Nowadays, there is a raising interest in the development of fast and robust tools to detect the consequences of settlements or loading changes in unreinforced masonry buildings, since they constitute a large part of world architectural heritage. Current tools, based on Finite Element Method or on Discrete Element Method are computationally cumbersome, from one side due to difficulties in dealing with unilateral materials, and on the other side, due to the need of formulating the problem as an explicit dynamics problem. The methods proposed here are based on the minimization problem of two different functionals, the Total Potential Energy, and the Total Complementary Energy, which allow to detect the stress and strain distribution developed under given load and given boundary settlements, through a minimization problem, which require a significantly lower computational cost and no material parameters, especially when rigidity assumption of the material is done. After illustrating the main characteristics of the two methods, they are applied to a case study, and the results are suitably described and discussed.
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