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Sur quelques théorèmes variationnels dans la théorie du fluage linéaire

Ivan Hlaváček — 1966

Aplikace matematiky

Par la méthode de transformation en problèmes équivalentes de la théorie d'élasticité, on établit deux théorèmes variationnels analogues aux principes du minimum d'énergie potentielle et de Castigliano dans la théorie d'élasticité, pour les corps homogénes isotropes tenant compte à l'hérédité et de l'âge du matérial.

Variational principles for parabolic equations

Ivan Hlaváček — 1969

Aplikace matematiky

New types of variational principles, each of them equivalent to the linear mixed problem for parabolic equation with initial and combined boundary conditions having been suggested by physicists, are discussed. Though the approach used here is purely mathematical so that it makes possible application to all mixed problems of mathematical physics with parabolic equations, only the example of heat conductions is used to show the physical interpretation. The principles under consideration are of two...

Derivation of non-classical variational principles in the theory of elasticity

Ivan Hlaváček — 1967

Aplikace matematiky

Generalized variational principles, suggested by Hu Hai-Chang and Washizu or Hellinger and Reissner respectively, are derived on the base of complementary energy respectively. Besides, a short survey of further variational theorems, which follow from the fundamental principles, and the proof of the convergence for a method based on one of them, are presented.

Variational principles in the linear theory of elasticity for general boundary conditions

Ivan Hlaváček — 1967

Aplikace matematiky

Mixed boundary-value problem of the classical theory of elasticity is considered, where not only displacements and tractions are prescribed on some parts of the boundary, but also conditions of contact and elastic supports for normal and tangential directions to the boundary surface separately. Classical variational principles are derived using functional analysis methods, especially methods of Hilbert space. Furthermore, generalized variational principles and bilateral estimates of errors are...

Dual finite element analysis for elliptic problems with obstacles on the boundary. I

Ivan Hlaváček — 1977

Aplikace matematiky

For an elliptic model problem with non-homogeneous unilateral boundary conditions, two dual variational formulations are presented and justified on the basis of a saddle point theorem. Using piecewise linear finite element models on the triangulation of the given domain, dual numerical procedures are proposed. By means of one-sided approximations, some a priori error estimates are proved, assuming that the solution is sufficiently smooth. A posteriori error estimates and two-sided bounds for the...

Shape optimization of elastic axisymmetric bodies

Ivan Hlaváček — 1989

Aplikace matematiky

The shape of the meridian curve of an elastic body is optimized within a class of Lipschitz functions. Only axisymmetric mixed boundary value problems are considered. Four different cost functionals are used and approximate piecewise linear solutions defined on the basis of a finite element technique. Some convergence and existence results are derived by means of the theory of the appropriate weighted Sobolev spaces.

Convergence of dual finite element approximations for unilateral boundary value problems

Ivan Hlaváček — 1980

Aplikace matematiky

A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author’s results on error estimates, no assumption of this kind is imposed here and still the L 2 -convergence is proved.

The density of solenoidal functions and the convergence of a dual finite element method

Ivan Hlaváček — 1980

Aplikace matematiky

A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation.

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