Un modèle relaxé pour les câbles inextensibles
Un problème issu de l'étude numérique d'un fil sans raideur soumis au frottement sec
Unconditionally stable mid-point time integration in elastic-plastic dynamics
The dynamic analysis of elastoplastic systems discretized by finite elements is dealt with. The material behaviour is described by a rather general internal variable model. The unknown fields are modelled in terms of suitable variables, generalized in Prager's sense. Time integrations are carried out by means of a generalized mid-point rule. The resulting nonlinear equations expressing dynamic equilibrium of the finite step problem are solved by means of a Newton-Raphson iterative scheme. The unconditional...
Unconstrained finite element for geometrical nonlinear dynamics of shells.
Une justification des équations de la thermoélasticité des poutres à section variable par des méthodes asymptotiques
Une méthode d'éléments finis mixte pour les équations de Von Kármán
Une méthode intégrale de frontière. Application au Laplacien et à l'élasticité.
The aim of the paper is to give a method to solve boundary value problems associated to the Helmholtz equation and to the operator of elasticity. We transform these problems in problems on the boundary Gamma of an open set of R3. After introducing a symplectic form on H1,2(G) x H-1,2(G) we obtain the adjoint of the boundary operator employed. Then the boundary problem has a solution if and only if the boundary conditions are orthogonal, for this bilinear form, to the elements of the kernel, in a...
Une méthode numérique pour les problèmes d'équilibre de corps hyperélastiques compressibles en grandes déformations.
Une modification du modèle de Mindlin pour les plaques minces en flexion présentant un bord libre
Uniform a priori estimates for discrete solution of nonlinear tensor diffusion equation in image processing
This paper concerns with the finite volume scheme for nonlinear tensor diffusion in image processing. First we provide some basic information on this type of diffusion including a construction of its diffusion tensor. Then we derive a semi-implicit scheme with the help of so-called diamond-cell method (see [Coirier1] and [Coirier2]). Further, we prove existence and uniqueness of a discrete solution given by our scheme. The proof is based on a gradient bound in the tangential direction by a gradient...
Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates
Unilateral contact applications using FEM software
Nonsmooth analysis, inequality constrained optimization and variational inequalities are involved in the modelling of unilateral contact problems. The corresponding theoretical and algorithmic tools, which are part of the area known as nonsmooth mechanics, are by no means classical. In general purpose software some of these tools (perhaps in a simplified way) are currently available. Two engineering applications, a rubber-coated roller contact problem and a masonry wall, solved with MARC, are briefly...
Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem
The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...
Variational and numerical analysis of the Signorini's contact problem in viscoplasticity with damage.
Variational formulation and analysis of a linearized 2-D model with no axial symmetry for a two-phase water-petroleum flow.
Variational inequalities in plasticity with strain-hardening - equilibrium finite element approach
The incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. Following Watwood and Hartz, the stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained...
Variational Principles and Convergence of Finite Element Approximations of a Holonomic Elastic-Plastic Problem.
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Verification of functional a posteriori error estimates for obstacle problem in 2D
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.