Enrique Pardo - Academia.edu (original) (raw)

Papers by Enrique Pardo

In this work we describe and analyze the application of a meshless method to static and dynamic c... more In this work we describe and analyze the application of a meshless method to static and dynamic calculation of Kirchhoff thin plate problems. The method is based on the use of blurred derivatives. Briefly, blurred derivatives allow to transform differential equations into an integral equation which does no contain derivatives of the unknown function. The final expression is an updating formula which only has physical meaning in a limit known as a functional integral, so that the technique is designated as the Functional Integral Formulation (FIM) of continuous problems. The application of this meshless method for modeling plate problems offers a number of advantages over the traditional finite element method. It considerably simplifies data preparation in highly irregular structures and allows to use “p-refinement” without modifying the net of nodes. In this work we first describe the basics of the method and its computational implementation. The method is the applied to a static pr...

Se llevaron a cabo experimentos computacionales de la indentacion del PMMA en el codigo de elemen... more Se llevaron a cabo experimentos computacionales de la indentacion del PMMA en el codigo de elementos finitos ABAQUS 6.9. Para la descripcion de la respuesta tension-deformacion del PMMA se implemento el modelo constitutivo elasto-viscoplastico de Arruda-Boyce (AB). Se utilizaron los coeficientes del modelo existentes en la literatura y a partir de estos, se generaron curvas de carga de indentacion vs profundidad de penetracion. Estas curvas sirvieron como datos de entrada para el esquema de optimizacion con el fin de evaluar la conveniencia de la aplicacion del metodo inverso para la obtencion de parametros constitutivos.

Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleand... more Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleando aproximaciones sin red, particularizandose para interpolantes minimos cuadrados moviles (IMCM). Con este metodo no es necesario discretizar el recinto en elementos, sino solo definir un conjunto de nodos, lo que lo torna atractivo para resolver problemas tridimensionales, fronteras libres etc. Se emplea un principio variacional debil que permite imponer las condiciones de Dirichlet, las cuales no pueden ser impuestas a posteriori como en elementos finitos. Las ecuaciones son discretizadas usando interpolantes minimos cuadrados moviles. Se analizan ejemplos con solucion analitica, discutiendose los diversos aspectos de la aproximacion numerica. Se discuten las ventajas de este interpolante frente a otros metodos sin red y se propone un esquema de integracion optimo.

Revista Internacional De Metodos Numericos Para Calculo Y Diseno En Ingenieria, 2000

Se describe una formulación de la termoelasticidad lineal basada en propagadores, que se presta n... more Se describe una formulación de la termoelasticidad lineal basada en propagadores, que se presta naturalmente a implementaciones computacionales "sin red". Ello es porque, a diferencia de las formulaciones débiles, no requiere integrales sobre el dominio de cálculo. Asimismo, y a diferencia de las formulaciones fuertes, no requiere el cálculo de las derivadas segundas de las funciones de forma. Estoúltimo torna atractivo al método para ser utilizado con métodos de interpolación de elevado orden de continuidad, tal como Mínimos Cuadrados Móviles, donde el cálculo de derivadas es la etapa más costosa del cómputo. En la presente implementación se utilizan funciones de interpolación sumamente sencillas (ajuste de polinomios cuadráticos en torno a cada nodo), con la que se obtienen resultados suaves, tanto en desplazamientos como en tensiones, y buena precisión, no requiriéndose alisado posterior de la solución.

Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleand... more Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleando aproximaciones sin red, particularizandose para interpolantes minimos cuadrados moviles (IMCM). Con este metodo no es necesario discretizar el recinto en elementos, sino solo definir un conjunto de nodos, lo que lo torna atractivo para resolver problemas tridimensionales, fronteras libres etc. Se emplea un principio variacional debil que permite imponer las condiciones de Dirichlet, las cuales no pueden ser impuestas a posteriori como en elementos finitos. Las ecuaciones son discretizadas usando interpolantes minimos cuadrados moviles. Se analizan ejemplos con solucion analitica, discutiendose los diversos aspectos de la aproximacion numerica. Se discuten las ventajas de este interpolante frente a otros metodos sin red y se propone un esquema de integracion optimo.

