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B free

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. https://resolver.caltech.edu/CaltechAUTHORS:20120516-085956246

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.cma.2012.01.019 DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/pii/S0045782512000308PublisherUNSPECIFIED
ORCID:
AuthorORCID
Romero, I.0000-0003-0364-6969
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.
Funders:
Funding AgencyGrant Number
Spanish Ministry of Science and InnovationBIA2010-18864
Spanish Ministry of Science and InnovationDPI2009-14305-C02-02
Caja Madrid FoundationUNSPECIFIED
Subject Keywords:Finite elements; Programming; Voigt notation; Solid mechanics
Record Number:CaltechAUTHORS:20120516-085956246
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120516-085956246
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.
ID Code:31495
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 May 2012 19:25
Last Modified:09 Mar 2020 13:19

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