Abstract
This Chapter is devoted to the application of unilateral models to the stress analysis of masonry structures. Some 2d applications of what we call the simplified models for masonry, are discussed and studied. Though the essentially unilateral behaviour of masonry is largely recognized, some prejudices still persist on the possibility of making the No-Tension (NT) assumption a practical model for designing engineers. The results here presented demonstrate that the unilateral model for masonry can be a useful tool for modeling real masonry structures. In the exposition the critical points are emphasized and strategies to handle them are suggested, both for the most primitive model (namely the Rigid NT material), and for the more accurate Normal Elastic NT and Masonry-Like (ML)materials. The first tool here introduced for applying the No-Tension model to structures is the systematic use of singular stress and strain fields. Next a number of closed form solutions for NENT and ML materials is discussed. Finally a numerical approach based on descent is proposed for handling the zero-energy modes typical of unilateral materials. Some numerical solutions and comparisons with analytical solutions and test results are also presented.
This Chapter is dedicated to Giovanni Castellano who inspired most of my work on masonry since my early steps.
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Bibliography
Dassault Systemes Abaqus, ver. 6.12 http://www.3ds.com/fileadmin/PRODUCTS/SIMULIA
G. Alfano, L. Rosati and N. Valoroso. A numerical strategy for finite element analysis of no-tension materials. Int. J. Numer. Methods Eng., 48 (3): 317–350, 2000.
L. Ambrosio, N. Fusco and D. Pallara . Functions of bounded variation and free discontinuity problems, Clarendon Press. 2000.
M. Angelillo and A. Fortunato. Compatibility of loads and distortions for unilateral materials. In preparation.
M. Angelillo and L. Giliberti. Statica delle strutture murarie. Giornale del genio Civile, 1988 (in Italian).
M. Angelillo and R.S. Olivito. Experimental analysis of masonry walls loaded horizontally in plane. Masonry International, 8 (3):91–100, 1995.
M. Angelillo and F. Rosso. On statically admissible stress fields for a plane masonry-like structure. Quarterly Of Applied Mathematics, 53 (4):731–751, 1995.
M. Angelillo, L. Cardamone, and A. Fortunato. A numerical model for masonry-like structures. Journal of Mechanics of Materials and Structures, 5:583–615, 2010.
M. Angelillo, E. Babilio, and A. Fortunato. Singular stress fields for masonry-like vaults. Continuum Mechanics And Thermodynamics, 2012.
M. Angelillo, A. Fortunato, M. Lippiello, and A. Montanino. Singular stress fields and the equilibrium of masonry walls. Meccanica, under revision, 2013.
A. Benedetti and E. Steli. Analytical models for shear-displacement curves of unreinforced and frp reinforced masonry panels. Constr. Build. Mater., 22 (3):175–185, 2008.
E. Benvenuto. An Introduction on the History of Structural Mechanics Part II: Vaulted Structures and Elastic Systems, Springer-Verlag. Springer Verlag, 1991.
G. Dal Maso, A. De Simone, and M.G. Mora. Quasistatic evolution problems for linearly elastic perfectly plastic materials. Arch. Rat. Mech. Anal., 2004.
E. De Giorgi. Congetture riguardanti alcuni problemi di evoluzione. Duke Math. J., 81(2):255–268, 1996.
G. Del Piero. Constitutive equation and compatibility of the external loads for linear elastic masonry–like materials. Meccanica, 24:150–162, 1989.
G. Del Piero. Limit analysis and no–tension materials. Int. J. Plasticity, 14:259–271, 1998.
F. Derand. L’architecture des voutes, Cramoisy. 1643.
C. L. Dym and I. H. Shames. Solid Mechanics: a variational approach, Mc Graw Hill. 1973.
M. Epstein. On the wrinkling of anisotropic elastic membranes. J. Elast., 55:99–108, 1999.
Eucentre. Prove murature. 2010. URL http://www.eucentre.it/provemurature.
A. Fortunato. Elastic solutions for masonry-like panels. J. Elas., 98:87–110, 2010.
M. Giaquinta and E. Giusti. Researches on the equilibrium of masonry structures. Arch. Rational Mech. Analysis, 88:359–392, 1985. ISSN 0950-2289.
E. M. Gurtin. The linear theory of elasticity, in Handbuch der Physik, band VIa/2, Springer-Verlag. 1972.
J. Heyman. The stone skeleton: structural engineering of masonry architecture. Cambridge University Press, 1995.
S. Huerta. Arcos, bovedas y cupulas. geometria y equilibrio en el calculo tradicional de estructuras de fabrica. Report: Instituto Juan de Herrera, 2004 (in Spanish).
S. Huerta. The analysis of masonry architecture: a historical approach. Arch. Sc. Review, 51(4):297–328, 2008.
C. T. Kelley. Iterative Methods for Optimization”, Frontiers in Applied Mathematics 18, SIAM. 1999.
E. Kreyszig. Introductory Functional Analysis with Applications, John Wiley. 1989.
C. Padovani M. Lucchesi and N. Zani. Masonry-like solids with bounded compressive stress. Int. J. Solids Struct., 33 (14):1961–1964, 1996.
M. Šilhavý, M. Lucchesi and N. Zani. Singular equilibrated stress fields for no-tension panels. In Lecture Notes in Applied and Computational Mechanics, 23, Springer, pages 255–265, 2005.
G. Pasquinelli M. Lucchesi, C. Padovani and N. Zani. Masonry constructions: mechanical models and numerical applications, Lecture Notes in Applied and Computational Mechanics 39, Springer. 2008.
E. H. Mansfield. Tension field theory. In Proc. 12th Int. Cong. App. Mech., M. Hetenyi and W. G. Vincenti (eds.), Springer, 1969.
E. H. Mansfield. The bending and stretching of plates, Cambridge University Press. 1989.
E. Mery. Memoire sur l’equilibre des voutes en berceau. Annales des pontes et chausees, 1 (2):50–57, 1840.
A. Mielke and M. Ortiz. A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. ESAIM Control Optim. Calc. Var., 14 (3):494–516, 2008.
M. Ortiz and J. C. Simo. An analysis of a new class of integration algorithms for elastoplastic constitutive relations. Int. J. Numer. Methods Eng., 23 (3):353–366, 1986.
D. J. Steigmann. Tension–field theory. Proc. R. Soc. Lond. A, 429:141–173, 1990.
R. Temam and G. Strang. Functions of bounded deformation. Arch. Rat. Mech. Anal., 75 (1):57–73, 1994. ISSN 1980.
S. Timoshenko and J. N. Goodier. Theory of elasticity, Mc Graw Hill. 1951.
Y. W. Wong and S. Pellegrino. Wrinkled membranes ii: analytical models. J. Mech. Mater. Struct., 1:27–60, 2006.
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Angelillo, M. (2014). Practical applications of unilateral models to Masonry Equilibrium. In: Angelillo, M. (eds) Mechanics of Masonry Structures. CISM International Centre for Mechanical Sciences, vol 551. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1774-3_4
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DOI: https://doi.org/10.1007/978-3-7091-1774-3_4
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