Closed-form expressions for the macroscopic flexural rigidity coefficients of periodic brickwork |
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| Affiliation: | 1. GRESPI/Thermomécanique, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Reims Cedex 2, France;2. Laboratoire d’Energétique Appliquée et de Pollution, Université Constantine 1, Constantine 25000, Algeria;3. Laboratoire de Mécanique, Physique et Modélisation Mathématique, Université de Médéa, 26000 Médéa, Algeria;4. Faculté des Hydrocarbures et Energies renouvelables et Sciences de la terre et de l’univers, Université Kasdi Merbah, 30000 Ouargla, Algeria;1. Mechanical Engineering Department, University of Larestan, Lar, Iran;2. Mechanical Engineering Department, Shiraz University, Shiraz, Iran;1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;3. Department of Mechanics, Shanghai University, Shanghai 200444, China;1. School of Physics and Electrical Information Science, Shangqiu Normal University, Shangqiu 476000, China;2. School of Aerospace, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | Approximate expressions for the macroscopic out-of-plane elastic coefficients of brick masonry with a regular pattern are derived in closed form using a homogenization approach for periodic media. Following an approach similar to the Method of Cells for fiber reinforced composites, a (piecewise-)differentiable expression depending on very a limited number of degrees of freedom and fulfilling suitable periodicity conditions is proposed for the microscopic transverse displacement field over any Representative Volume Element (RVE). Some of the equilibrium conditions at the interfaces between bricks and mortar joints are also fulfilled. By averaging the moment and curvature fields over the RVE, the macroscopic bending stiffness coefficients can be explicitly obtained. Using the FE solution of a masonry panel subjected to elementary load conditions as a benchmark, the proposed approach is found to accurately match the numerically obtained stiffness coefficients, for masonry elements of different geometry and different mechanical properties. In several instances, the proposed expressions agree with the numerical predictions better than other analytical expressions available in the literature. |
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| Keywords: | Masonry Homogenization Macroscopic stiffness Transverse loads Out-of-plane |
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