Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Analyse par la méthode des éléments finis du comportement en rupture du ciment de l'implant femoral

La tenue mécanique de la prothèse totale de hanche dépend essentiellement de la nature du ciment utilisé. Le rôle principal du ciment est d'assurer une bonne adhésion implant–os et de minimiser le transfert de charge de l'implant à l'os. Sous l'effet des sollicitations mécaniques, le ciment doit pouvoir résister à l'initiation et à la propagation de fissure pouvant conduire à sa ruine et par conséquent au descellement de la prothèse. Notre travail s'inscrit dans ce contexte et a pour objectif l'analyse par la méthode des éléments finis du comportement en rupture du ciment fixant l'implant à l'os. Le champ de cette analyse s'étend sur différentes zones du ciment (proximale, médiane et distale) des côtés extérieur et intérieur du fémur. Nous montrons clairement l'effet de la position et de l'orientation de la fissure dans le ciment sur les variations du facteur d'intensité de contrainte en pointe de fissure

The Mechanical Behavior of Bone Cement in THR in the Presence of Cavities

In this work we analyze three-dimensionally using the finite element method, the level and the Von Mises stress equivalent distribution induced around a cavity and between two cavities located in the proximal and distal bone cement polymethylmethacrylate (PMMA). The effects of the position around two main axes (vertical and horizontal) of the cavity with respect to these axes, of the cavity - cavity interdistance and of the type of loading (static) on the mechanical behavior of cement orthopedic are highlighted. We show that the breaking strain of the cement is largely taken when the cement in its proximal-lateral part contains cavities very close adjacent to each other. This work highlights not only the effect of the density of cavities, in our case simulated by cavity-cavity interdistance, but also the nature of the activity of the patient (patient standing corresponding to static efforts) on the mechanical behavior of cement.</jats:p

Finite element analysis of the behaviour of a crack in the orthopedic cement

In this paper, the finite element method is used to analyse the crack behaviour in the orthopedic cement of the total hip replacement by computing the stress intensity factors (SIFs) arround the crack tip. In this work, three cases are studied: crack emanating from a cavity, interaction effect of the crack emanating from a cavity with another cavity and the interaction effect of two cracks emanatingfrom two cavities. The stress intensity factors under mixed mode problems at the crack tip are computed for three zones of prosthesis: proximal, median and distal. The obtained results show that the crack initiated from a micro-cavity in the distal zone of cement can be propagated at the same time by opening and shearing of its lips. It is contrary to that initiated in the proximal zone which cannot be propagated. The mechanical behaviour of cracks in the medial zone depends of the crack initiation position