Finite-Element Analysis of Polyhedra under Point and Line Forces in Second-Strain Gradient Elasticity

AbstractIn 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 poly...

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Bibliographic Details
Published in:Journal of engineering mechanics 2017-02, Vol.143 (2)
Main Authors: Reiher, Jörg Christian, Giorgio, Ivan, Bertram, Albrecht
Format: Article
Language:English
Subjects:
Deformation
Elasticity
Finite element method
Mathematical analysis
Polyhedrons
Singularities
Technical Papers
Variational principles
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Summary:AbstractIn 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.
ISSN:0733-9399
1943-7889
DOI:10.1061/(ASCE)EM.1943-7889.0001184