Maria InГЄs Martins Copetti Google Scholar Citations. A FINITE ELEMENT FORMULATION FOR NONLINEAR 3D CONTACT PROBLEMS Federico J. Cavalieri, Alberto Cardona, Víctor D. Fachinotti and José Risso Centro Internacional de …, A FINITE ELEMENT MODEL FOR THE TIME-DEPENDENT JOULE HEATING PROBLEM CHARLES M. ELLIOTT AND STIG LARSSON Abstract. We study a spatially semidiscrete and a completely discrete finite element model for a nonlinear system consisting of an elliptic and a parabolic partial differential equation describing the electric heating of a conducting body..

### Finite element discretization of a nonlinear thermoelastic

Finite element analysis of an unilateral contact problem. Thermomechanical Finite Element Analysis of Problems in Electronic Packaging Using the Disturbed State Concept: Part 1 Theory and Formulation Accurate prediction of the thermomechanical cyclic behavior of joints and interfaces in semiconductor devices is essential for their reliable design. In …, This paper presents a computational model capable of predicting the nonlinear quasistatic response of uncoupled thermoviscoelastic frictional contact problems. The contact problem, as a variational inequality constrained model, is handled by using the Lagrange multiplier method to incorporate the inequality contact constraints..

Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given. FINITE ELEMENT APPROXIMATION OF THE VIBRATION PROBLEM FOR A TIMOSHENKO CURVED ROD E. HERNANDEZ´ ∗, E. OTAROLA´ †, R. RODR´IGUEZ‡, AND F. SANHUEZA§ Abstract. The aim of this paper is to analyze a mixed ﬁnite element method for computing the vibration modes of a Timoshenko curved rod with arbitrary geometry.

ERROR ANALYSIS FOR A FINITE ELEMENT APPROXIMATION OF ELLIPTIC DIRICHLET BOUNDARY CONTROL PROBLEMS S. MAY∗, R. RANNACHER∗‡, AND B. VEXLER†‡ Abstract. We consider the Galerkin ﬁnite element approximation of an elliptic Dirichlet bound-ary control model problem governed by the Laplacian operator. The functional theoretical setting This paper is concerned with the existence, uniqueness and numerical solution of a system of equations modelling the evolution of a quasi-static thermoviscoelastic beam that may be in contact with two rigid obstacles. A finite element approximation is proposed and …

On the reliable solution of contact problems in engineering design NAGI ELABBASI1, JUNG-WUK HONG2, contact problem using constraint functions is ﬁrst summarized. Then we address general reliability issues and those Finite element discretization Employing standard ﬁnite element discretization of Eqs. (7) and (11), we obtain 1.4 Engineering Applications of the Finite Element Method 9 1.5 General Description of the Finite Element Method 9 1.6 One-Dimensional Problems with Linear Interpolation Model 12 1.7 One-Dimensional Problems with Cubic Interpolation Model 24 1.8 Derivation of Finite …

Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given. The Mortar Finite Element Method for Contact Problems F. Ben Belgacem, P. Hild, P. Laborde Math ematiques pour l’Industrie et la Physique, Unit e Mixte de Recherche CNRS{UPS{INSAT (UMR 5640), Universit e Paul Sabatier, 118 route de Narbonne, 31062 TOULOUSE Cedex, FRANCE.

3 FINITE ELEMENT FORMULATION The reduced system (5) has often been used as a starting point in the analytical treat-ment and could also be thought to be a natural starting point for the ﬂnite element formulation. However, special care has to be taken in the ﬂnite element approximation of 3 FINITE ELEMENT FORMULATION The reduced system (5) has often been used as a starting point in the analytical treat-ment and could also be thought to be a natural starting point for the ﬂnite element formulation. However, special care has to be taken in the ﬂnite element approximation of

### On the reliable solution of contact problems in

Method of Finite Elements I вЂ“ Structural Mechanics and. their stability investigated. Recently, the quasi-static thermoviscoelastic nonlinear contact problem for an Euler{Bernoulli beam was numerically studied by Copetti and Fern andez [4]; in the latter case, a nite element discretization was proposed and analyzed and some numerical experiments were performed., In the analysis of frictional contact problems with large deformation, the use of a convected coordinate system is a natural approach, by which the frame indifference of friction law can be maintained. However, in the case of the finite element method, a problem arises due to the discontinuity of.

