Remarks to weakly continuous inverse operators and an application in hyperelasticity
Removing holes in topological shape optimization
The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical examples...
Removing holes in topological shape optimization
The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical...
Representation of solutions of some boundary value problems of elasticity by a sum of the solutions of other boundary value problems.
Representations of hypersurfaces and minimal smoothness of the midsurface in the theory of shells
Research of nonlinear vibrations of orthotropic plates of a complex form.
Residual a posteriori error estimators for contact problems in elasticity
This paper is concerned with the unilateral contact problem in linear elasticity. We define two a posteriori error estimators of residual type to evaluate the accuracy of the mixed finite element approximation of the contact problem. Upper and lower bounds of the discretization error are proved for both estimators and several computations are performed to illustrate the theoretical results.
Résolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en et séries de Fourier en
Resolution of a fixed point problem by an incremental method and application in nonlinear elasticity
Resolution of the time dependent Pn equations by a Godunov type scheme having the diffusion limit
We consider the Pn model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by Gosse to solve the P1 model...
Résonances de Rayleigh en dimension 2
Nous étudions les résonances de Rayleigh créées par un obstacle strictement convexe à bord analytique en dimension 2. Nous montrons qu’il existe exactement deux suites de résonances et convergeant exponentiellement vite vers l’axe réel dans un voisinage polynomial de l’axe réel, et exponentiellement proches d’une suite de quasimodes réels. De plus, est un symbole analytique d’ordre 0 en la variable dont on donne le premier terme du développement. Nous construisons pour cela des quasimodes...
Résonances de Rayleigh en dimension deux
Résumé d'une Conférence sur la théorie mathématique de l'élasticité, faite aux élèves de l'École Polytechnique (promotion de 1877-1879).
Rheological models and hysteresis effects
Rheologies quasi wave number independent in a sphere and splitting the spectral line
The solution of the equations which govern the slow motions (for which the inertia forces are negligible) in an elastic sphere is studied for a great variety of rheological models and surface tractions with rotational symmetry (Caputo 1984a). The solution is expressed in terms of spherical harmonics and it is shown that its time dependent component is dependent on the order of the harmonic. The dependence of the time component of the solution on the order of the harmonic number is studied. The problem...
Riesz basis property of Timoshenko beams with boundary feedback control.
Rigidity for the hyperbolic Monge-Ampère equation
Some properties of nonlinear partial differential equations are naturally associated with the geometry of sets in the space of matrices. In this paper we consider the model case when the compact set is contained in the hyperboloid , where , the set of symmetric matrices. The hyperboloid is generated by two families of rank-one lines and related to the hyperbolic Monge-Ampère equation . For some compact subsets containing a rank-one connection, we show the rigidity property of by imposing...
Robust optimal design of beams subject to uncertain loads.
Roots of the circular cylindrical shell characteristic equation
Rotating shells in general relativity