Skip to Main content Skip to Navigation
Journal articles

Numerical Analysis of a Method for Solving 2D Linear Isotropic Elastodynamics with Free Boundary Condition using Potentials and Finite Elements

Jorge Albella Martínez 1 Sébastien Imperiale 2, 3 Patrick Joly 4 Jerónimo Rodríguez 1
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
LMS - Laboratoire de mécanique des solides, Inria Saclay - Ile de France
4 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : When solving 2D linear elastodynamic equations in a homogeneous isotropic media, a Helmholtz decomposition of the displacement field decouples the equations into two scalar wave equations that only interact at the boundary. It is then natural to look for numerical schemes that independently solve the scalar equations and couple the solutions at the boundary. The case of rigid boundary condition was treated In [3, 2]. However in [4] the case of free surface boundary condition was proven to be unstable if a straight- forward approach is used. Then an adequate functional framework as well as a time domain mixed formulation to circumvent these issues was presented. In this work we first review the formulation presented in [4] and propose a subsequent discretised formulation. We provide the complete stability analysis of the corresponding numerical scheme. Numerical results that illustrate the theory are also shown.
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download

https://hal.inria.fr/hal-02345808
Contributor : Sébastien Imperiale Connect in order to contact the contributor
Submitted on : Monday, November 4, 2019 - 4:21:19 PM
Last modification on : Friday, October 8, 2021 - 2:46:04 PM
Long-term archiving on: : Wednesday, February 5, 2020 - 11:21:06 PM

File

ElastoPotential.pdf
Files produced by the author(s)

Identifiers

Citation

Jorge Albella Martínez, Sébastien Imperiale, Patrick Joly, Jerónimo Rodríguez. Numerical Analysis of a Method for Solving 2D Linear Isotropic Elastodynamics with Free Boundary Condition using Potentials and Finite Elements. Mathematics of Computation, American Mathematical Society, In press, ⟨10.1007/s10915-018-0768-9⟩. ⟨hal-02345808⟩

Share

Metrics

Record views

246

Files downloads

830