Calcul des charges limites d'une structure élastoplastique en contraintes planes
Cartesian currents and variational problems for mappings into spheres
Cholesky-like factorizations of skew-symmetric matrices.
Comparison of crack propagation criteria in linear elastic fracture mechanics
In linear fracture mechanics, it is common to use the local Irwin criterion or the equivalent global Griffith criterion for decision whether the crack is propagating or not. In both cases, a quantity called the stress intensity factor can be used. In this paper, four methods are compared to calculate the stress intensity factor numerically; namely by using the stress values, the shape of a crack, nodal reactions and the global energetic method. The most accurate global energetic method is used to...
Computation of displacements for nonlinear elastic beam models using monotone iterations.
Computation of generalized stress intensity factors for bonded elastic structures
COMPUTATION of generalized stress intensity factors for bonded elastic structures
We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural singularities....
Computational methods for estimation in the modeling of nonlinear elastomers
Computational study of the Willmore flow on graphs
Constrained and unconstrained optimization formulations for structural elements in unilateral contact with an elastic foundation.
Construction of entropy solutions for one dimensional elastodynamics via time discretisation
Contact between elastic bodies. II. Finite element analysis
The paper deals with the approximation of contact problems of two elastic bodies by finite element method. Using piecewise linear finite elements, some error estimates are derived, assuming that the exact solution is sufficiently smooth. If the solution is not regular, the convergence itself is proven. This analysis is given for two types of contact problems: with a bounded contact zone and with enlarging contact zone.
Contact between elastic bodies. III. Dual finite element analysis
The problem of a unilateral contact between elastic bodies with an apriori bounded contact zone is formulated in terms of stresses via the principle of complementary energy. Approximations are defined by means of self-equilibriated triangular block-elements and an -error estimate is proven provided the exact solution is regular enough.
Contact between elastic perfectly plastic bodies
If the material of the bodies is elastic perfectly plastic, obeying the Hencky's law, the formulation in terms of stresses is more suitable than that in displacements. The Haar-Kármán principle is first extended to the case of a unilateral contact between two bodies without friction. Approximations are proposed by means of piecewise constant triangular finite elements. Convergence of the method is proved for any regular family of triangulations.
Contact problem of two elastic bodies. II
The goal of the paper is the study of the contact problem of two elastic bodies which is applicable to the solution of displacements and stresses of the earth continuum and the tunnel wall. In this first part the variational formulation of the continuous and discrete model is stated. The second part covers the proof of convergence of finite element method to the solution of continuous problem while in the third part some practical applications are illustrated.
Contact problems with bounded friction. Semicoercive case
Control in obstacle-pseudoplate problems with friction on the boundary. approximate optimal design and worst scenario problems
In addition to the optimal design and worst scenario problems formulated in a previous paper [3], approximate optimization problems are introduced, making use of the finite element method. The solvability of the approximate problems is proved on the basis of a general theorem of [3]. When the mesh size tends to zero, a subsequence of any sequence of approximate solutions converges uniformly to a solution of the continuous problem.
Convergence analysis of a nonconforming finite element method solving a plate with ribs
Convergence analysis of the iterative methods for quasi-complementarity problems.
Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb's friction law
In this paper, the convergence of a Neumann-Dirichlet algorithm to approximate Coulomb's contact problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.