Contribution à l'étude de quelques problèmes sur des ouverts ondulés et des plaques perforées

Abstract : At the beginning of the first part, we consider the thermal stationnary equation upon three corrugated opens, with a constant thickness e and a constant medium radius of the corrogatings R: corrogated sheet iron T, tin and section of this lasts. We study the limit of the temperature when e, then R tend to O. In each case the limit is one and is solution of a differential equation of the second order. The inversion of the limits is realised. Regarding the elasticity problem upon T, the shell theory obliges us to choose a straight section more regular. Then, the displacement converges, when e tend to O, to a function which is defined in one manner and solution of a differential equation of the fourth order. Then, when R tend to O, the displacement converges to O. The initial displacement converges also to O, with e being constant. In the second part, we consider the linearized elasticity equations upon a rectangular plate, perforated with square section holes which are distributed in a periodic fashion and supposed horizontal. The study of the displacement's limit when the thickness tend to O, leads us to differentiate two cases, functions of the elasticity coefficients of the materials. Then in each one, we study the limit of displacement when the period of the holes, and then the parameter which caracterises the distance between two holes tend to O. In the first case, the three limits exist in a single manner and are solutions of differential equations of the second order : case of membranes. In the second one, the three limits still exist in one single manner, but they are solutions of differential equations of the second order for the horizontal components, and of the fourth order for the vertical component : case of thin plates
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Robert Kauffmann. Contribution à l'étude de quelques problèmes sur des ouverts ondulés et des plaques perforées. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1994. Français. ⟨NNT : 1994METZ048S⟩. ⟨tel-01776799⟩

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