Gustav Kirchhoff

Résumé

Gustav Kirchhoff (prononcé en allemand ) (né le à Königsberg, en province de Prusse-Orientale et décédé à Berlin le ) est l’un des plus grands physiciens du , avec des contributions essentielles à l’électrodynamique, la physique du rayonnement et la théorie mathématique de l'élasticité. Biographie Gustav Kirchhoff est le fils benjamin de l'avocat Friedrich Kirchhoff de Kœnigsberg (Prusse orientale), et de Johanna Henriette Wittke, épouse Clara Richelot. Elle était la fille de Friedrich Julius Richelot, professeur de mathématiques. Après un doctorat de physique obtenu en 1847 à l'université de Königsberg où il a suivi les cours de Franz Ernst Neumann, Gustav Kirchhoff est recruté comme professeur surnuméraire à l'université de Breslau. C'est là qu'il fait la connaissance de Robert Bunsen, avant d'accepter en 1854 un poste de professeur à l'université de Heidelberg. En 1862, la médaille Rumford lui est décernée pour avoir démontré l'existence de raies lumineuses fixes dans l

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https://fr.wikipedia.org/wiki/Gustav_Kirchhoff

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Transition of the mushy zone from continuous liquid films to a coherent solid

Michel Rappaz, Stéphane Vernède

While studies of solidification microstructures have focused mainly on the tips of the dendrites, the last stage solidification is equally important from the point of view of defect formation (porosity, hot tearing), mechanical strength build-up and precipitation of phases. In particular, the transition from continuous liquid films to a coherent solid in low concentration alloys is of crucial importance for hot tearing formation, and more generally speaking for liquid feeding ability and coherency development. Based on a fairly recent theoretical model of coalescence which will be recalled briefly, new results obtained for a population of equiaxed grains will be presented. A granular-type model based on a Voronoi tessellation has been used for the description of the gradual disappearance of liquid films and the clustering of equiaxed grains. This percolation-type approach has been used then to calculate the pressure drop in the mushy zone on the assumptions of a Poiseuille flow in between the grains and a Kirchhoff model for the connectivity of the liquid films including the Losses associated with solidification shrinkage (i.e, PKL model). Comparison with a standard average pressure drop calculation based on Carman-Kozeny’s relationship will be presented.

2006

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We obtain the affine Euler-Poincare equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff's rod, where they provide a unified geometric interpretation.

2009

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Application of the isogeometric method is illustrated for free and forced vibration analyzes of sinusoidally corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) thin panels. These panels can be used as a potential structure for morphing skin applications. The nanocomposite panel is fabricated from a polymeric matrix which is reinforced by carbon nanotubes (CNTs). The volume fraction of CNTs varies based on the four models of functionally graded (FG). The Kirchhoff-Love (KL) shell theory is employed to model the kinematic behavior of sinusoidally corrugated panels (SCPs) with a variable radius of curvature. The multiple patches approach is approved to model the structure. In this model, the bending strip method (BSM) is applied at the intersection of the patches. The temporal response of the panel under different transverse dynamical loadings is predicted via the Newmark time-marching scheme. A detailed comparison study is performed to demonstrate the validity and efficiency of the proposed isogeometric analysis (IGA). The numerical results demonstrate that the computationally effective IGA can provide accurate results due to the capability of precisely approximating any segments of the corrugation. Furthermore, the effects of different configurations of CNTs and various geometrical parameters such as corrugation amplitude, number of corrugation units and panel aspect ratio are presented on the natural frequency and dynamic response of the sinusoidally corrugated FG-CNTRC panels.

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