International Journal for Computational Methods in Engineering Science and Mechanics, Dec 16, 2016
This paper shows that the well-known nonlinear boundary value problem of the differential equatio... more This paper shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.
There are several methods in dynamic substructuring for numerical simulation of complex structure... more There are several methods in dynamic substructuring for numerical simulation of complex structures in the lowfrequency range, that is to say in the modal range. For instance, the Craig-Bampton method is a very efficient and popular method in linear structural dynamics. Such a method is based on the use of the first structural modes of each substructure with fixed coupling interface. In the medium-frequency range, i.e. in the nonmodal range, and for complex structures, a large number of structural modes should be computed with finite element models having a very large number of degrees of freedom. Such an approach would not be efficient at all and generally, cannot be carried out. In this paper, we present a new approach in dynamic substructuring for numerical calculation of complex structures in the medium-frequency range. This approach is still based on the use of the Craig-Bampton decomposition of the admissible displacement field but the reduced matrix model of each substructure with fixed coupling interface, which is not constructed using the structural modes, is constructed using the first eigenfunctions of the mechanical energy operator of the substructure with fixed coupling interface related to the medium-frequency band. The method and a numerical example is presented.
This paper aims to find the exact solution in an implicit form for the wellknown nonlinear bounda... more This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).
Computers & mathematics with applications, Nov 1, 2016
In this paper, inverted finite element method is used for solving two-dimensional second order el... more In this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients.
Il existe plusieurs methodes de sous-structuration dynamique pour la simulation numerique du comp... more Il existe plusieurs methodes de sous-structuration dynamique pour la simulation numerique du comportement dynamique lineaire des structures complexes, modelisees par la methode des elements finis, dans le domaine modal dit des basses frequences, par exemple, la methode craig et bampton introduite en 1968. Dans ce travail de recherche, nous presentons une nouvelle approche en sous-structuration dynamique dans le domaine des moyennes frequences, pour les calculs numeriques par elements finis des structures. L'approche proposee est basee sur la decomposition, pour chaque sous-structure, du champ de deplacement admissible introduit par craig et bampton en vue de construire son modele matriciel reduit. Cette approche consiste a remplacer, pour chaque sous-structure a interface de couplage fixe, les premiers modes propres de vibration de la sous-structure non amortie, par les vecteurs propres associes aux valeurs propres dominantes de l'operateur d'energie mecanique relatif a la bande moyenne frequence, de la sous-structure avec son modele de dissipation. Cela revient donc, pour la reponse dynamique, a faire la substitution de la base modale par une base adaptee a la bande moyenne frequence, qui prenne en compte la dissipation et qui permette d'avoir une strategie claire de troncature. Dans ce travail, on presente la theorie dans le cas de la viscoelastodynamique linearisee tridimensionnelle non homogene et non isotrope. La formulation variationnelle et la discretisation par la methode des elements finis sont developpees. Les methodes numeriques specifiques sont introduites. La validation de la methode et les analyses de convergence sont presentees au travers d'exemples.
Mathematical and Computer Modelling of Dynamical Systems, Jul 31, 2009
Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic appro... more Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both ...
Japan Journal of Industrial and Applied Mathematics, Feb 6, 2015
This paper is the second in a series devoted to the development of inverted finite element method... more This paper is the second in a series devoted to the development of inverted finite element method for elliptic problems in unbounded domains. Here, focus is on degenerate elliptic equations having singular or/and unbounded coefficients. A specific emphasis is being placed on radial solutions of second order elliptic equations. After giving an exposition of the fundamentals of the method and proving its convergence, we display some computational tests which demonstrate its efficiency.
Japan Journal of Industrial and Applied Mathematics, 2015
This paper is the second in a series devoted to the development of inverted finite element method... more This paper is the second in a series devoted to the development of inverted finite element method for elliptic problems in unbounded domains. Here, focus is on degenerate elliptic equations having singular or/and unbounded coefficients. A specific emphasis is being placed on radial solutions of second order elliptic equations. After giving an exposition of the fundamentals of the method and proving its convergence, we display some computational tests which demonstrate its efficiency.
