Opérateurs monotones dans la théorie de plasticité
Optimal design of cylindrical shells
The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient...
Plane stress elasto-plastic constitutive equations obtained by homogenizing one-dimensional structures
Prise en compte d'une force linéique de frontière dans un modèle de plaques de Hencky comportant une non-linéarité géométrique
Quasilinear hyperbolic equations with hysteresis
Quasilinear hyperbolic equations with hysteresis
Hysteresis operators are illustrated, and a weak formulation is studied for an initial- and boundary-value problem associated to the equation ; here is a (possibly discontinuous) hysteresis operator, is a second order elliptic operator, is a known function. Problems of this sort arise in plasticity, ferromagnetism, ferroelectricity, and so on. In particular an existence result is outlined.
Quasistatic processes for elastic-viscoplastic materials with internal state variables
Regularity of solutions to a one dimensional plasticity model
Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function
Maximization problems are formulated for a class of quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. Approximate problems are introduced on the basis of cubic Hermite splines and finite elements. The solvability of both continuous and approximate problems is proved and some convergence analysis presented.
Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory
Rheological models and hysteresis effects
Rotující kotouč v plastickém stavu
Shape optimization of elasto-plastic axisymmetric bodies
A minimization of a cost functional with respect to a part of a boundary is considered for an elasto-plastic axisymmetric body obeying Hencky's law. The principle of Haar-Kármán and piecewise linear stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.
Sottopotenziali energia libera per l'isteresi meccanica
This paper deals with free-energy lower-potentials for some rate-independent one-dimensional models of isothermal finite elastoplasticity proposed in [1]. Extending the thermodynamic arguments of Coleman and Owen [3] to large deformations, the existence, non-uniqueness and regularity of free-energy as function of state are deduced rather than assumed. This approach, along with some optimal control techniques, enables us to construct maximum and minimum free-energy functions and a wide class of differentiable...
Su alcune classi di potenziali termodinamici come conseguenza dell'esistenza di particolari onde di discontinuità nella meccanica dei continui con deformazioni finite
Sul teorema di Liouville per deformazioni conformi
Sur les équations du type ψ(x,h)=0 (I)
The Bernoulli manifolds for nonelliptic quasilinear systems of first order and applications in continuum mechanics
Un espace fonctionnel pour les équations de la plasticité