Polymer Testing, 1997

The bending sttjjness of composite beams measured at different temperatures can be used to determ... more The bending sttjjness of composite beams measured at different temperatures can be used to determine interphase composition profiles generated by polymer-polymer interdiffusion, or solvent dijjksion into one face of the polymer beam. A suitable method to solve the inverse problem thus generated is presented here, which allows calculation of beam composition profiles. A simple numerical procedure is also outlined. Error propagation analysis is included, together with a precise guide to minimize experimental error.

Macromolecular Rapid Communications, 2000

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International Journal for Numerical Methods in Engineering, 2003

In this work we ÿrst introduce and describe the concept of blurred derivatives. It is shown how t... more In this work we ÿrst introduce and describe the concept of blurred derivatives. It is shown how they can be used both to approximate di erential equations and to re-express them in alternative ways. In particular, formulations in terms of functional integrals can be obtained using blurred derivatives and extended to non-linear problems. Blurred derivatives are shown to provide higher exibility for selection of approximation functions than strong and weak formulations. Some computational implementations of one-dimensional problems are discussed and the relationship between several well-known numerical methods is analysed. Finally a meshless numerical scheme for the Poisson equation is described in detail. Its performance is compared with linear ÿnite elements and generalized ÿnite di erences on unstructured meshes of points. Copyright ? 2002 John Wiley & Sons, Ltd.

International Journal for Numerical Methods in Engineering, 2000

Abstract A Path Integral (PI) formulation of linear elastostatics is first presented. For this, N... more Abstract A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equations are modified by adding a fictitious 'time'derivative of displacements so that equilibrium corresponds to the steady state of the resulting diffusion-like equations. The ...

International Journal for Numerical Methods in Engineering, 2000

Abstract Numerical modelling of polymer blends production and processing, while technologically i... more Abstract Numerical modelling of polymer blends production and processing, while technologically important, poses a considerable computational challenge when one or more of the polymer species is polydisperse. The mathematical formulation of such problems, ...

Communications in Numerical Methods in Engineering, 1998

Abstract In this paper a numerical solution for incompressible Stokes equations using moving leas... more Abstract In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D ...

Computer Methods in Applied Mechanics and Engineering, 2002

This paper addresses convergence rate and accuracy of a numerical technique for linear elastostat... more This paper addresses convergence rate and accuracy of a numerical technique for linear elastostatics based on a path integral formulation [Int. J. Numer. Math. Eng. 47 (2000) 1463]. The computational implementation combines a simple polynomial approximation of the ...

Engineering analysis with boundary elements, 2005

It is shown in this paper that self-consistent boundary conditions for numerical methods based on... more It is shown in this paper that self-consistent boundary conditions for numerical methods based on blurred derivatives can be derived from a suitable change of variables of the fundamental blurred approximation of the differential equation, followed by application of ...

Polymer testing, 1997

The bending stiffness of composite beams measured at different temperatures can be used to determ... more The bending stiffness of composite beams measured at different temperatures can be used to determine interphase composition profiles generated by polymer-polymer interdiffusion, or solvent diffusion into one face of the polymer beam. A suitable method to solve the ...

International Journal for …, 2000

Numerical modelling of polymer blends production and processing, while technologically important,... more Numerical modelling of polymer blends production and processing, while technologically important, poses a considerable computational challenge when one or more of the polymer species is polydisperse. The mathematical formulation of such problems, ...

International journal for numerical methods in …, 2003

In this work we first introduce and describe the concept of blurred derivatives. It is shown how ... more In this work we first introduce and describe the concept of blurred derivatives. It is shown how they can be used both to approximate differential equations and to re-express them in alternative ways. In particular, formulations in terms of functional integrals can be ...

… in numerical methods …, 1998

In this paper a numerical solution for incompressible Stokes equations using moving least-squares... more In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D ...

Computer methods in applied mechanics and …, 2002

This paper addresses convergence rate and accuracy of a numerical technique for linear elastostat... more This paper addresses convergence rate and accuracy of a numerical technique for linear elastostatics based on a path integral formulation [Int. J. Numer. Math. Eng. 47 (2000) 1463]. The computational implementation combines a simple polynomial approximation of the ...

International Journal for Numerical Methods in …, 2000

A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equ... more A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equations are modified by adding a fictitious 'time'derivative of displacements so that equilibrium corresponds to the steady state of the resulting diffusion-like equations. The ...

