In this article, we work with a generalized Saint Venant operator introduced by Vladimir Sharafutdinov [Inverse and ill-posed problems series, VSP, Utrecht, 1994] to describe the kernel of integral moment transforms over symmetric m <mml:annotation e...

A nonlinearly elastic shell is modeled either by the nonlinear threedimensional shell model or by a nonlinear two-dimensional shell model. We show how such two-dimensional shell models can be derived from the minimization problem associated with the nonlinear three-dimensional shell model. For shells made of a Saint Venant-Kirchhoff material, we obtain in particular the nonlinear shell models o...

In dynamics, Saint-Venant s principle of exponential decay of stress resulting from a self-equilibrating load is not valid. For a beam type structure, a self-equilibrated load may penetrate well inside the beam. Although this effect has been known for a long time, at least since Lamb s paper [Proc. Roy. Soc. Lon. Ser. A 93 (1916) 114], it was not clear how to characterize it quantitatively. In ...

Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson’s equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here the literature is unified and extended by identifying 17 physical analogies for unidi...