RT Journal Article
T1 Solving 2D Linear Isotropic Elastodynamics by Means of Scalar Potentials: A New Challenge for Finite Elements
A1 Albella Martínez, Jorge
A1 Imperiale, Sebastien
A1 Joly, Patrick
A1 Rodríguez García, Jerónimo
K1 Elastic wave propagation
K1 Helmholtz decomposition
K1 Potentials
K1 Stability of the evolution problem
AB In this work we present a method for the computation of numerical solutions of 2D homogeneous isotropic elastodynamics equations by solving scalar wave equations. These equations act on the potentials of a Helmholtz decomposition of the displacement field and are decoupled inside the propagation domain. We detail how these equations are coupled at the boundary depending on the nature of the boundary condition satisfied by the displacement field. After presenting the case of rigid boundary conditions, that presents no specific difficulty, we tackle the challenging case of free surface boundary conditions that presents severe stability issues if a straightforward approach is used. We introduce an adequate functional framework as well as a time domain mixed formulation to circumvent these issues. Numerical results confirm the stability of the proposed approach.
PB Springer
SN 0885-7474
YR 2018
FD 2018
LK http://hdl.handle.net/10347/32706
UL http://hdl.handle.net/10347/32706
LA eng
NO Albella Martínez, J., Imperiale, S., Joly, P., & Rodríguez, J. (2018). Solving 2D Linear Isotropic Elastodynamics by Means of Scalar Potentials: A New Challenge for Finite Elements. Journal of Scientific Computing, 77(3), 1832-1873. https://doi.org/10.1007/S10915-018-0768-9
NO This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10915-018-0768-9
NO The research of the first and fourth authors was partially funded by FEDER and the Spanish Ministry of Science and Innovation through Grants MTM2013-43745-R and MTM2017-86459-R and by Xunta de Galicia through grant ED431C 2017/60.
DS Minerva
RD 30 abr 2026