English
Related papers

Related papers: A variational approach to a stationary free bounda…

200 papers

In this paper we consider and generalize a model, recently proposed and analytically investigated in its quasi-stationary approximation by the authors, for visco-elasticity with large deformations and conditional compatibility, where the…

Analysis of PDEs · Mathematics 2024-03-14 Abramo Agosti , Michel Fremond

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…

Analysis of PDEs · Mathematics 2017-03-14 M. Campo , J. R. Fernández , Á. Rodríguez-Arós , J. M. Rodríguez

We report on low temperature measurements performed on micro-electro-mechanical systems (MEMS) driven deeply into the non-linear regime. The materials are kept in their elastic domain, while the observed non-linearity is purely of…

Mesoscale and Nanoscale Physics · Physics 2015-06-18 Eddy Collin , Yuriy M. Bunkov , Henri Godfrin

We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…

Numerical Analysis · Mathematics 2022-12-21 Alvin Chen , N. Sukumar

Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…

Optimization and Control · Mathematics 2025-11-07 Siva Prasad Chakri Dhanakoti

In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…

Analysis of PDEs · Mathematics 2021-04-13 Ourania Drosinou , Nikos I. Kavallaris , Christos V. Nikolopoulos

Motivated by active wing flutter suppression in high-Mach-number flight, this paper presents a rapid boundary stabilization strategy for a two-dimensional PDE-modeled elastic plate with in-domain instabilities, where the exponential…

Systems and Control · Electrical Eng. & Systems 2026-03-03 Xingzhi Huang , Ji Wang

The occurrence of a finite time singularity is shown for a free boundary problem modeling microelectromechanical systems (MEMS) when the applied voltage exceeds some value. The model involves a singular nonlocal reaction term and a…

Analysis of PDEs · Mathematics 2014-02-03 Joachim Escher , Philippe Laurencot , Christoph Walker

A dual hybrid Virtual Element scheme for plane linear elastic problems is presented and analysed. In particular, stability and convergence results have been established. The method, which is first order convergent, has been numerically…

Numerical Analysis · Mathematics 2019-02-14 Edoardo Artioli , Stefano de Miranda , Carlo Lovadina , Luca Patruno

We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic…

Dynamical Systems · Mathematics 2021-12-01 Shirali Kadyrov , Ardak Kashkynbayev , Piotr Skrzypacz , Konstantinos Kaloudis , Anastasios Bountis

In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…

Computational Engineering, Finance, and Science · Computer Science 2025-11-19 Abhishek Arora , Caglar Oskay

Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be…

Numerical Analysis · Mathematics 2023-10-02 Gašper Vuga , Boštjan Mavrič , Božidar Šarler

We consider two models, a free boundary problem and a simplification thereof, which describe a soap film bridge subjected to an electrostatic force. For both models, we construct stationary solutions if the force is small, analyse their…

Analysis of PDEs · Mathematics 2024-09-30 Lina Sophie Schmitz

We present a mathematical and numerical framework for thin-film fluid flows over planar surfaces including dynamic contact angles. In particular, we provide algorithmic details and an implementation of higher-order spatial and temporal…

Numerical Analysis · Mathematics 2022-06-15 Dirk Peschka , Luca Heltai

A contact problem of the theory of electroelasticity for piecewise-homogeneous plate of piezo-electric material with infinite cut and elastic finite inclusion of variable bending rigidity is considered. By using methods of the theory of…

Mathematical Physics · Physics 2024-05-21 Nugzar Shavlakadze , Nana Odishelidze , Francisco Criado-Aldeanueva

A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…

Analysis of PDEs · Mathematics 2019-02-19 Leonard Kreutz , Paolo Piovano

A semilinear parabolic equation with constraint modeling the dynamics of a microelectromechanical system (MEMS) is studied. In contrast to the commonly used MEMS model, the well-known pull-in phenomenon occurring above a critical potential…

Analysis of PDEs · Mathematics 2017-07-13 Philippe Laurencot , Christoph Walker

We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic membranes proving the existence of equilibria and finding…

Analysis of PDEs · Mathematics 2024-06-28 Francesco Ballarin , Giulia Bevilacqua , Luca Lussardi , Alfredo Marzocchi

The problem of quasistatic and rate-independent evolution of elastic-plastic-brittle delamination at small strains is considered. Delamination processes for linear elastic bodies glued by an adhesive to each other or to a rigid outer…

Numerical Analysis · Mathematics 2012-12-12 C. G. Panagiotopoulos , V. Mantic , T. Roubicek

Based on the mathematical-physical model of pavement mechanics, a multilayer elastic system with interlayer friction conditions is constructed. Given the complex boundary conditions, the corresponding variational inequalities of the partial…

Numerical Analysis · Mathematics 2024-06-04 Zhizhuo Zhang , Xiaobing Nie , Jinde Cao