Well-posedness of a free boundary problem for electrostatic microelectromechanical systems (MEMS) is investigated when nonlinear bending effects are taken into account. The model describes the evolution of the deflection of an electrically conductive elastic membrane suspended above a fixed ground plate together with the electrostatic potential in the free domain between the membrane and the fi...

In a previous paper from the authors, the bounds from Kelsey et al. (1958) were applied to a sandwich panel including a folded core in order to estimate its shear forces stiffness (Lebée and Sab, 2010b). The main outcome was the large discrepancy of the bounds. Recently, Lebée and Sab (2011a) suggested a new plate theory for thick plates –the Bending-Gradient plate theory– which is the extensio...

The mixed method for the biharmonic problem introduced in [12] is extended to the Reissner-Mindlin plate model. The Reissner-Mindlin problem is written as a system of first order equations and all the resulting variables are approximated. However, the hybrid form of the method allows one to eliminate all the variables and have a final system only involving the Lagrange multipliers that approxim...

Subducting plate (SP) curvature exerts a key control on the amount of bending dissipation associated with subduction, and the magnitude of the subduction-resisting bending force. However, the factors controlling the development of SP curvature are not well understood. We use numerical models to quantify the role of SP rheology on the minimum radius of curvature, Rmin. We find that Rmin depends ...

Neural-tube closure is a critical step of embryogenesis, and its failure causes serious birth defects. Coordination of two morphogenetic processes--convergent extension and neural-plate apical constriction--ensures the complete closure of the neural tube. We now provide evidence that planar cell polarity (PCP) signaling directly links these two processes. In the bending neural plates, we find t...

This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy leads to the Von-Kármán’s equations (or the linear model for smaller forces) in the plate and to a one dimensional rod-model at the limit. The junction condition...