Premium
A variationally consistent mesh adaptation method for triangular elements in explicit Lagrangian dynamics
Author(s) -
Lahiri Sudeep K.,
Bonet Javier,
Peraire Jaume
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2784
Subject(s) - polygon mesh , mathematics , projection (relational algebra) , lagrangian , angular momentum , momentum (technical analysis) , field (mathematics) , adaptation (eye) , projection method , mathematical optimization , computer science , algorithm , classical mechanics , dykstra's projection algorithm , geometry , physics , pure mathematics , finance , optics , economics
In this paper a variational formulation for mesh adaptation procedures, involving local mesh changes for triangular meshes, is presented. Such local adaptive changes are very well suited for explicit methods as they do not involve significant computational expense. They also greatly simplify the projection of field variables from the old to the new meshes. Crucially, the variational nature of the formulation used to derive the equilibrium equations at steps where adaptation takes place ensures that conservation of linear and angular momentum is obtained ( Int. J. Numer. Meth. Engng 2000; 49 :1295–1325). Several examples in 2‐D showing the application of the proposed adaptive algorithms are used to demonstrate the validity of the methodology proposed. Copyright © 2009 John Wiley & Sons, Ltd.