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On a type of Signorini problem without friction in linear thermoelasticity

Jiří Nedoma (1983)

Aplikace matematiky

In the paper the Signorini problem without friction in the linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and unicity of the solution of the Signorini problem without friction for the steady-state case in the linear thermoelasticity as well as its finite element approximation is proved. It is known that...

On the Cauchy problem in linear viscoelasticity

Pasquale Renno (1983)

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

Con riferimento all’operatore integrodifferenziale della viscoelasticità lineare nella formulazione creep, si determina la soluzione fondamentale E in corrispondenza di un’arbitraria funzione di memoria. Di conseguenza viene risolto esplicitamente il problema di Cauchy relativo al moto unidimensionale di un sistema viscoelastico ℬ , omogeneo ed isotropo, determinato da dati iniziali e storia di stress comunque prefissati. Successivamente, nell’ambito di opportune ipotesi di memoria labile, si dimostrano...

On the domain of influence in thermoelasticity of bodies with voids

Marin Marin (1997)

Archivum Mathematicum

The domain of influence, proposed by Cowin and Nunziato, is extended to cover the thermoelasticity of bodies with voids. We prove that for a finite time t > 0 the displacement field u i , the temperature θ and the change in volume fraction σ generate no disturbance outside a bounded domain B t .

On the dynamical behaviour of plates in unilateral contact with an elastic foundation: a finite element approach.

Luigi Ascione, Domenico Bruno, Renato S. Olivito (1984)

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

In questo lavoro viene studiato il comportamento dinamico di una piastra vincolata monolateralmente su una fondazione elastica alla Winkler. Si presentano alcuni risultati numerici ottenuti mediante discretizzazione agli elementi finiti. Tali risultati mettono in luce l'influenza di alcuni fattori tipici come le funzioni di forma, il parametro di mesh e l'ampiezza dell'intervallo con cui si realizza l'integrazione nel tempo delle equazioni del moto. Si istituiscono infine dei confronti con risultati...

On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions

Igor Bock, Ivan Hlaváček, Ján Lovíšek (1984)

Aplikace matematiky

A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.

On the solution of boundary value problems for sandwich plates

Igor Bock, Ivan Hlaváček, Ján Lovíšek (1986)

Aplikace matematiky

A mathematical model of the equilibrium problem of elastic sandwich plates is established. Using the theory of inequalities of Korn's type for a general class of elliptic systems the existence and uniqueness of a variational solution is proved.

On the two-step iterative method of solving frictional contact problems in elasticity

Todor Angelov, Asterios Liolios (2005)

International Journal of Applied Mathematics and Computer Science

A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.

Optimal design of cylindrical shell with a rigid obstacle

Ján Lovíšek (1989)

Aplikace matematiky

The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1...

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