Nicolae Pop | North University Baia Mare (original) (raw)
Papers by Nicolae Pop
Mathematics and mathematics education, Jan 1, 2002
Abstract. In this article to demonstrate the existence of the solution of the equation modelling ... more Abstract. In this article to demonstrate the existence of the solution of the equation modelling the static problem of elastic contact using the Brezis' fundamental theorem of pseudo-monotonous operators [4]. The existence of a solution of the equation modelling the ...
Proceedings of the 10th WSEAS international …, Jan 1, 2008
Abstract: The aim of this paper is to give an algorithm for solving nondifferentiable equations u... more Abstract: The aim of this paper is to give an algorithm for solving nondifferentiable equations using the generalized Jacobians with applications in contact problems. In contact problems, the functional which describes the contact conditions and the influence of the frictions is ...
atlas-conferences.com
We propose a Newton-Uzawa hybrid method obtained by combining the inexact Uzawa method and inexac... more We propose a Newton-Uzawa hybrid method obtained by combining the inexact Uzawa method and inexact generalized Newton method, in order to solve a nonlinear saddle point problem with nondifferentiable mapping. We discuss the convergence and some ...
AIP Conference Proceedings, Jan 1, 2009
In this paper, we consider numerical approximations of the quasi‐static contact problem with dry ... more In this paper, we consider numerical approximations of the quasi‐static contact problem with dry friction, using finite elements for the displacements and finite difference for the temporal derivative of the displacements. The quasistatic problem will be resolved step by step, ...
cs.ubbcluj.ro
The aim of the paper is to prove the convergence of a Uzawa type algorithm for a dual mixed varia... more The aim of the paper is to prove the convergence of a Uzawa type algorithm for a dual mixed variational formulation of a quasi-static contact problem with friction. This problem is considered as a saddle point problem which is approximated with the mixed finite element, where the stress, displacement and tangential displacement on the contact boundary will be simultaneously computed.
imsar.ro
The importance of contact processes in structural mechanic and mechanical systems is given by a b... more The importance of contact processes in structural mechanic and mechanical systems is given by a big effort that has been made for modelling and numerical simulations and by the extensive literature concerning this topic. In this paper we deal with the numerical analysis ...
Computational Materials Science
ABSTRACT We formulate some problems modeling the local hardening behavior of a plastic material f... more ABSTRACT We formulate some problems modeling the local hardening behavior of a plastic material following a Prandtl-Reuss law. Directional linear hardening, which is similar to Bauschinger’s effect in metals, is characterized by an anisotropic factor. The flow process of the material is revealed by translation in the direction shown by deformation using an absolutely continuous guiding function. The possibility of choice of a plastic strain component for the mechanical system with hardening requires an algebraic factorization of the space of processes. If the quasi-static deformation is seen as a limit case of the dynamic deformation, corresponding to low speeds and low inertial forces, we obtain an existence and uniqueness result. In this context there exists an admissible plastic strain rate, as follows by choosing a permissible elastic stress as a solution for a sweeping process problem.
PAMM, Jan 1, 2008
After finite element discretization of the elastic contact problems with friction, we obtain a bi... more After finite element discretization of the elastic contact problems with friction, we obtain a big sparse non-symmetric and nonlinear systems of equations, and in many cases ill-conditioned. Solving these systems by direct methods or classical iterative methods are non efficient and with bad convergence properties. One way to overcome these difficulties is to use the preconditioned Uzawa-type algorithms. On this paper we focus on the transformation of the generalized Signorini elastic contact problems into a saddle point problem of some augmented Lagrangian functional and give a preconditioning technique for Uzawa algorithm.
imsar.ro
This paper studies numerical analysis of a coupled problem which consists from a elasto-quasistat... more This paper studies numerical analysis of a coupled problem which consists from a elasto-quasistatic contact problem with friction, and a inclusion parabolic equation for the evolution of the damage field that results from internal compression or tension. The mathematical ...
