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Modeling and numerical analysis of masonry structures
Author(s) -
Ainsworth Mark,
Mihai L. Angela
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20253
Subject(s) - piecewise , mathematics , variational inequality , unilateral contact , linear complementarity problem , polynomial , nonlinear system , masonry , mixed complementarity problem , mathematical analysis , finite element method , structural engineering , physics , quantum mechanics , engineering
We model masonry structures as elastodynamic systems assembled from a large number of elastic bodies (bricks or stone‐blocks) in unilateral, frictional contact. The problem is formulated as a quasi‐variational inequality and discretised using piecewise polynomial finite elements in conjunction with an energy consistent time integration scheme. At each time‐step, the quasi‐variational inequality is reformulated as a nonlinear complementarity problem. An iterative splitting of the contact problem into normal contact and frictional contact, together with a primal‐dual active‐set method is employed to calculate deformations and openings in the model structures. Numerical results are presented to illustrate the efficiency of the resulting approach in predicting the mechanical behaviour of a bidimensional arch‐ring made of bricks, deformed due to body forces and surface tractions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 798–816, 2007