In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization...
We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational...
This article is devoted to the presentation of a new contact algorithm for bodies undergoing finite deformations. We only address the kinematic aspect of the contact problem, that is the numerical treatment of the non-intersection constraint. In consequence, mechanical aspects like friction, adhesion or wear are not investigated and we restrict our analysis to the simplest frictionless case. On the other hand, our method allows us to treat contacts and self-contacts, thin or non-thin structures...
This article is devoted to the presentation of a new contact algorithm for bodies undergoing finite deformations. We only address the kinematic aspect of the contact problem, that is the numerical treatment of the non-intersection constraint. In consequence, mechanical aspects like friction, adhesion or wear are not investigated and we restrict our analysis to the simplest frictionless case. On the other hand, our method allows us to treat contacts and self-contacts, thin or non-thin structures...
We study a mathematical model for frictionless contact between an elastic-viscoplastic body and a foundation. We model the material with a general elastic-viscoplastic constitutive law with internal state variable and the contact with a normal compliance condition. We derive a variational formulation of the model. We establish existence and uniqueness of a weak solution, using general results on first order nonlinear evolution equations with monotone operators and fixed point arguments. Finally,...
We study a two-grid scheme fully discrete in time and space for solving the Navier-Stokes system. In the first step, the fully non-linear problem is discretized in space on a coarse grid with mesh-size H and time step k. In the second step, the problem is discretized in space on a fine grid with mesh-size h and the same time step, and linearized around the velocity uH computed in the first step. The two-grid strategy is motivated by the fact that under suitable assumptions, the contribution of uH...
This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that our result holds without the imposition of the equal speed of wave propagation condition, and differentiation...
The goal of this paper is to establish a general homogenization result for linearized elasticity of an eigenvalue problem defined over perforated domains, beyond the periodic setting, within the framework of the -convergence theory. Our main homogenization result states that the knowledge of the fourth-order tensor , the -limit of , is sufficient to determine the homogenized eigenvalue problem and preserve the structure of the spectrum. This theorem is proved essentially by using Tartar’s method...