Proceedings of the 7th Conference on 7th WSEAS …, Jan 1, 2007
The paper is concerned with the numerical solution of the quasi-variational inequality modelling ... more The paper is concerned with the numerical solution of the quasi-variational inequality modelling a contact problem with Coulomb friction. After discretization of the problem by mixed finite elements and with Lagrangian formulation of the problem by choosing appropriate multipliers, the duality approach is improved by splitting the normal and tangential stresses. The novelty of our approach in the present paper consists in the splitting of the normal stress and tangential stress, which leads to a better convergence of the solution, due to a better conditioned stiffness matrix. This better conditioned matrix is based on the fact that the obtained diagonal blocks matrices, contain coefficients of the same size order. For the saddle point formulation of the problem, using static condensation, we obtain a quadratic programming problem.
American Journal of Applied Sciences, Jan 1, 2008
The quasistatic contact problem with dry friction, contributes to the achievement of a numerical ... more The quasistatic contact problem with dry friction, contributes to the achievement of a numerical model for the simultaneity of different kinds of viscoplastic, incompressible materials forming. Starting from a variational formulation of the problem, which extends the static case, a perturbed Lagrangean, discrete formulation within the framework of finite element method is obtained. On the contact boundary we have used a method based on contact finite elements, with three nodes, for the unilateral contact conditions with the friction law. One numerical example is presented.
8th International Conference on …, Jan 1, 2009
Abstract: In this paper, we consider numerical approximations of 3D quasistatic contact problem w... more Abstract: In this paper, we consider numerical approximations of 3D quasistatic contact problem with dry friction, using finite contact elements. Lagrange incremental multipliers method and penalty functions are used to enforce finite element surface contact constrains ...
Applied Analysis and Differential Equations, Jan 1, 2007
Approximate solutions of two-point boundary value problems for linear differential equations are ... more Approximate solutions of two-point boundary value problems for linear differential equations are studied. An approximative solution is a partial sum of a series constructed by means of Newton interpolating polynomials which verify the boundary conditions. Keywords: ...
Journal of Difference Equations and Applications, Jan 1, 2008
Carpathian Journal of Mathematics, Jan 1, 2008
Mathematics and mathematics education, Jan 1, 2002
Abstract. In this article to demonstrate the existence of the solution of the equation modelling ... more Abstract. In this article to demonstrate the existence of the solution of the equation modelling the static problem of elastic contact using the Brezis' fundamental theorem of pseudo-monotonous operators [4]. The existence of a solution of the equation modelling the ...
Proceedings of the 10th WSEAS international …, Jan 1, 2008
Abstract: The aim of this paper is to give an algorithm for solving nondifferentiable equations u... more Abstract: The aim of this paper is to give an algorithm for solving nondifferentiable equations using the generalized Jacobians with applications in contact problems. In contact problems, the functional which describes the contact conditions and the influence of the frictions is ...
atlas-conferences.com
We propose a Newton-Uzawa hybrid method obtained by combining the inexact Uzawa method and inexac... more We propose a Newton-Uzawa hybrid method obtained by combining the inexact Uzawa method and inexact generalized Newton method, in order to solve a nonlinear saddle point problem with nondifferentiable mapping. We discuss the convergence and some ...
AIP Conference Proceedings, Jan 1, 2009
In this paper, we consider numerical approximations of the quasi‐static contact problem with dry ... more In this paper, we consider numerical approximations of the quasi‐static contact problem with dry friction, using finite elements for the displacements and finite difference for the temporal derivative of the displacements. The quasistatic problem will be resolved step by step, ...
cs.ubbcluj.ro
The aim of the paper is to prove the convergence of a Uzawa type algorithm for a dual mixed varia... more The aim of the paper is to prove the convergence of a Uzawa type algorithm for a dual mixed variational formulation of a quasi-static contact problem with friction. This problem is considered as a saddle point problem which is approximated with the mixed finite element, where the stress, displacement and tangential displacement on the contact boundary will be simultaneously computed.
imsar.ro
The importance of contact processes in structural mechanic and mechanical systems is given by a b... more The importance of contact processes in structural mechanic and mechanical systems is given by a big effort that has been made for modelling and numerical simulations and by the extensive literature concerning this topic. In this paper we deal with the numerical analysis ...
