Finite-Element Analysis of Polyhedra under Point and Line Forces in Second-Strain Gradient Elasticity
Publication: Journal of Engineering Mechanics
Volume 143, Issue 2
Abstract
In this paper, a finite-element implementation of linear second-strain gradient elasticity is introduced based on a Hellinger-Reissner variational principle in order to use standard finite-element methods. Displacement boundary conditions are applied to one or more vertices of different polyhedrons. As a result, a smooth deformation around deformed vertices of the polyhedrons can be observed, in contrast to the appearance of singularities in the first-order theory, i.e., a Cauchy continuum, where strain singularities appear in such cases.
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Acknowledgments
The first author has been financially supported by Graduiertenkolleg 1554: Micro-Macro-Interactions in structured Media and Particle Systems of the DFG (German Science Foundation). Helpful comments and suggestions by Rainer Glüge are gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 2 • February 2017
Copyright
©2016 American Society of Civil Engineers.
History
Received: Apr 29, 2016
Accepted: Aug 24, 2016
Published online: Oct 28, 2016
Published in print: Feb 1, 2017
Discussion open until: Mar 28, 2017
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