International Journal for Computational Methods in Engineering Science and Mechanics, 2016
This paper shows that the well-known nonlinear boundary value problem of the differential equatio... more This paper shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.
This paper aims to find the exact solution in an implicit form for the wellknown nonlinear bounda... more This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).
Mathematical and Computer Modelling of Dynamical Systems, 2009
Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic appro... more Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both ...
In this paper, inverted finite element method is used for solving two-dimensional second order el... more In this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients.
Herein, we study the numerical solution with the help of Chebyshev spectral collocation method fo... more Herein, we study the numerical solution with the help of Chebyshev spectral collocation method for the ordinary differential equations which describe the flow of viscoelastic fluid over a stretching sheet embedded in a porous medium with viscous dissipation and slip velocity. The novel effects for the parameters which affect the flow and heat transfer, such as the Eckert number coupled with a porous medium and the velocity slip parameter, are studied. Also, the convergence analysis for the proposed method is addressed.
IN the low-frequency range, that is, in the modal range, the dynamic substructuring methods1¡ 7 a... more IN the low-frequency range, that is, in the modal range, the dynamic substructuring methods1¡ 7 are suffi cient to calculate the linear dynamical response of complex structures modeled by the fi nite element method. For instance, the CraigBampton method1 is very ...
This article shows that the well-known nonlinear boundary value problem of the differential equat... more This article shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.
n this paper, inverted finite element method is used for solving two-dimensional second order ell... more n this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients.
his paper aims to find the exact solution in an implicit form for the well-known nonlinear bounda... more his paper aims to find the exact solution in an implicit form for the well-known nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).
International Journal for Computational Methods in Engineering Science and Mechanics, Dec 16, 2016
This paper shows that the well-known nonlinear boundary value problem of the differential equatio... more This paper shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.
There are several methods in dynamic substructuring for numerical simulation of complex structure... more There are several methods in dynamic substructuring for numerical simulation of complex structures in the lowfrequency range, that is to say in the modal range. For instance, the Craig-Bampton method is a very efficient and popular method in linear structural dynamics. Such a method is based on the use of the first structural modes of each substructure with fixed coupling interface. In the medium-frequency range, i.e. in the nonmodal range, and for complex structures, a large number of structural modes should be computed with finite element models having a very large number of degrees of freedom. Such an approach would not be efficient at all and generally, cannot be carried out. In this paper, we present a new approach in dynamic substructuring for numerical calculation of complex structures in the medium-frequency range. This approach is still based on the use of the Craig-Bampton decomposition of the admissible displacement field but the reduced matrix model of each substructure with fixed coupling interface, which is not constructed using the structural modes, is constructed using the first eigenfunctions of the mechanical energy operator of the substructure with fixed coupling interface related to the medium-frequency band. The method and a numerical example is presented.
This paper aims to find the exact solution in an implicit form for the wellknown nonlinear bounda... more This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).
Computers & mathematics with applications, Nov 1, 2016
In this paper, inverted finite element method is used for solving two-dimensional second order el... more In this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients.
Il existe plusieurs methodes de sous-structuration dynamique pour la simulation numerique du comp... more Il existe plusieurs methodes de sous-structuration dynamique pour la simulation numerique du comportement dynamique lineaire des structures complexes, modelisees par la methode des elements finis, dans le domaine modal dit des basses frequences, par exemple, la methode craig et bampton introduite en 1968. Dans ce travail de recherche, nous presentons une nouvelle approche en sous-structuration dynamique dans le domaine des moyennes frequences, pour les calculs numeriques par elements finis des structures. L'approche proposee est basee sur la decomposition, pour chaque sous-structure, du champ de deplacement admissible introduit par craig et bampton en vue de construire son modele matriciel reduit. Cette approche consiste a remplacer, pour chaque sous-structure a interface de couplage fixe, les premiers modes propres de vibration de la sous-structure non amortie, par les vecteurs propres associes aux valeurs propres dominantes de l'operateur d'energie mecanique relatif a la bande moyenne frequence, de la sous-structure avec son modele de dissipation. Cela revient donc, pour la reponse dynamique, a faire la substitution de la base modale par une base adaptee a la bande moyenne frequence, qui prenne en compte la dissipation et qui permette d'avoir une strategie claire de troncature. Dans ce travail, on presente la theorie dans le cas de la viscoelastodynamique linearisee tridimensionnelle non homogene et non isotrope. La formulation variationnelle et la discretisation par la methode des elements finis sont developpees. Les methodes numeriques specifiques sont introduites. La validation de la methode et les analyses de convergence sont presentees au travers d'exemples.
