Vol. 3, No. 4, 2008

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Integration of measures and admissible stress fields for masonry bodies

Massimiliano Lucchesi, Miroslav Šilhavý and Nicola Zani

Vol. 3 (2008), No. 4, 675–696

We study the compatibility of loads for bodies made of a no-tension (masonry) material. Loads are defined as weakly compatible if they can be equilibrated by an admissible stress field represented by a tensor valued measure, and strongly compatible if they can be equilibrated by a square integrable function. In the present study, we examine situations in which weak compatibility implies strong compatibility. For families of loads that depend on a parameter and the families of measures that equilibrate these loads, we find that, under some conditions, averaging with respect to the parameter leads to a measure with a square integrable density that equilibrates the loads. We illustrate the procedure on two-dimensional rectangular panels free from gravity, clamped at the bottom, and subjected to various loads on the free part of the boundary.

masonry bodies, compatibility of loads, stresses represented by measures
Received: 31 May 2007
Accepted: 28 November 2007
Published: 1 June 2008
Massimiliano Lucchesi
Dipartimento di Costruzioni
Università di Firenze
Piazza Brunelleschi 6
50121 Firenze
Miroslav Šilhavý
Mathematical Institute of the AV ČR
Zitná 25
115 67, Prague 1
Czech Republic
Nicola Zani
Dipartimento di Costruzioni
Università di Firenze
Piazza Brunelleschi 6
50121 Firenze