2020/03/31 by Philippe Laurençot, Laurençot, Philippe, Katerina Nik +3
Computer Science · Decision Sciences · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2003.14000
openalex publication_date 2020/03/31 · openalex created_date 2021/12/06 · openalex updated_date 2026/07/28
A model for a MEMS device, consisting of a fixed bottom plate and an elastic\nplate, is studied. It was derived in a previous work as a reinforced limit when\nthe thickness of the insulating layer covering the bottom plate tends to zero.\nThis asymptotic model inherits the dielectric properties of the insulating\nlayer. It involves the electrostatic potential in the device and the\ndeformation of the elastic plate defining the geometry of the device. The\nelectrostatic potential is given by an elliptic equation with mixed boundary\nconditions in the possibly non-Lipschitz region between the two plates. The\ndeformation of the elastic plate is supposed to be a critical point of an\nenergy functional which, in turn, depends on the electrostatic potential due to\nthe force exerted by the latter on the elastic plate. The energy functional is\nshown to have a minimizer giving the geometry of the device. Moreover, the\ncorresponding Euler-Lagrange equation is computed and the maximal regularity of\nthe electrostatic potential is established.\n