Unilateral contact of elastic bodies (moment theory).
Unilateral dynamic contact of von Kármán plates with singular memory
The solvability of the contact problem is proved provided the plate is simply supported. The singular memory material is assumed. This makes it possible to get a priori estimates important for the strong convergence of gradients of velocities of solutions to the penalized problem.
Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem
The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...
Unique global solvability of 1D Fried-Gurtin model
We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified assumptions...
Uniqueness in an inverse problem for an elasticity system.
Uniqueness of critical points for semi-linear Dirichlet problems in convex domains.
Uniqueness of the solution of the boundary-initial value problem for a linear elastic Cosserat continuum
Univalent -harmonic mappings : applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Univalent σ-harmonic mappings: applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Unstable simple modes for a class of Kirchhoff equations
Unsteady hydromagnetic free convection flow on a vertical infinite flat plate with suction
Variational and numerical analysis of the Signorini's contact problem in viscoplasticity with damage.
Variational characterization of eigenvalues of a non-symmetric eigenvalue problem governing elastoacoustic vibrations
Small amplitude vibrations of an elastic structure completely filled by a fluid are considered. Describing the structure by displacements and the fluid by its pressure field one arrives at a non-selfadjoint eigenvalue problem. Taking advantage of a Rayleigh functional we prove that its eigenvalues can be characterized by variational principles of Rayleigh, minmax and maxmin type.
Variational characterization of interior interfaces in phase transition models on convex plane domains.
Variational formulation and analysis of a linearized 2-D model with no axial symmetry for a two-phase water-petroleum flow.
Variational inequalities in plasticity with strain-hardening - equilibrium finite element approach
The incremental finite element method is applied to find the numerical solution of the plasticity problem with strain-hardening. Following Watwood and Hartz, the stress field is approximated by equilibrium triangular elements with linear functions. The field of the strain-hardening parameter is considered to be piecewise linear. The resulting nonlinear optimization problem with constraints is solved by the Lagrange multipliers method with additional variables. A comparison of the results obtained...
Variational Principles and Convergence of Finite Element Approximations of a Holonomic Elastic-Plastic Problem.
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Various kinds of sensitive singular perturbations
We consider variational problems of P. D. E. depending on a small parameter when the limit process implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first...
Vector variational problems and applications to optimal design
We examine how the use of typical techniques from non-convex vector variational problems can help in understanding optimal design problems in conductivity. After describing the main ideas of the underlying analysis and providing some standard material in an attempt to make the exposition self-contained, we show how those ideas apply to a typical optimal desing problem with two different conducting materials. Then we examine the equivalent relaxed formulation to end up with a new problem whose numerical...