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A model for a MEMS device, consisting of a fixed bottom plate and an elastic plate, is studied. It was derived in a previous work as a reinforced limit when the thickness of the insulating layer covering the bottom plate tends to zero. This…

Analysis of PDEs · Mathematics 2020-04-01 Philippe Laurençot , Katerina Nik , Christoph Walker

A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…

Analysis of PDEs · Mathematics 2020-06-24 Shokhrukh Yu. Kholmatov , Paolo Piovano

Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…

Analysis of PDEs · Mathematics 2019-02-20 Friedrich Lippoth , Mark A. Peletier , Georg Prokert

The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…

Numerical Analysis · Mathematics 2021-12-14 Shashwat Sharma , Piero Triverio

The dynamical and stationary behaviors of a fourth-order equation in the unit ball with clamped boundary conditions and a singular reaction term are investigated. The equation arises in the modeling of microelectromechanical systems (MEMS)…

Analysis of PDEs · Mathematics 2017-05-17 Philippe Laurencot , Christoph Walker

Electrified liquids are well known to be prone to a variety of interfacial instabilities that result in the onset of apparent interfacial singularities and liquid fragmentation. In the case of electrically conducting liquids, one of the…

Analysis of PDEs · Mathematics 2016-07-19 Cyrill B. Muratov , Matteo Novaga

We describe a variational approach to solving optimal stopping problems for diffusion processes, as an alternative to the traditional approach based on the solution of the free-boundary problem. We study smooth pasting conditions from a…

Probability · Mathematics 2015-08-06 V. I. Arkin , A. D. Slastnikov

We study the local well-posedness of the solution to a coupled nonlinear elliptic-parabolic system which models electrical discharge in a Micro-Electro-Mechanical System (MEMS). A simple MEMS capacitor device contains two plates acting as…

Analysis of PDEs · Mathematics 2026-02-26 Heiko Gimperlein , Runan He , Andrew A. Lacey

This work focuses on model preparation for electrostatic simulations of CAD designs to realize a rapid virtual prototyping concept. We present a boundary element method (BEM) allowing discontinuous fields between surfaces. The corresponding…

Computational Engineering, Finance, and Science · Computer Science 2024-12-13 Benjamin Marussig , Thomas Rüberg , Jürgen Zechner , Lars Kielhorn , Thomas-Peter Fries

Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…

Computational Engineering, Finance, and Science · Computer Science 2023-06-27 Ghina Jezdan , Sanjay Govindjee , Klaus Hackl

Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary…

Materials Science · Physics 2014-12-02 Oliviero Andreussi , Nicola Marzari

In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…

Numerical Analysis · Mathematics 2017-01-12 Tingsong Xiang , Sundararajan Natarajan , Hou Man , Chongmin Song , Wei Gao

We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…

Classical Physics · Physics 2023-12-21 Basant Lal Sharma , Prashant Saxena

The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a…

Analysis of PDEs · Mathematics 2025-03-24 Eleonora Maggiorelli , Filippo Riva , Edoardo Giovanni Tolotti

Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures with cross-sections of the order of microns ($\mu m$) and lengths of the order of tens or hundreds of microns. These structures are often plates or array of…

Computational Physics · Physics 2007-05-23 N. Majumdar , S. Mukhopadhyay

We present the construction and application of a first order stabilization-free virtual element method to problems in plane elasticity. Well-posedness and error estimates of the discrete problem are established. The method is assessed on a…

Numerical Analysis · Mathematics 2023-03-17 Alvin Chen , N. Sukumar

The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior.…

Numerical Analysis · Mathematics 2024-04-17 Raj Narayan Dhara , Krzysztof E. Rutkowski , Katarzyna Szulc

A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…

Numerical Analysis · Mathematics 2025-03-05 Jinye Shen , Heng Dai , Weizhang Huang

This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…

Computational Engineering, Finance, and Science · Computer Science 2023-05-23 Juan F. Giraldo , Victor M. Calo

This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize…

Dynamical Systems · Mathematics 2024-01-24 Charles Naudet , Alan E. Lindsay