Compatible strain-based upper bound limit analysis model for masonry walls under in-plane loading
Nicola Grillanda, Vincenzo Mallardo
Abstract
We present a novel numerical model for the upper bound limit analysis of in-plane loaded masonry structures . The construction is represented as a continuum model composed of planar elements whose kinematics combines rigid body velocities and plastic strain rates . The global velocity field remains continuous and crack configurations are described via plastic strain rates . Homogenization ensures the compatibility between the continuum’s plastic strain rate field and the kinematics of the heterogeneous material : idealizing masonry as an assembly of rigid bricks and frictional zero-thickness joints , the associative flow rule is expressed through homogenized kinematic relations defining a domain of compatible plastic strain rates. The derived limit analysis problem is written as a linear programming problem , yielding an upper bound of the load-bearing capacity along with rigid body velocities and a compatible plastic strain rate field. Finally, a local mesh refinement strategy governed by the L 2 -norm of plastic strain rates optimizes the mechanism representation. The presented formulation offers advantages over the conventional homogenized limit analysis methods by defining a failure domain via strain rates, rather than stress, providing a more compact and computationally efficient numerical approach. Its efficacy is proven through numerical examples and comparisons with well-established analytical and numerical models.