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Shakedown theorems in poroplastic dynamics

Giuseppe Cocchetti, Giulio Maier (2002)

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

The constitutive model assumed in this Note is poroplastic two-phase (solid-fluid) with full saturation and stable in Drucker’s sense. A solid or structure of this material is considered, subjected to dynamic external actions, in particular periodic or intermittent, in a small deformation regime. A sufficient condition and a necessary one are established, by a «static» approach, for shakedown (or adaptation), namely for boundedness in time of the cumulative dissipated energy.

Smoothness of the motion of a rigid body immersed in an incompressible perfect fluid

Olivier Glass, Franck Sueur, Takéo Takahashi (2012)

Annales scientifiques de l'École Normale Supérieure

We consider the motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain. For such a system the Cauchy problem is well-posed locally in time if the initial velocity of the fluid is in the Hölder space C 1 , r . In this paper we prove that the smoothness of the motion of the rigid body may be only limited by the smoothness of the boundaries (of the body and of the domain). In particular for analytic boundaries the motion of the rigid body is analytic...

Solutions faibles pour des problèmes d’interaction fluide-structure

Benoît Desjardins, Maria J. Esteban (1999/2000)

Séminaire Équations aux dérivées partielles

Nous présentons dans cette note une nouvelle façon d’aborder les questions d’existence de solutions faibles pour certains problèmes d’interaction fluide-structure. Dans l’état actuel, cette approche permet de traiter le cas de solides rigides ou très faiblement déformables, immergés dans un fluide visqueux incompressible ou dans un fluide visqueux compressible dont l’évolution est isentropique.

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

Martin Balazovjech, Miloslav Feistauer, Jaromír Horáček, Martin Hadrava, Adam Kosík (2018)

Applications of Mathematics

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic...

Spectral/hp elements in fluid structure interaction

Pech, Jan (2021)

Programs and Algorithms of Numerical Mathematics

This work presents simulations of incompressible fluid flow interacting with a moving rigid body. A numerical algorithm for incompressible Navier-Stokes equations in a general coordinate system is applied to two types of body motion, prescribed and flow-induced. Discretization in spatial coordinates is based on the spectral/hp element method. Specific techniques of stabilisation, mesh design and approximation quality estimates are described and compared. Presented data show performance of the solver...

Stability for dissipative magneto-elastic systems

Reinhard Racke (2003)

Banach Center Publications

In this survey we first recall results on the asymptotic behavior of solutions in classical thermoelasticity. Then we report on recent results in linear magneto-thermo-elasticity and magneto-elasticity, respectively.

Stabilization of a layered piezoelectric 3-D body by boundary dissipation

Boris Kapitonov, Bernadette Miara, Gustavo Perla Menzala (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a linear coupled system of quasi-electrostatic equations which govern the evolution of a 3-D layered piezoelectric body. Assuming that a dissipative effect is effective at the boundary, we study the uniform stabilization problem. We prove that this is indeed the case, provided some geometric conditions on the region and the interfaces hold. We also assume a monotonicity condition on the coefficients. As an application, we deduce exact controllability of the system with boundary control...

Strong asymptotic stability for n-dimensional thermoelasticity systems

Mohammed Aassila (1998)

Colloquium Mathematicae

We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.

Sulla propagazione e sull'evoluzione di onde nei solidi termoelastici. Nota II

Sergio Bressan (1984)

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

According to a thermodynamic theory proposed by G. Grioli, we consider the problem of determining the solutions for the growth of acceleration waves in an elastic body. At first we determine a property of the velocities of waves propagation and we determine some limitations for the free energy; then we resolve the above mentioned problem for the «small» waves working on the iperacceleration waves.

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