We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a twomesh 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.
On the correspondence between 2D force networks and polyhedral stress functions
FRATERNALI, Fernando;CARPENTIERI, GERARDO
2014
Abstract
We formulate and discuss the relationship between polyhedral stress functions and internally self-equilibrated frameworks in 2D, and a twomesh 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