Mathematical and Computer Modelling of Dynamical Systems, Jul 31, 2009
Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic appro... more Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both ...
Japan Journal of Industrial and Applied Mathematics, Feb 6, 2015
This paper is the second in a series devoted to the development of inverted finite element method... more This paper is the second in a series devoted to the development of inverted finite element method for elliptic problems in unbounded domains. Here, focus is on degenerate elliptic equations having singular or/and unbounded coefficients. A specific emphasis is being placed on radial solutions of second order elliptic equations. After giving an exposition of the fundamentals of the method and proving its convergence, we display some computational tests which demonstrate its efficiency.
Japan Journal of Industrial and Applied Mathematics, 2015
This paper is the second in a series devoted to the development of inverted finite element method... more This paper is the second in a series devoted to the development of inverted finite element method for elliptic problems in unbounded domains. Here, focus is on degenerate elliptic equations having singular or/and unbounded coefficients. A specific emphasis is being placed on radial solutions of second order elliptic equations. After giving an exposition of the fundamentals of the method and proving its convergence, we display some computational tests which demonstrate its efficiency.
International Journal for Computational Methods in Engineering Science and Mechanics, 2016
This paper shows that the well-known nonlinear boundary value problem of the differential equatio... more This paper shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.
This paper aims to find the exact solution in an implicit form for the wellknown nonlinear bounda... more This paper aims to find the exact solution in an implicit form for the wellknown nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).
Mathematical and Computer Modelling of Dynamical Systems, 2009
Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic appro... more Recently, the basic dynamics of fruit characteristics have been modelled using a stochastic approach. The time evolution of apple quality attributes was represented by means of a system of differential equations in which the initial conditions and model parameters are both ...
In this paper, inverted finite element method is used for solving two-dimensional second order el... more In this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients.
Herein, we study the numerical solution with the help of Chebyshev spectral collocation method fo... more Herein, we study the numerical solution with the help of Chebyshev spectral collocation method for the ordinary differential equations which describe the flow of viscoelastic fluid over a stretching sheet embedded in a porous medium with viscous dissipation and slip velocity. The novel effects for the parameters which affect the flow and heat transfer, such as the Eckert number coupled with a porous medium and the velocity slip parameter, are studied. Also, the convergence analysis for the proposed method is addressed.
IN the low-frequency range, that is, in the modal range, the dynamic substructuring methods1¡ 7 a... more IN the low-frequency range, that is, in the modal range, the dynamic substructuring methods1¡ 7 are suffi cient to calculate the linear dynamical response of complex structures modeled by the fi nite element method. For instance, the CraigBampton method1 is very ...
This article shows that the well-known nonlinear boundary value problem of the differential equat... more This article shows that the well-known nonlinear boundary value problem of the differential equation for temperature distribution of convective straight fins with temperature-dependent thermal conductivity is exactly solvable in an implicit form. Furthermore, an exact solution in an explicit form is derived. Also, an accurate analytic solution (series solution) is obtained by a new variation of the Adomian decomposition method.
n this paper, inverted finite element method is used for solving two-dimensional second order ell... more n this paper, inverted finite element method is used for solving two-dimensional second order elliptic equations with a Dirichlet boundary condition in an exterior domain. After laying down the method, and after giving an estimate of the error, we detail how its implementation can be accomplished. Numerical results show the high efficiency and the accuracy of the method, especially for equations with infinitely varying coefficients.
his paper aims to find the exact solution in an implicit form for the well-known nonlinear bounda... more his paper aims to find the exact solution in an implicit form for the well-known nonlinear boundary value problem, namely the MHD Jeffery-Hamel problem, which can be described as the flow between two planes that meet at an angle. Also, two accurate approximate analytic solutions (series solution) are obtained by the variation of the power series method (VPS) and the Duan-Rach modified Adomian decomposition method (DRMA).
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