Vol. 1, No. 3, 2006

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A new class of equilibrated stress fields for no-tension bodies

Massimiliano Lucchesi, Miroslav Šilhavý and Nicola Zani

Vol. 1 (2006), No. 3, 503–539

We study the equilibrium problem for bodies made of a no-tension material, subjected to distributed or concentrated loads on their boundary. Admissible and equilibrated stress fields are interpreted as tensor-valued measures with distributional divergence represented by a vector-valued measure, as outlined in two 2005 papers by Lucchesi et al. Such stress fields are generalizations of ordinary functions, which allows us to consider stress concentrations on surfaces and lines. The general framework for this approach is presented first and then illustrated on examples of two-dimensional panels under different loads. In the general framework we determine weak divergences and the surface tractions of several stress field measures via the (surface) divergence theorem. Combinations of these stress fields are shown to give the solutions for the panels, which we assume to be clamped at the bottom, and subjected to various loads on the top and possibly on the sides of the panel. The shapes of the singular lines and stresses are explicitly determined in these cases.

masonry panels, equilibrium, divergence measures
Received: 4 December 2005
Accepted: 7 February 2005
Published: 1 July 2006
Massimiliano Lucchesi
Dipartimento di Costruzioni
Università di Firenze
Piazza Brunelleschi 6
50121 Florence
Miroslav Šilhavý
Dipartimento di Matematica
Università di Pisa
Largo Bruno Pontecorvo 5
56127 Pisa
Mathematical Institute of the AV ČR
Žitna 25
115 67, Prague 1
Czech Republic
Nicola Zani
Dipartimento di Costruzioni
Università di Firenze
Piazza Brunelleschi 6
50121 Florence