Planas, J. and Romero, I. and Sancho, J. M. (2012) B free. Computer Methods in Applied Mechanics and Engineering, 217-220 . pp. 226-235. ISSN 0045-7825 http://resolver.caltech.edu/CaltechAUTHORS:20120516-085956246
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The linearized strain matrix and the matrix of material elasticities — commonly referred to as the B and D matrices — have been traditionally presented as convenient operators that enable the matrix formulation and finite element implementation of field theories in continuum mechanics. In this article it is argued that the opposite is true: neither matrix is necessary, they both complicate the finite element formulation of field theories and, moreover, they do not necessarily lead to the most efficient implementations. Examples are provided to back this statement in the context of infinitesimal and finite strain solid mechanics. For these problems, the finite element equilibrium equations and their linearization are fully derived using a formulation which is simpler, more compact, often computationally cheaper ... and free of both B and D matrices.
|Additional Information:||© 2012 Elsevier B.V. Received 18 July 2011. Revised 24 December 2011. Accepted 29 January 2012. Available online 6 February 2012. The authors acknowledge partial financial support from the Spanish Ministry of Science and Innovation under grants BIA2010-18864 (J. Planas and J.M. Sancho) and DPI2009-14305- C02-02 (I. Romero). In addition, I. Romero would like to thank the Caja Madrid Foundation for a mobility grant funding his stay at Caltech. The authors thank the reviewers, who have expressed alternative points of view to the one supported heretofore, and have helped to express the comparison between the classical and intrinsic approaches in a fairer manner.|
|Subject Keywords:||Finite elements; Programming; Voigt notation; Solid mechanics|
|Official Citation:||J. Planas, I. Romero, J.M. Sancho, B free, Computer Methods in Applied Mechanics and Engineering, Volumes 217–220, 1 April 2012, Pages 226-235, ISSN 0045-7825, 10.1016/j.cma.2012.01.019.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||16 May 2012 19:25|
|Last Modified:||16 May 2012 19:25|
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