Régularité de la solution d'un problème variationnel
Regularity and optimal control of quasicoupled and coupled heating processes
Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...
Regularity for a clamped grid equation on a domain with a corner.
Regularity for Signorini's Problem in linear eleasticity.
Regularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity...
Regularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to...
Regularity of displacement solutions in Hencky plasticity. II: The main result
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity. In the second part, we prove that the displacement...
Regularity of displacement solutions in Hencky plasticity. I: The extremal relation
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. A non-homogeneous material whose elastic-plastic properties change discontinuously is considered. We find (in an explicit form) the extremal relation between the displacement formulation (defined on the space of bounded deformation) and the stress formulation of the variational problem in Hencky plasticity. This extremal relation is used in the proof of the regularity of displacements. ...
Regularity of minimizers for a class of membrane energies
Regularity of solutions in plasticity. I: Continuum
The aim of this paper is to study the problem of regularity of solutions in Hencky plasticity. We consider a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.
Regularity of solutions in plasticity. II: Plates
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. We consider a plate made of a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.
Regularity of solutions to a one dimensional plasticity model
Regularity result for the problem of vibrations of a nonlinear beam.
Regularization of noncoercive constraints in Hencky plasticity
The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.
Reinforcement problems in the calculus of variations
Reissner-Mindlin model for plates of variable thickness. Solution by mixed-interpolated elements
Hard clamped and hard simply supported elastic plate is considered. The mixed finite element analysis combined with some interpolation, proposed by Brezzi, Fortin and Stenberg, is extended to the case of variable thickness and anisotropic material.
Reissner-Mindlin plate theory for elastodynamics.
Reissnerovske algoritmy 1. druhu v teorii válcových skořepin
Relating phase field and sharp interface approaches to structural topology optimization
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for...
Relativistic and nonrelativistic elastodynamics with small shear strains