Analysis of masonry vaults as a topology optimization problem

Abstract

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.