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Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution

Jaroslav Haslinger, Tomáš Ligurský (2009)

Applications of Mathematics

The paper presents the analysis, approximation and numerical realization of 3D contact problems for an elastic body unilaterally supported by a rigid half space taking into account friction on the common surface. Friction obeys the simplest Tresca model (a slip bound is given a priori) but with a coefficient of friction ℱ which depends on a solution. It is shown that a solution exists for a large class of ℱ and is unique provided that ℱ is Lipschitz continuous with a sufficiently small modulus of...

Approximation and numerical solution of contact problems with friction

Jaroslav Haslinger, Miroslav Tvrdý (1983)

Aplikace matematiky

The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function ℒ on a certain convex set K × Λ . The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.

Approximation of a Martensitic Laminate with Varying Volume Fractions

Bo Li, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We give results for the approximation of a laminate with varying volume fractions for multi-well energy minimization problems modeling martensitic crystals that can undergo either an orthorhombic to monoclinic or a cubic to tetragonal transformation. We construct energy minimizing sequences of deformations which satisfy the corresponding boundary condition, and we establish a series of error bounds in terms of the elastic energy for the approximation of the limiting macroscopic deformation and...

Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Jindřich Nečas, Tomáš Roubíček (1990)

Aplikace matematiky

The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...

Approximation of the arch problem by residual-free bubbles

A. Agouzal, M. El Alami El Ferricha (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, a conforming mixed finite element method which takes into account an approximation of the middle line of the arch is given. But for a very small thickness such a method gives poor error bounds. the conforming Galerkin method is then enriched with residual-free bubble functions.

Approximation of the arch problem by residual-free bubbles

A. Agouzal, M. El Alami El Ferricha (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a general loaded arch problem with a small thickness. To approximate the solution of this problem, a conforming mixed finite element method which takes into account an approximation of the middle line of the arch is given. But for a very small thickness such a method gives poor error bounds. the conforming Galerkin method is then enriched with residual-free bubble functions.

Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

Erwin Hernández (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling is...

Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

Erwin Hernández (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze an isoparametric finite element method to compute the vibration modes of a plate, modeled by Reissner-Mindlin equations, in contact with a compressible fluid, described in terms of displacement variables. To avoid locking in the plate, we consider a low-order method of the so called MITC (Mixed Interpolation of Tensorial Component) family on quadrilateral meshes. To avoid spurious modes in the fluid, we use a low-order hexahedral Raviart-Thomas elements and a non conforming coupling...

Currently displaying 381 – 400 of 434