Finite Element Analysis of Masonry Vaults using a Three-dimensional No-Tension Approach

Assuming masonry to behave as a linear elastic no-tension material, an original approach is proposed to analyze three-dimensional masonry structural elements, with special attention to masonry vaults. Masonry is replaced by a suitable equivalent orthotropic material with spatially varying elastic properties. Using an interpolation typical of topology optimization, the stiffness of the equivalent material is given negligible values in any direction along which tensile stresses must be prevented. An energy-based algorithm is implemented to define the distribution and the orientation of the equivalent material for a given load, so as to obtain a purely compressive state of stress throughout the element. The collapse load of masonry structural elements can also be predicted running a sequence of independent analyses. The capabilities of the approach in predicting no-tension stress solutions in masonry vaults of different shape is shown.