Integration within Polygonal Finite Elements
Publication: Journal of Aerospace Engineering
Volume 16, Issue 1
Abstract
Engineering mechanics formulations of aerospace industry problems overwhelmingly rely upon spatial averaging techniques. Crucial applications in the area of dynamic response analysis and stochastic estimation of material degradation can be cited as important cases. Integration procedures on finite domains underlie physically acceptable averaging processes. Unlike one-dimensional cases, integrals within arbitrary areas and volumes cannot be approximated by a Gaussian form of numerical quadrature. Here the divergence theorem is applied once and twice, respectively, for polygonal and polyhedral integration domains, to construct integrals on boundary wireframes. The sum of Gaussian quadrature values on linear segments of the wireframe yields the final result of numerical integration on a finite element.
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Published In
Journal of Aerospace Engineering
Volume 16 • Issue 1 • January 2003
Pages: 9 - 18
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Feb 22, 2002
Accepted: Jun 10, 2002
Published online: Dec 13, 2002
Published in print: Jan 2003
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