In this work we describe and analyze the application of a meshless method to static and dynamic c... more In this work we describe and analyze the application of a meshless method to static and dynamic calculation of Kirchhoff thin plate problems. The method is based on the use of blurred derivatives. Briefly, blurred derivatives allow to transform differential equations into an integral equation which does no contain derivatives of the unknown function. The final expression is an updating formula which only has physical meaning in a limit known as a functional integral, so that the technique is designated as the Functional Integral Formulation (FIM) of continuous problems. The application of this meshless method for modeling plate problems offers a number of advantages over the traditional finite element method. It considerably simplifies data preparation in highly irregular structures and allows to use “p-refinement” without modifying the net of nodes. In this work we first describe the basics of the method and its computational implementation. The method is the applied to a static pr...

Se llevaron a cabo experimentos computacionales de la indentacion del PMMA en el codigo de elemen... more Se llevaron a cabo experimentos computacionales de la indentacion del PMMA en el codigo de elementos finitos ABAQUS 6.9. Para la descripcion de la respuesta tension-deformacion del PMMA se implemento el modelo constitutivo elasto-viscoplastico de Arruda-Boyce (AB). Se utilizaron los coeficientes del modelo existentes en la literatura y a partir de estos, se generaron curvas de carga de indentacion vs profundidad de penetracion. Estas curvas sirvieron como datos de entrada para el esquema de optimizacion con el fin de evaluar la conveniencia de la aplicacion del metodo inverso para la obtencion de parametros constitutivos.

Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleand... more Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleando aproximaciones sin red, particularizandose para interpolantes minimos cuadrados moviles (IMCM). Con este metodo no es necesario discretizar el recinto en elementos, sino solo definir un conjunto de nodos, lo que lo torna atractivo para resolver problemas tridimensionales, fronteras libres etc. Se emplea un principio variacional debil que permite imponer las condiciones de Dirichlet, las cuales no pueden ser impuestas a posteriori como en elementos finitos. Las ecuaciones son discretizadas usando interpolantes minimos cuadrados moviles. Se analizan ejemplos con solucion analitica, discutiendose los diversos aspectos de la aproximacion numerica. Se discuten las ventajas de este interpolante frente a otros metodos sin red y se propone un esquema de integracion optimo.

Revista Internacional De Metodos Numericos Para Calculo Y Diseno En Ingenieria, 2000

Se describe una formulación de la termoelasticidad lineal basada en propagadores, que se presta n... more Se describe una formulación de la termoelasticidad lineal basada en propagadores, que se presta naturalmente a implementaciones computacionales "sin red". Ello es porque, a diferencia de las formulaciones débiles, no requiere integrales sobre el dominio de cálculo. Asimismo, y a diferencia de las formulaciones fuertes, no requiere el cálculo de las derivadas segundas de las funciones de forma. Estoúltimo torna atractivo al método para ser utilizado con métodos de interpolación de elevado orden de continuidad, tal como Mínimos Cuadrados Móviles, donde el cálculo de derivadas es la etapa más costosa del cómputo. En la presente implementación se utilizan funciones de interpolación sumamente sencillas (ajuste de polinomios cuadráticos en torno a cada nodo), con la que se obtienen resultados suaves, tanto en desplazamientos como en tensiones, y buena precisión, no requiriéndose alisado posterior de la solución.

Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleand... more Se presenta un esquema para la resolucion de las ecuaciones de elasticidad bidimensional empleando aproximaciones sin red, particularizandose para interpolantes minimos cuadrados moviles (IMCM). Con este metodo no es necesario discretizar el recinto en elementos, sino solo definir un conjunto de nodos, lo que lo torna atractivo para resolver problemas tridimensionales, fronteras libres etc. Se emplea un principio variacional debil que permite imponer las condiciones de Dirichlet, las cuales no pueden ser impuestas a posteriori como en elementos finitos. Las ecuaciones son discretizadas usando interpolantes minimos cuadrados moviles. Se analizan ejemplos con solucion analitica, discutiendose los diversos aspectos de la aproximacion numerica. Se discuten las ventajas de este interpolante frente a otros metodos sin red y se propone un esquema de integracion optimo.