(PDF) Rubber covered rollsвЂ”the thermoviscoelastic problem. Finite element algorithms for contact problems. Authors; of a contact problem in time and space is of great importance and has to be chosen with regard to the nature of the contact problem. Thus the standard discretization schemes will be discussed as well as techiques to search for contact in case of large deformations. Johannson, L, A FINITE ELEMENT FORMULATION FOR NONLINEAR 3D CONTACT PROBLEMS Federico J. Cavalieri, Alberto Cardona, Víctor D. Fachinotti and José Risso Centro Internacional de ….

### An Error Estimate for the Signorini Problem with Coulomb

Finite element analysis of an unilateral contact problem. We consider the numerical approximation of a one-dimensional quasi-static contact problem in linear thermoviscoelasticity. A finite element approximation based on a penalized problem is proposed and analyzed. We furnish an a priori estimate of the difference between the true and numerical solutions. The results of some computations are also presented. https://en.wikipedia.org/wiki/Finite_element_analysis Computational Contact Mechanics deals with problems related to contact problems in the area of classical mechanics using computational means (like finite or boundary element methods). With increase in computational power, significant progress has been made towards robust numerical solutions to complicated contact problems..

the different classes of the problem, involving different nonlinearities due to the material property, finite geometry changes, or friction effects[1]. The contact problem is inherently a nonlinear problem. The finite element method(FEM) is one of the most efficient tools for … We consider the numerical approximation of a one-dimensional quasi-static contact problem in linear thermoviscoelasticity. A finite element approximation based on a penalized problem is proposed and analyzed. We furnish an a priori estimate of the difference between the true and numerical solutions. The results of some computations are also presented.

FINITE ELEMENT APPROXIMATION OF THE VIBRATION PROBLEM FOR A TIMOSHENKO CURVED ROD E. HERNANDEZ´ ∗, E. OTAROLA´ †, R. RODR´IGUEZ‡, AND F. SANHUEZA§ Abstract. The aim of this paper is to analyze a mixed ﬁnite element method for computing the vibration modes of a Timoshenko curved rod with arbitrary geometry. Computational Contact Mechanics deals with problems related to contact problems in the area of classical mechanics using computational means (like finite or boundary element methods). With increase in computational power, significant progress has been made towards robust numerical solutions to complicated contact problems.

Finite Element Modeling of Contact and Impact Problems Using Python model and the physical system is shown in the next ﬁgure. Dropping Mass Foam Block FEA setup for this problem Introduction to SfePy SfePy stands for Simple Finite Elements for Python. It is … We consider the numerical approximation of a one-dimensional quasi-static contact problem in linear thermoviscoelasticity. A finite element approximation based on a penalized problem is proposed and analyzed. We furnish an a priori estimate of the difference between the true and numerical solutions. The results of some computations are also presented.

3 FINITE ELEMENT FORMULATION The reduced system (5) has often been used as a starting point in the analytical treat-ment and could also be thought to be a natural starting point for the ﬂnite element formulation. However, special care has to be taken in the ﬂnite element approximation of The Mortar Finite Element Method for Contact Problems F. Ben Belgacem, P. Hild, P. Laborde Math ematiques pour l’Industrie et la Physique, Unit e Mixte de Recherche CNRS{UPS{INSAT (UMR 5640), Universit e Paul Sabatier, 118 route de Narbonne, 31062 TOULOUSE Cedex, FRANCE.

In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported. The Finite Element Method in Heat Transfer and Fluid Dynamics Third Edition J. N. Reddy Department of Mechanical Engineering Texas A&M University College Station, Texas, USA 77843—3123

## Finite Element Modeling of a Cylindrical Contact Using

A Finite Element Method for Solving 2D Contact Problems. The Finite Element Method in Heat Transfer and Fluid Dynamics Third Edition J. N. Reddy Department of Mechanical Engineering Texas A&M University College Station, Texas, USA 77843—3123, The present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the.

### Finite Element Methods for Contact Problems

San Jose State University Department of Mechanical. TY - JOUR AU - Han, Weimin AU - Sofonea, Mircea TI - Analysis and numerical approximation of an elastic frictional contact problem with normal compliance JO - Applicationes Mathematicae PY - 1999 VL - 26 IS - 4 SP - 415 EP - 435 AB - We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive, Formulation of the displacement-based finite element method FORMULATION OF THE DISPLACEMENT BASED FINITE ELEMENT METHOD-A very general formulation-Providesthe basis of almost all finite ele mentanalyses per formed in practice-Theformulation is really a modern appli cation of the Ritz/ Gelerkin procedures discussed in lecture 2.

Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given. A FINITE ELEMENT MODEL FOR THE TIME-DEPENDENT JOULE HEATING PROBLEM CHARLES M. ELLIOTT AND STIG LARSSON Abstract. We study a spatially semidiscrete and a completely discrete finite element model for a nonlinear system consisting of an elliptic and a parabolic partial differential equation describing the electric heating of a conducting body.

We consider a nonlinear model for a thermoelastic beam that can enter in contact with obstacles. We fi rst prove the well-posedness of this problem. Next, we propose a discretization by Euler and Crank-Nicolson schemes in time and finite elements in space and perform the a priori analysis of the discrete problem. Some numerical experiments confi rm the interest of this approach. We consider the numerical approximation of a one-dimensional quasi-static contact problem in linear thermoviscoelasticity. A finite element approximation based on a penalized problem is proposed and analyzed. We furnish an a priori estimate of the difference between the true and numerical solutions. The results of some computations are also presented.

This paper is concerned with the existence, uniqueness and numerical solution of a system of equations modelling the evolution of a quasi-static thermoviscoelastic beam that may be in contact with two rigid obstacles. A finite element approximation is proposed and … Download PDF Download. Share. Export. Advanced In this article, a finite element approximation, based on a variational inequality, to the solution of a one-dimensional quasi-static Signorini contact problem in linear thermoviscoelasticity is proposed. K. Kuttler, M. ShillorA one-dimensional thermoviscoelastic contact problem. Adv. Math

Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given. THE THERMOVISCOELASTIC PROBLEM A FINITE ELEMENT SOLUTION R. C. BATRA University of Missouri-Rolla, Rolla. 4 states that the radial stress is continuous across the arc of contact and ensures that a contact problem rather than a punch problem is solved. vection type on the whole surface would seem to be a good approximation. The problem

R. J. Gu and M. Shillor, Thermal and wear finite elements analysis of an elastic beam in sliding contact, Internat. J. Solids Structures, to appear Lars Johansson and Anders Klarbring, Thermoelastic frictional contact problems: modelling, finite element approximation and numerical realization, Comput. Methods Appl. Mech. Engrg. Finite Element Modeling of Contact and Impact Problems Using Python model and the physical system is shown in the next ﬁgure. Dropping Mass Foam Block FEA setup for this problem Introduction to SfePy SfePy stands for Simple Finite Elements for Python. It is …

Their combined citations are counted only for the first article. Finite element approximation to a contact problem for a nonlinear thermoviscoelastic beam. A dynamic thermoviscoelastic contact problem with the second sound effect. A Berti, MIM Copetti, JR Fernández, MG Naso. Thermomechanical Finite Element Analysis of Problems in Electronic Packaging Using the Disturbed State Concept: Part 1 Theory and Formulation Accurate prediction of the thermomechanical cyclic behavior of joints and interfaces in semiconductor devices is essential for their reliable design. In …

Aug 01, 2005 · In this article, a finite element approximation, based on a variational inequality, to the solution of a one-dimensional quasi-static Signorini contact problem in … The results on the finite element approximation of the second-order obstacle problem are generalized and applied to the adaptive solution of the Reynolds cavitation problem, modeled as a second-order elliptic variational inequality with variable coefficients. As a numerical example we consider the hydrodynamic lubrication of journal bearings.

Formulation of the displacement-based finite element method FORMULATION OF THE DISPLACEMENT BASED FINITE ELEMENT METHOD-A very general formulation-Providesthe basis of almost all finite ele mentanalyses per formed in practice-Theformulation is really a modern appli cation of the Ritz/ Gelerkin procedures discussed in lecture 2 Thermomechanical Finite Element Analysis of Problems in Electronic Packaging Using the Disturbed State Concept: Part 1 Theory and Formulation Accurate prediction of the thermomechanical cyclic behavior of joints and interfaces in semiconductor devices is essential for their reliable design. In …

the different classes of the problem, involving different nonlinearities due to the material property, finite geometry changes, or friction effects[1]. The contact problem is inherently a nonlinear problem. The finite element method(FEM) is one of the most efficient tools for … Numerical analysis of a thermoviscoelastic frictional contact problem viscoelastic frictional contact problem, with the finite element method used to discretize the spatial domain

