NDLI: The Wave Finite Element Method Applied to a One-Dimensional Linear Elastodynamic Problem With Unilateral Constraints

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Yoong, Carlos Thorin, Anders Legrand, Mathias
Copyright Year	2015
Abstract	The Wave Finite Element Method (WFEM) is implemented to accurately capture travelling waves propagating at a finite speed within a bouncing rod system and induced by unilateral contact collisions with a rigid foundation; friction is not accounted for. As opposed to the traditional Finite Element Method (FEM) within a time-stepping framework, potential discontinuous deformation, stress and velocity wave fronts are accurately described, which is critical for the problem of interest. A one-dimensional benchmark with an analytical solution is investigated. The WFEM is compared to two time-stepping solution methods formulated on a FEM semi-discretization in space: (1) an explicit technique involving Lagrange multipliers and (2) a non-smooth approach implemented in the Siconos package. Attention is paid to the Gibb’s phenomenon generated during and after contact occurrences together with the time evolution of the total energy of the system. It is numerically found that the WFEM outperforms the FEM and Siconos solution methods because it does not induce any spurious oscillations or dispersion and diffusion of the shock wave. Furthermore, energy is not dissipated over time. More importantly, the WFEM does not require any impact law to close the system of governing equations.
Sponsorship	Design Engineering Division Computers and Information in Engineering Division
File Format	PDF
ISBN	9780791857168
DOI	10.1115/DETC2015-46919
Volume Number	Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
Conference Proceedings	ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
Language	English
Publisher Date	2015-08-02
Publisher Place	Boston, Massachusetts, USA
Access Restriction	Subscribed
Subject Keyword	Shock waves Collisions (physics) Deformation Friction Oscillations Traveling waves Finite element methods Waves Diffusion (physics) Stress
Content Type	Text
Resource Type	Article

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