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### A discretization method for the problem of a membrane constrained by elastic obstacle

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questo lavoro sono dati alcuni modelli matematici per il problema di contatto tra una membrana ed un suolo od ostacolo elastico. Viene costruita una approssimazione lineare a tratti della soluzione e, tramite una disequazione variazionale discreta, se ne dà il corrispondente teorema di convergenza.

### A dual method for some class of systems of variational inequalities

Annales Polonici Mathematici

### A finite element analysis for elastoplastic bodies obeying Hencky's law

Aplikace matematiky

Using the Haar-Kármán principle, approximate solutions of the basic boundary value problems are proposed and studied, which consist of piecewise linear stress fields on composite triangles. The torsion problem is solved in an analogous manner. Some convergence results are proven.

### A frictionless contact problem for viscoelastic materials.

Journal of Applied Mathematics

### A hypercomplex method of calculating stresses in three-dimensional bodies

Proceedings of the 12th Winter School on Abstract Analysis

### A viscoelastic contact problem with normal damped response and friction

Annales Polonici Mathematici

We study an evolution problem which describes the quasistatic contact of a viscoelastic body with a foundation. We model the contact with normal damped response and a local friction law. We derive a variational formulation of the model and we establish the existence of a unique weak solution to the problem. The proof is based on monotone operators and fixed point arguments. We also establish the continuous dependence of the solution on the contact boundary conditions.

### An analysis of a contact problem for a cylindrical shell: A primary and dual formulation

Aplikace matematiky

In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.

### Analysis and Numerical Approximation of an Electro-elastic Frictional Contact Problem

Mathematical Modelling of Natural Phenomena

We consider the problem of frictional contact between an piezoelectric body and a conductive foundation. The electro-elastic constitutive law is assumed to be nonlinear and the contact is modelled with the Signorini condition, nonlocal Coulomb friction law and a regularized electrical conductivity condition. The existence of a unique weak solution of the model is established. The finite elements approximation for the problem is presented, and error...

### Analysis of a viscoelastic antiplane contact problem with slip-dependent friction

International Journal of Applied Mathematics and Computer Science

We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational inequalities....

### Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems

Aplikace matematiky

The authors study problems of existence and uniqueness of solutions of various variational formulations of the coupled problem of dynamical thermoelasticity and of the convergence of approximate solutions of these problems. First, the semidiscrete approximate solutions is defined, which is obtained by time discretization of the original variational problem by Euler’s backward formula. Under certain smoothness assumptions on the date authors prove existence and uniqueness of the solution and establish...

### Approximation and numerical solution of contact problems with friction

Aplikace matematiky

The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function $ℒ$ on a certain convex set $K×\Lambda$. The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa’s algorithm is used. Some examples are given in the conclusion.

### Approximation of a Bending Plate Problem With a Boundary Unilateral Constraint.

Numerische Mathematik

### Asymptotic behavior of eigenfunctions and eigenfrequencies of oscillation boundary value problems of the linear theory of elastic mixtures.

Georgian Mathematical Journal

### Convergenza per l'equazione degli integrali primi associata al problema del rimbalzo

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we present a few results on convergence for the prime integrals equations connected with the bounce problem. This approach allows both to prove uniqueness for the one-dimensional bounce problem for almost all permissible Cauchy data (see also [6]) and to deepen previous results (see [3], [5], [7]).

### Dissipatività e unicità per il problema dinamico unidimensionale della viscoelasticità lineare

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Fissato lo spazio di Sobolev $H^{1,2}$ come ambiente del problema dinamico per un corpo viscoelastico unidimensionale si dimostra un teorema di unicità per la classe delle funzioni di rilassamento convesse. Si fa inoltre vedere come tale unicità sia strettamente legata allo spazio ambiente considerato.

### Elasticity of initially stressed bodies with voids. Weak solutions

Rendiconti del Seminario Matematico della Università di Padova

### Esistenza e unicità della soluzione nella statica di solidi termoelastici incomprimibili

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this work we prove that the thermoelastic equilibrium problem in the context of the linear theory for thermoelastic incompressible solids has one and only one solution.

### Existence and uniqueness of the solution to a 3D thermoviscoelastic system.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Existence theorem in the linear theory of multipolar elasticity

Aplikace matematiky

### Finite element methods for coupled thermoelasticity and coupled consolidation of clay

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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