In the analysis of frictional contact problems with large deformation, the use of a convected coordinate system is a natural approach, by which the frame indifference of friction law can be maintained. However, in the case of the finite element method, a problem arises due to the discontinuity of Method of Finite Elements I • The MFE is only a way of solving the mathematical model • The solution of the physical problem depends on the quality of the mathematical model – the choice of the mathematical model is crucial • The chosen mathematical model is reliable if the required response can be predicted within a given level of accuracy

This paper is concerned with the existence, uniqueness and numerical solution of a system of equations modelling the evolution of a quasi-static thermoviscoelastic beam that may be in contact with two rigid obstacles. A finite element approximation is proposed and … 1.4 Engineering Applications of the Finite Element Method 9 1.5 General Description of the Finite Element Method 9 1.6 One-Dimensional Problems with Linear Interpolation Model 12 1.7 One-Dimensional Problems with Cubic Interpolation Model 24 1.8 Derivation of Finite …

(PDF) Rubber covered rollsвЂ”the thermoviscoelastic problem. We consider the numerical approximation of a one-dimensional quasi-static contact problem in linear thermoviscoelasticity. A finite element approximation based on a penalized problem is proposed and analyzed. We furnish an a priori estimate of the difference between the true and numerical solutions. The results of some computations are also presented., How much contact force or pressure occurs in the interface. If there is a relative motion after contact in the interface. Finite element analysis procedure for contact problem. Find whether a material point in the boundary of a body is in contact with the other body. If it is in contact, the corresponding contact force must be calculated.

### FORMULATION OF THE DISPLACEMENT-BASED FINITE

Finite Element Approximation of the Enthalpy Method for. Numerical analysis of a thermoviscoelastic frictional contact problem viscoelastic frictional contact problem, with the finite element method used to discretize the spatial domain, Method of Finite Elements I • The MFE is only a way of solving the mathematical model • The solution of the physical problem depends on the quality of the mathematical model – the choice of the mathematical model is crucial • The chosen mathematical model is reliable if the required response can be predicted within a given level of accuracy.

(PDF) Numerical analysis of a thermoviscoelastic. TY - JOUR AU - Han, Weimin AU - Sofonea, Mircea TI - Analysis and numerical approximation of an elastic frictional contact problem with normal compliance JO - Applicationes Mathematicae PY - 1999 VL - 26 IS - 4 SP - 415 EP - 435 AB - We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive, R. J. Gu and M. Shillor, Thermal and wear finite elements analysis of an elastic beam in sliding contact, Internat. J. Solids Structures, to appear Lars Johansson and Anders Klarbring, Thermoelastic frictional contact problems: modelling, finite element approximation and numerical realization, Comput. Methods Appl. Mech. Engrg..

### The Finite Element Method in Engineering

Finite Element Methods for Contact Problems. 184 M.I.M. Copetti / Journal of Computational and Applied Mathematics 180 (2005) 181–190 Theorem 2. There exists a unique solution for problem (8)–(9). https://fr.wikipedia.org/wiki/Approximation Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given..

Finite element algorithms for contact problems. Authors; of a contact problem in time and space is of great importance and has to be chosen with regard to the nature of the contact problem. Thus the standard discretization schemes will be discussed as well as techiques to search for contact in case of large deformations. Johannson, L This paper presents a computational model capable of predicting the nonlinear quasistatic response of uncoupled thermoviscoelastic frictional contact problems. The contact problem, as a variational inequality constrained model, is handled by using the Lagrange multiplier method to incorporate the inequality contact constraints.

A FINITE ELEMENT MODEL FOR THE TIME-DEPENDENT JOULE HEATING PROBLEM CHARLES M. ELLIOTT AND STIG LARSSON Abstract. We study a spatially semidiscrete and a completely discrete finite element model for a nonlinear system consisting of an elliptic and a parabolic partial differential equation describing the electric heating of a conducting body. 184 M.I.M. Copetti / Journal of Computational and Applied Mathematics 180 (2005) 181–190 Theorem 2. There exists a unique solution for problem (8)–(9).

