Etude de problèmes d'homogénéisation définis sur des plaques minces perforées périodiquement

Abstract : In the first part of this work, we are interested in the study of an evolution problem, defined on a perforated thin plate. We make the thickness of the plate, the period of the holes, and the ratio between this period and the thickness of the bars tend towards zero, and we give the coefficients of the limit material. Several geometries are studied. One of them gives an example of a limit material, of which the Poisson ratio is negative. Next, we study a problem with Fourier conditions, defined on a similar thin plate. At first, we make tend the thickness of the plate, and then the period, towards zero (in this order). After that, we pass to the limit again, but in the reverse order. We give the two limit problems we obtain. In the third part, we give a computer tool assigned to the calculation of homogenized coefficients related to thermal and elasticity problems. Numerical results related to the different geometries are given in this third part
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Jean-Marc Sac-Epée. Etude de problèmes d'homogénéisation définis sur des plaques minces perforées périodiquement. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1994. Français. ⟨NNT : 1994METZ038S⟩. ⟨tel-01776730⟩

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