Analysis of masonry vaults as a topology optimization problem

An innovative approach is proposed to analyze 3D masonry vaults, assuming masonry to behave as a linear elastic no-tension material. Masonry is replaced by a suitable equivalent orthotropic material with spatially varying elastic properties and negligible stiffness 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, minimizing the potential energy so as to achieve a purely compressive state of stress. The algorithm is embedded within a numerical procedure that performs a non-incremental analysis under given loads. The collapse load of masonry structural elements can also be predicted running a sequence of independent analyses. The capabilities of the approach in predicting the crack pattern in typical masonry vaults are also shown.