Polymer Testing, 1997

The bending sttjjness of composite beams measured at different temperatures can be used to determ... more The bending sttjjness of composite beams measured at different temperatures can be used to determine interphase composition profiles generated by polymer-polymer interdiffusion, or solvent dijjksion into one face of the polymer beam. A suitable method to solve the inverse problem thus generated is presented here, which allows calculation of beam composition profiles. A simple numerical procedure is also outlined. Error propagation analysis is included, together with a precise guide to minimize experimental error.

Macromolecular Rapid Communications, 2000

Skip to Main Content. ...

International Journal for Numerical Methods in Engineering, 2003

In this work we ÿrst introduce and describe the concept of blurred derivatives. It is shown how t... more In this work we ÿrst introduce and describe the concept of blurred derivatives. It is shown how they can be used both to approximate di erential equations and to re-express them in alternative ways. In particular, formulations in terms of functional integrals can be obtained using blurred derivatives and extended to non-linear problems. Blurred derivatives are shown to provide higher exibility for selection of approximation functions than strong and weak formulations. Some computational implementations of one-dimensional problems are discussed and the relationship between several well-known numerical methods is analysed. Finally a meshless numerical scheme for the Poisson equation is described in detail. Its performance is compared with linear ÿnite elements and generalized ÿnite di erences on unstructured meshes of points. Copyright ? 2002 John Wiley & Sons, Ltd.

International Journal for Numerical Methods in Engineering, 2000

Abstract A Path Integral (PI) formulation of linear elastostatics is first presented. For this, N... more Abstract A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equations are modified by adding a fictitious 'time'derivative of displacements so that equilibrium corresponds to the steady state of the resulting diffusion-like equations. The ...

International Journal for Numerical Methods in Engineering, 2000

Abstract Numerical modelling of polymer blends production and processing, while technologically i... more Abstract Numerical modelling of polymer blends production and processing, while technologically important, poses a considerable computational challenge when one or more of the polymer species is polydisperse. The mathematical formulation of such problems, ...

Communications in Numerical Methods in Engineering, 1998

Abstract In this paper a numerical solution for incompressible Stokes equations using moving leas... more Abstract In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D ...

Computer Methods in Applied Mechanics and Engineering, 2002

This paper addresses convergence rate and accuracy of a numerical technique for linear elastostat... more This paper addresses convergence rate and accuracy of a numerical technique for linear elastostatics based on a path integral formulation [Int. J. Numer. Math. Eng. 47 (2000) 1463]. The computational implementation combines a simple polynomial approximation of the ...

Engineering analysis with boundary elements, 2005

It is shown in this paper that self-consistent boundary conditions for numerical methods based on... more It is shown in this paper that self-consistent boundary conditions for numerical methods based on blurred derivatives can be derived from a suitable change of variables of the fundamental blurred approximation of the differential equation, followed by application of ...

Polymer testing, 1997

The bending stiffness of composite beams measured at different temperatures can be used to determ... more The bending stiffness of composite beams measured at different temperatures can be used to determine interphase composition profiles generated by polymer-polymer interdiffusion, or solvent diffusion into one face of the polymer beam. A suitable method to solve the ...

International Journal for …, 2000

Numerical modelling of polymer blends production and processing, while technologically important,... more Numerical modelling of polymer blends production and processing, while technologically important, poses a considerable computational challenge when one or more of the polymer species is polydisperse. The mathematical formulation of such problems, ...

International journal for numerical methods in …, 2003

In this work we first introduce and describe the concept of blurred derivatives. It is shown how ... more In this work we first introduce and describe the concept of blurred derivatives. It is shown how they can be used both to approximate differential equations and to re-express them in alternative ways. In particular, formulations in terms of functional integrals can be ...

… in numerical methods …, 1998

In this paper a numerical solution for incompressible Stokes equations using moving least-squares... more In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D ...

Computer methods in applied mechanics and …, 2002

This paper addresses convergence rate and accuracy of a numerical technique for linear elastostat... more This paper addresses convergence rate and accuracy of a numerical technique for linear elastostatics based on a path integral formulation [Int. J. Numer. Math. Eng. 47 (2000) 1463]. The computational implementation combines a simple polynomial approximation of the ...

International Journal for Numerical Methods in …, 2000

A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equ... more A Path Integral (PI) formulation of linear elastostatics is first presented. For this, Navier equations are modified by adding a fictitious 'time'derivative of displacements so that equilibrium corresponds to the steady state of the resulting diffusion-like equations. The ...