least squares (MLS) and implements a reduced numerical integration. Since the ILMF model implements the singularity subtraction technique that performs a regularization of the stress field, the mesh-free analysis does not require a refined discretization to obtain accurate results and therefore, is a very efficient numerical analysis.
Método Sem Malha Local Com Integração Reduzida Para Configuração Nodal Com Grande Irregularidade
Tópicos em ciências exatas e da Terra, 2021
Generalized-strain mesh-free method (GSMF) for two-dimensional elasticity problems
Comparative Study of the Weak-Form Collocation Meshless Formulation and Other Meshless Methods
Abstract. This paper is concerned with the numerical comparison of the weak-form collocation, a n... more Abstract. This paper is concerned with the numerical comparison of the weak-form collocation, a new local meshless method, and other meshless methods, for the solution of two-dimensional problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain Mesh-free (GSMF) formulation, the Rigid-body Displacement Mesh-free (RBDMF) formulation, the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume Method (MLPG FVM). While the RBDMF, EFG and MLPG FVM rely on integration and quadrature process to obtain the stiffness matrix, the GSMF is completely integration free, working as a weighted-residual weak-form collocation. This weak-form collocation readily overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and instability of the solution. A numerical example was analyzed with these methods, in order to assess the accuracy and the computational effort. The results obtained are in agreement with those of...
Finite Elements Using Maple, 2002
I hereby declare that all information in this document has been obtained and presented in accorda... more I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.
Local Meshfree Method Optimization with Genetic Algorithms
Coleção desafios das engenharias: Engenharia de computação 3
Trefftz boundary element method applied to fracture mechanics
The linear elastic problem is solved by means of Trefftz functions which automatically satisfy th... more The linear elastic problem is solved by means of Trefftz functions which automatically satisfy the elasticity equations in a 2D domain. Using Kolosov–Muskhelishvili's complex variable representation, complex potentials are expanded in power series. Trial elementary elastic ...
The present paper further develops the boundary element singularity subtraction technique, to pro... more The present paper further develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed-mode deformation of two-dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. Extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the Williams solution; the procedure can take into account any number of terms of the series expansion. The standard boundary element method is modified to handle additional unknowns and extra boundary conditions. Analysis of plates with symmetry boundary conditions is shown to be straightforward, with the modified boundary element method. In the case of non-symmetrical plates, the singular tip-tractions are not primary boundary element unknowns. The boundary element method must be further modified to introduce the boundary integral stress equations of an internal point, approaching the notch-tip, as primary unknowns in the formulation. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed-mode problems. New results are presented for the mixed-mode analysis of a non-symmetrical configuration of a single edge notched plate.
This paper describes an application of the dual boundary element method to the analysis of mixed-... more This paper describes an application of the dual boundary element method to the analysis of mixed-mode crack growth in linear elastic fracture mechanics. Crack-growth processes are simulated with an incremental crack-extension analysis based on the maximum principal stress criterion which is expressed in terms of the stress intensity factors. For each increment of the crack extension, the dual boundary element method is applied to perform a single-region stress analysis of the cracked structure and the J-integral technique is used to compute the stress intensity factors. When the crack extension is modelled with new boundary elements, remeshing is not required because of the single-region analysis, an intrinsic feature of the dual boundary element method. Results of this incremental crack-extension analysis are presented for several geometries. The analysis of fatigue crack-growth is introduced as a post-processing procedure on the crack-extension results and an example is presented.
Boundary solutions for the linear theory of structures and the generalization of the work theorem
Formulation of local numerical methods in linear elasticity
Multidiscipline Modeling in Materials and Structures
PurposeThis paper is concerned with new formulations of local meshfree and finite element numeric... more PurposeThis paper is concerned with new formulations of local meshfree and finite element numerical methods, for the solution of two-dimensional problems in linear elasticity.Design/methodology/approachIn the local domain, assigned to each node of a discretization, the work theorem establishes an energy relationship between a statically admissible stress field and an independent kinematically admissible strain field. This relationship, derived as a weighted residual weak form, is expressed as an integral local form. Based on the independence of the stress and strain fields, this local form of the work theorem is kinematically formulated with a simple rigid-body displacement to be applied by local meshfree and finite element numerical methods. The main feature of this paper is the use of a linearly integrated local form that implements a quite simple algorithm with no further integration required.FindingsThe reduced integration, performed by this linearly integrated formulation, play...
Performance of the Weak-form Collocation Meshless Formulation
Proceedings of the 6th International Symposium on Solid Mechanics
Cracked plate analysis with the dual boundary element method and Williams׳ eigenexpansion
Engineering Analysis with Boundary Elements
ABSTRACT This paper provides a numerical verification that the singular term of Williams׳ series ... more ABSTRACT This paper provides a numerical verification that the singular term of Williams׳ series eigenexpansion can be used as a singular solution, valid in the neighborhood of each crack tip, in a single-region dual boundary element analysis of two-dimensional piece-wise flat multi-cracked plates, either with edge or internal cracks, in mixed-mode deformation, as an intermediate and necessary research step towards the implementation of the singularity subtraction technique.