On the Correspondence between 2D Force Networks and Polyhedral Stress Functions

We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a two-mesh technique for the prediction of the stress field associated with such systems. We generalize classical results concerned with smooth Airy stress functions t...

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Bibliographic Details
Published in:International journal of space structures 2014-09, Vol.29 (3), p.145-159
Main Authors: Fraternali, Fernando, Carpentieri, Gerardo
Format: Article
Language:English
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Summary:We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a two-mesh technique for the prediction of the stress field associated with such systems. We generalize classical results concerned with smooth Airy stress functions to polyhedral functions associated with arbitrary triangulations of a simply-connected domain. We also formulate a regularization technique that smoothly projects the stress function corresponding to an unstructured force network over a structured triangulation. The paper includes numerical examples dealing with a benchmark problem of plane elasticity, and the stress fields associated with truss models of a cantilever beam and an elliptical membrane.
ISSN:0956-0599
2059-8033
DOI:10.1260/0266-3511.29.3.145