Computational Materials Science
ABSTRACT We formulate some problems modeling the local hardening behavior of a plastic material f... more ABSTRACT We formulate some problems modeling the local hardening behavior of a plastic material following a Prandtl-Reuss law. Directional linear hardening, which is similar to Bauschinger’s effect in metals, is characterized by an anisotropic factor. The flow process of the material is revealed by translation in the direction shown by deformation using an absolutely continuous guiding function. The possibility of choice of a plastic strain component for the mechanical system with hardening requires an algebraic factorization of the space of processes. If the quasi-static deformation is seen as a limit case of the dynamic deformation, corresponding to low speeds and low inertial forces, we obtain an existence and uniqueness result. In this context there exists an admissible plastic strain rate, as follows by choosing a permissible elastic stress as a solution for a sweeping process problem.
PAMM, Jan 1, 2008
After finite element discretization of the elastic contact problems with friction, we obtain a bi... more After finite element discretization of the elastic contact problems with friction, we obtain a big sparse non-symmetric and nonlinear systems of equations, and in many cases ill-conditioned. Solving these systems by direct methods or classical iterative methods are non efficient and with bad convergence properties. One way to overcome these difficulties is to use the preconditioned Uzawa-type algorithms. On this paper we focus on the transformation of the generalized Signorini elastic contact problems into a saddle point problem of some augmented Lagrangian functional and give a preconditioning technique for Uzawa algorithm.
imsar.ro
This paper studies numerical analysis of a coupled problem which consists from a elasto-quasistat... more This paper studies numerical analysis of a coupled problem which consists from a elasto-quasistatic contact problem with friction, and a inclusion parabolic equation for the evolution of the damage field that results from internal compression or tension. The mathematical ...
Proceedings of the 7th Conference on 7th WSEAS …, Jan 1, 2007
The paper is concerned with the numerical solution of the quasi-variational inequality modelling ... more The paper is concerned with the numerical solution of the quasi-variational inequality modelling a contact problem with Coulomb friction. After discretization of the problem by mixed finite elements and with Lagrangian formulation of the problem by choosing appropriate multipliers, the duality approach is improved by splitting the normal and tangential stresses. The novelty of our approach in the present paper consists in the splitting of the normal stress and tangential stress, which leads to a better convergence of the solution, due to a better conditioned stiffness matrix. This better conditioned matrix is based on the fact that the obtained diagonal blocks matrices, contain coefficients of the same size order. For the saddle point formulation of the problem, using static condensation, we obtain a quadratic programming problem.
American Journal of Applied Sciences, Jan 1, 2008
The quasistatic contact problem with dry friction, contributes to the achievement of a numerical ... more The quasistatic contact problem with dry friction, contributes to the achievement of a numerical model for the simultaneity of different kinds of viscoplastic, incompressible materials forming. Starting from a variational formulation of the problem, which extends the static case, a perturbed Lagrangean, discrete formulation within the framework of finite element method is obtained. On the contact boundary we have used a method based on contact finite elements, with three nodes, for the unilateral contact conditions with the friction law. One numerical example is presented.
8th International Conference on …, Jan 1, 2009
Abstract: In this paper, we consider numerical approximations of 3D quasistatic contact problem w... more Abstract: In this paper, we consider numerical approximations of 3D quasistatic contact problem with dry friction, using finite contact elements. Lagrange incremental multipliers method and penalty functions are used to enforce finite element surface contact constrains ...
Applied Analysis and Differential Equations, Jan 1, 2007
Approximate solutions of two-point boundary value problems for linear differential equations are ... more Approximate solutions of two-point boundary value problems for linear differential equations are studied. An approximative solution is a partial sum of a series constructed by means of Newton interpolating polynomials which verify the boundary conditions. Keywords: ...
Journal of Difference Equations and Applications, Jan 1, 2008
Carpathian Journal of Mathematics, Jan 1, 2008