Abstract
In this paper we consider masonry bodies undergoing loads that can be represented by vector valued measures, and prove a result which is an appropriate formulation to this context of the static theorem of the limit analysis. As applications, we study the equilibrium of panels that are subjected both to distributed loads and concentrated forces, and determine equilibrated tensor valued measures. Then, by using an integration procedure for parametric measures, we explicitly calculate equilibrated stress fields that are represented by integrable functions. The obtained solutions are discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adams RA, Fournier JJF (2003) Sobolev spaces. 2nd edn. Academic Press, New York
Ambrosio L, Fusco N, Pallara D (2000) Functions of bounded variation and free discontinuity problems. Clarendon Press, Oxford
Anzellotti G (1985) A class of convex non-corecive functionals and masonry-like materials. Ann Inst Henri Poincaré 2:261–307
Del Piero G (1989) Constitutive equations and compatibility of the external loads for linear elastic masonry-like material materials. Meccanica 24:150–162
Del Piero G (1998) Limit analysis and no-tension materials. Int J Plasticity 14:259–271
Fonseca I, Leoni G (2007) Modern methods in the calculus of variations: L p spaces. Springer, New York
Giaquinta M, Giusti G (1985) Researches on the equilibrium of masonry structures. Arch Rational Mech Anal 88:359–392
Gurtin ME (1981) An introduction to continuum mechanics. Academic Press, Boston
Heymann J (1966) The stone skeleton. Int J Solids Struct 2:249–256
Lucchesi M, Padovani C, Pagni A (1994) A numerical method for solving equilibrium problems of masonry—like solids. Meccanica 24:175–193
Lucchesi M, Padovani C, Šilhavý M (2010) An energetic view on the limit analysis of normal bodies. Quart Appl Math 68:713–746
Lucchesi M, Padovani C, Zani N (1996) Masonry—like materials with bounded compressive strength. Int J Solids Struct 33:1961–1994
Lucchesi M, Šilhavý M, Zani N (2006) A new class of equilibrated stress fields for no-tension bodies. J Mech Mater Struct 1:503–539
Lucchesi M, Šilhavý M, Zani N (2007) A note on equilibrated stress fields for no-tension bodies under gravity. Quart Appl Math 65:605–624
Lucchesi M, Šilhavý M, Zani N (2008) Integration of measures and admissible stress fields for masonry bodies. J Mech Mater Struct 3:675–696
Lucchesi M, Šilhavý M, Zani N (2008) Equilibrated divergence measure stress tensor fields for heavy masonry bodies. Eur J Mech A Solids 28:223–232
Müller S (1999) Variational models for microstructure and phase transitions. In: Calculus of variations and geometric evolution problems (Cetraro, 1996) Lecture notes in Math. 1713 Hildebrandt S, Struwe M (ed.), Springer, Berlin, pp 85–210
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lucchesi, M., Šilhavý, M. & Zani, N. Integration of parametric measures and the statics of masonry panels. Ann. Solid Struct. Mech. 2, 33–44 (2011). https://doi.org/10.1007/s12356-011-0016-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12356-011-0016-6