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Group‐theoretic exploitations of symmetry in computational solid and structural mechanics
Author(s) -
Zingoni A.
Publication year - 2009
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.2576
Subject(s) - group (periodic table) , group theory , symmetry group , symmetry (geometry) , computational mechanics , structural mechanics , finite element method , computer science , development (topology) , mathematics , calculus (dental) , engineering , structural engineering , geometry , physics , mathematical analysis , quantum mechanics , medicine , dentistry
The use of group theory in simplifying the study of problems involving symmetry is a well‐established approach in various branches of physics and chemistry, and major applications in these areas date back more than 70 years. Within the engineering disciplines, the search for more systematic and more efficient strategies for exploiting symmetry in the computational problems of solid and structural mechanics has led to the development of group‐theoretic methods over the past 40 years. This paper reviews the advances made in the application of group theory in areas such as bifurcation analysis, vibration analysis and finite element analysis, and summarizes the various implementation procedures currently available. Illustrative examples of typical solution procedures are drawn from recent work of the author. It is shown how the group‐theoretic approach, through the characteristic vector‐space decomposition, enables considerable simplifications and reductions in computational effort to be achieved. In many cases, group‐theoretic considerations also allow valuable insights on the behaviour or properties of a system to be gained, before any actual calculations are carried out. Copyright © 2009 John Wiley & Sons, Ltd.