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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 16
CIVIL ENGINEERING COMPUTATIONS: TOOLS AND TECHNIQUES Edited by: B.H.V. Topping
Chapter 10
Modelling Masonry with Limit Analysis Finite Elements: Review, Applications and New Directions G. Milani^{1} and P.B. Lourenço^{2}
^{1}Department of Civil Engineering, University of Ferrara, Italy G. Milani, P.B. Lourenço, "Modelling Masonry with Limit Analysis Finite Elements: Review, Applications and New Directions", in B.H.V. Topping, (Editor), "Civil Engineering Computations: Tools and Techniques", SaxeCoburg Publications, Stirlingshire, UK, Chapter 10, pp 217242, 2007. doi:10.4203/csets.16.10
Keywords: masonry, limit analysis, constitutive behaviour, homogenization techniques.
Summary
A homogenization limit analysis model based on a plate and shell upper bound FE formulation is presented. In the model, the elementary cell is subdivided along its thickness into several layers. For each layer, fully equilibrated stress fields are assumed, adopting polynomial expressions for the stress tensor components in a finite number of subdomains. The continuity of the stress vector on the interfaces between adjacent subdomains and suitable antiperiodicity conditions on the boundary surface are further imposed. In this way, linearized homogenized surfaces in six dimensions (polytopes) for masonry in and outofplane loaded are obtained. Such surfaces are then implemented in a FE limit analysis code for the analysis at collapse of entire threedimensional structures and meaningful examples of technical relevance are discussed in detail.
The micromechanical model presented competes favourably with more traditional approaches, such as for instance full threedimensional heterogeneous techniques and "at hand" calculations based on the assumption of zero resistance of masonry in tension. In fact, full threedimensional analyses performed on entire buildings by means of the homogenization model presented, require a reduced computational cost (less than 150 seconds for a single optimization reported in Section 4), do not require an apriori evaluation of the collapse mechanisms and can take into account important features of masonry at failure. Furthermore, limit analysis is able to give important information at failure, such as failure mechanisms, collapse loads, stress distribution, plastic dissipation zones, etc. Therefore, the model presented results in a valuable tool for practitioners involved in advanced analyses of full threedimensional masonry structures subjected to seismic actions. The limited computational effort of the optimization problems obtained in this framework allows one to tackle interesting engineering problems, such as for instance the evaluation of collapse loads stochastic distribution of masonry structures when mortar mechanical properties (i.e. input parameters) are assumed as random variables. The combination of homogenization, limit analysis and response surface approximation allows one to obtain reliable predictions of failure loads distribution when metamodels are built starting from few points sampled randomly and making use of both traditional Monte Carlo approaches and Latin Hypercube sampling. In this way, a reliable estimation of output collapse loads distribution can be obtained avoiding performance of expensive Monte Carlo simulations with several points. purchase the fulltext of this chapter (price £20)
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