We consider the numerical approximation of a one-dimensional quasi-static contact problem in linear thermoviscoelasticity. A finite element approximation based on a penalized problem is proposed and analyzed. We furnish an a priori estimate of the difference between the true and numerical solutions. The results of some computations are also presented. The present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the

We consider a nonlinear model for a thermoelastic beam that can enter in contact with obstacles. We fi rst prove the well-posedness of this problem. Next, we propose a discretization by Euler and Crank-Nicolson schemes in time and finite elements in space and perform the a priori analysis of the discrete problem. Some numerical experiments confi rm the interest of this approach. Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given.

We consider a nonlinear model for a thermoelastic beam that can enter in contact with obstacles. We fi rst prove the well-posedness of this problem. Next, we propose a discretization by Euler and Crank-Nicolson schemes in time and finite elements in space and perform the a priori analysis of the discrete problem. Some numerical experiments confi rm the interest of this approach. This paper is concerned with the existence, uniqueness and numerical solution of a system of equations modelling the evolution of a quasi-static thermoviscoelastic beam that may be in contact with two rigid obstacles. A finite element approximation is proposed and …

The Finite Element Method in Heat Transfer and Fluid Dynamics Third Edition J. N. Reddy Department of Mechanical Engineering Texas A&M University College Station, Texas, USA 77843—3123 The results on the finite element approximation of the second-order obstacle problem are generalized and applied to the adaptive solution of the Reynolds cavitation problem, modeled as a second-order elliptic variational inequality with variable coefficients. As a numerical example we consider the hydrodynamic lubrication of journal bearings.

ON THE TREATMENT OF INEQUALITY CONSTRAINTS ARISING FROM CONTACT CONDITIONS IN FINITE ELEMENT ANALYSIS A. L. ETEROVIC and K. J. BATHE Massachusetts Institute of Technology, Department of Mechanical Engineering, Room 3-356, Cambridge, MA 02139, U.S.A. THE THERMOVISCOELASTIC PROBLEM A FINITE ELEMENT SOLUTION R. C. BATRA University of Missouri-Rolla, Rolla. 4 states that the radial stress is continuous across the arc of contact and ensures that a contact problem rather than a punch problem is solved. vection type on the whole surface would seem to be a good approximation. The problem

The present paper is concerned with the unilateral contact model and the Coulomb friction law in linear elastostatics. We consider a mixed formulation in which the unknowns are the displacement field and the normal and tangential constraints on the contact area. The chosen finite element method involves continuous elements of degree one and continuous piecewise affine multipliers on the FINITE ELEMENT APPROXIMATION OF THE VIBRATION PROBLEM FOR A TIMOSHENKO CURVED ROD E. HERNANDEZ´ ∗, E. OTAROLA´ †, R. RODR´IGUEZ‡, AND F. SANHUEZA§ Abstract. The aim of this paper is to analyze a mixed ﬁnite element method for computing the vibration modes of a Timoshenko curved rod with arbitrary geometry.

Aug 01, 2005 · In this article, a finite element approximation, based on a variational inequality, to the solution of a one-dimensional quasi-static Signorini contact problem in … IntroductionFinite Element DiscretisationStabilityExistence and UniquenessSummary Finite Element Approximation of the Enthalpy Method for the Stefan

In this paper we consider a hyperbolic-parabolic problem that models the longitudinal deformations of a thermoviscoelastic rod supported unilaterally by an elastic obstacle. The existence and uniqueness of a strong solution is shown. A finite element approximation is proposed and its convergence is proved. Numerical experiments are reported. 184 M.I.M. Copetti / Journal of Computational and Applied Mathematics 180 (2005) 181–190 Theorem 2. There exists a unique solution for problem (8)–(9).

Jan 01, 2007 · This paper deals with the numerical solution of nonlinear integro-differential equations modelling a one-dimensional quasi-static contact problem in thermoviscoelasticity. A finite element approximation is proposed and analysed and some numerical results are given. solutions to. It is an initial boundary value problem, and as such it is quite typical of the models with which structural engineers have to deal. In what follows, we shall ﬂnd out how to formulate an algorithm, the so-called Galerkin ﬂnite element method, which will supply an approximate solution to this problem.

solutions to. It is an initial boundary value problem, and as such it is quite typical of the models with which structural engineers have to deal. In what follows, we shall ﬂnd out how to formulate an algorithm, the so-called Galerkin ﬂnite element method, which will supply an approximate solution to this problem. 184 M.I.M. Copetti / Journal of Computational and Applied Mathematics 180 (2005) 181–190 Theorem 2. There exists a unique solution for problem (8)–(9).