In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be use...

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...

This study investigates the hydro-elastic behaviors of fully submerged horizontal cylinders in different regular waves. Two methods were proposed and compared this study. The first method was based on potential theory frequency domain discrete-module-beam (DMB) method, which discretizes a floating elastic structure into sufficient number rigid bodies while simultaneously representing behavior f...

This practice and experience paper describes a robust C++ implementation of several nonlinear solid 3D deformable object strategies commonly employed in computer graphics, named the Vega FEM simulation library. Deformable models supported include co-rotational linear FEM elasticity, Saint-Venant Kirchhoff FEM model, mass-spring system, and invertible FEM models: neo-Hookean, Saint-Venant Kirchh...

The aim of this paper is to present a kinetic formulation of a model for the coupling of transient free surface and pressurised flows. Firstly, we revisit the system of Saint-Venant equations for free surface flow: we state some properties of Saint-Venant equations, we propose a kinetic formulation and we verify that this kinetic formulation leads to a Gibbs equilibrium that minimises (in some ...

The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables— displacements, electric potential, and magnetic potential, as well as their duality variables— lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-ei...

We develop a second-order central-upwind scheme for the non-hydrostatic version of the Saint-Venant system recently proposed in [M.-O. Bristeau and J. Sainte-Marie, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), pp. 733–759]. The designed scheme is both well-balanced (capable of exactly preserving the “lake-at-rest” steady state) and positivity preserving. We then use the central-upwind scheme ...

This paper deals with the stability study of Partial Differential nonlinear Equation (PDE) of Saint-Venant. The proposed approach is based on the Multi-Models concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows to describe the dynamic of this nonlinear system in infinite dimension over a wide operating range. A st...