An Extension of Kelvin and Bredt Formulas

International audienceIn dell'Isola and Ruta, and dell'Isola and Rosa is suggested a "perturbative approach" (Nayfeh; Trabucho and Viano) to the Saint-Venant problem for thin cross sections, however, the papers deal with closed cross section or with cross section of constant thickness only (see also Wheeler and Horgan). Here we generalize the proposed procedure by giving a method for treating the case of open or closed sections of variable thickness. We find all the known formulas (Trabucho and Viano; Feodosyev; Chase and Cliver; Baldacci) due to Kelvin and Bredt as first non-vanishing-terms of our perturbative development and give the corrections to these formulas, too. This seems to be a first step toward solving the open problem formulated in Trabucho and Viano, pp. 162-164