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Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method

Jindřich Nečas, Tomáš Roubíček (1990)

Aplikace matematiky

The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...

Betti's reciprocal theorem for Cosserat elastic shells

Franco Pastrone (1991)

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

It is proved that, as in three-dimensional elasticity, Betti's theorem represents a criterion for the existence of a stored-energy function for a Cosserat elastic shell.

Bloch wave homogenization of linear elasticity system

Sista Sivaji Ganesh, Muthusamy Vanninathan (2005)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...

Bloch wave homogenization of linear elasticity system

Sista Sivaji Ganesh, Muthusamy Vanninathan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a regular Bloch spectrum is not guaranteed. The aim here is to develop all necessary spectral tools to overcome...

Boundary stabilization of the linear elastodinamic system by a Lyapunov-type method.

Rabah Bey, Amar Heminna, Jean-Pierre Lohéac (2003)

Revista Matemática Complutense

We propose a direct approach to obtain the boundary stabilization of the isotropic linear elastodynamic system by a natural feedback; this method uses local coordinates in the expression of boundary integrals as a main tool. It leads to an explicit decay rate of the energy function and requires weak geometrical conditions: for example, the spacial domain can be the difference of two star-shaped sets.

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