Existence and uniqueness of the solution to a 3D thermoviscoelastic system.
Existence for problems of viscoplastic contact with Coulomb friction.
Existence of a solution for a nonlinearly elastic plane membrane “under tension”
Existence of a solution for a nonlinearly elastic plane membrane “under tension”
A justification of the two-dimensional nonlinear “membrane” equations for a plate made of a Saint Venant-Kirchhoff material has been given by Fox et al. [9] by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of , is equivalent to finding the critical points...
Existence of equilibrium states of hollow elastic cylinders submerged in a fluid.
Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions
Existence results for unilateral quasistatic contact problems with friction and adhesion
Existence Results for Unilateral Quasistatic Contact Problems With Friction and Adhesion
We consider a two dimensional elastic body submitted to unilateral contact conditions, local friction and adhesion on a part of his boundary. After discretizing the variational formulation with respect to time we use a smoothing technique to approximate the friction term by an auxiliary problem. A shifting technique enables us to obtain the existence of incremental solutions with bounds independent of the regularization parameter. We finally obtain the existence of a quasistatic solution...
Existence theorem for nonlinear micropolar elasticity
In this paper we give an existence theorem for the equilibrium problem for nonlinear micropolar elastic body. We consider the problem in its minimization formulation and apply the direct methods of the calculus of variations. As the main step towards the existence theorem, under some conditions, we prove the equivalence of the sequential weak lower semicontinuity of the total energy and the quasiconvexity, in some variables, of the stored energy function.
Existence theorem in the linear theory of multipolar elasticity
Explicit solutions of the basic boundary value problems of statics of the elastic mixture theory for an annulus.
Finite element analysis of free material optimization problem
Free material optimization solves an important problem of structural engineering, i.e. to find the stiffest structure for given loads and boundary conditions. Its mathematical formulation leads to a saddle-point problem. It can be solved numerically by the finite element method. The convergence of the finite element method can be proved if the spaces involved satisfy suitable approximation assumptions. An example of a finite-element discretization is included.
Finite element methods for coupled thermoelasticity and coupled consolidation of clay
First boundary value problem of electroelasticity for a transversally isotropic plane with curvilinear cuts.
Flambage des plaques élastiques multiperforées
Formules de l'élasticité des corps amorphes que des compressions permanentes et inégales ont rendus hétérotropes.
Frictional contact of an anisotropic piezoelectric plate
The purpose of this paper is to derive and study a new asymptotic model for the equilibrium state of a thin anisotropic piezoelectric plate in frictional contact with a rigid obstacle. In the asymptotic process, the thickness of the piezoelectric plate is driven to zero and the convergence of the unknowns is studied. This leads to two-dimensional Kirchhoff-Love plate equations, in which mechanical displacement and electric potential are partly decoupled. Based on this model numerical examples are presented...
Fundamental tones and buckling loads of clamped plates
General method of regularization. I: Functionals defined on BD space
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis problem.
General method of regularization. II: Relaxation proposed by suquet
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.