We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using...

A layer-wise third order shear and normal deformable plate/shell theory (TSNDT) incorporating all geometric nonlinearities is used to study finite transient deformations of a curved laminated beam composed of a St. Venant–Kirchhoff material. In the TSNDT all displacement components of a point are expressed as 3rd order polynomials in the thickness coordinate in each layer while maintaining the ...

The viscous Shallow Water Equations and Quasi-Geostrophic Equations are considered in this paper. Some new terms, related to the Coriolis force, are revealed thanks to a rigorous asymptotic analysis. After providing well-posedness arguments for the new models, the authors perform some numerical computations that confirm the role played by the cosine effect in various physical configurations. Ke...

Supposing that A(z) is an exponential polynomial of the formA(z)=H0(z)+H1(z)eζ1zn+⋯+Hm(z)eζmzn, where Hj's are entire and order <n, it demonstrated function H0(z) geometric location leading coefficients ζ1,…,ζm play a key role in oscillation solutions differential equation f″+A(z)f=0. The tools consist value distribution properties polynomials, elementary Phragmén-Lindelöf indicator function. I...

In this paper, certain well-known upwind schemes for hyperbolic equations are extended to solve the two-dimensional Saint-Venant (or shallow water) equations. We consider unstructured meshes and a new type of nite volume to obtain a suitable treatment of the boundary conditions. The source term involving the gradient of the depth is upwinded in a similar way as the ux terms. The resulting schem...