The three-dimensional problem of statics of the elastic mixture theory with displacements given on the boundary.
The topological asymptotic expansion for the Quasi-Stokes problem
In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized...
The topological asymptotic expansion for the Quasi-Stokes problem
In this paper, we propose a topological sensitivity analysis for the Quasi-Stokes equations. It consists in an asymptotic expansion of a cost function with respect to the creation of a small hole in the domain. The leading term of this expansion is related to the principal part of the operator. The theoretical part of this work is discussed in both two and three dimensional cases. In the numerical part, we use this approach to optimize the locations of a fixed number of air injectors in an eutrophized...
The transversal creeping vibrations of a nonhomogeneous beam with fractional derivative order constitutive relation.
The treatment of “pinching locking” in -shell elements
We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source...
The treatment of “pinching locking” in 3D-shell elements
We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific source of...
The unbonded contact problem of a rectangular plate resting on an elastic foundation
In questo lavoro viene analizzato il problema di equilibrio statico di una piastra rettangolare in contatto unilaterale e senza attrito con un mezzo elastico. Si esaminano i due modelli di fondazione alla Winkler e di semispazio elastico. Il problema viene risolto mediante discretizzazione agli elementi finiti utilizzando un approccio di tipo «penalty». La rapida convergenza del metodo e la sua efficienza sono dimostrate dagli esempi studiati, che riguardano sia piastre quadrate che rettangolari...
The variational contact problem for elastic objects of different dimensions.
The warping, the torsion and the Neumann problems in a quasi-periodically perforated domain
The weak boundary effect in a field as a source approaches the boundary.
The weak solution of an antiplane contact problem for electro-viscoelastic materials with long-term memory
We study a mathematical model which describes the antiplane shear deformation of a cylinder in frictionless contact with a rigid foundation. The material is assumed to be electro-viscoelastic with long-term memory, and the friction is modeled with Tresca's law and the foundation is assumed to be electrically conductive. First we derive the classical variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement field with a time-dependent...
Théorème d'existence et d'unicité pour un problème de coque élastique dans le cas d'un modèle linéaire de P. M. Naghdi
Theoretical analysis of discrete contact problems with Coulomb friction
A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction depending on the spatial variable is analysed. It is shown that a solution exists for any and is globally unique if is sufficiently small. The Lipschitz continuity of this unique solution as a function of as well as a function of the load vector is obtained. Furthermore, local uniqueness of solutions for arbitrary is studied. The question of existence of locally Lipschitz-continuous...
Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition
This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math.107 (2007) 295–314; IMA J. Appl. Math.71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important...
Theoretical aspects of a multiscale analysis of the eigenoscillations of the Earth.
The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....
Theoretical study and optimization of a fluid-structure interaction problem
Theoretical study of a chain sliding on a fixed support.
Théorie mathématique de l'élasticité [Book]
Thermal stresses in a two-layer strip in the case of a non-ideal thermal contact
Thermal stresses in an initially stressed circular cylinder with a smooth rigid insulating cover on the curved surface