Rotations in computational solid mechanics

S. N. Atluri, A. Cazzani

Research output: Contribution to journalArticlepeer-review

104 Scopus citations

Abstract

A survey of variational principles, which form the basis for computational methods in both continuum mechanics and multi-rigid body dynamics is presented: all of them have the distinguishing feature of making an explicit use of the finite rotation tensor. A coherent unified treatment is therefore given, ranging from finite elasticity to incremental updated Lagrangean formulations that are suitable for accomodating mechanical nonlinearities of an almost general type, to time-finite elements for dynamic analyses. Selected numerical examples are provided to show the performances of computational techniques relying on these formulations. Throughout the paper, an attempt is made to keep the mathematical abstraction to a minimum, and to retain conceptual clarity at the expense of brevity. It is hoped that the article is self-contained and easily readable by nonspecialists. While a part of the article rediscusses some previously published work, many parts of it deal with new results, documented here for the first time.

Original languageEnglish
Pages (from-to)49-138
Number of pages90
JournalArchives of Computational Methods in Engineering
Volume2
Issue number1
DOIs
StatePublished - Mar 1995

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