A novel Lower Bound Limit Analysis model with hexahedron elements for the failure analysis of laboratory and thin infill masonry walls in two-way bending

Abstract

A novel Lower Bound (LB) Limit Analysis (LA) Finite Element (FE) model for the study at failure of laboratory and thin infill masonry walls in two-way bending is presented. In the model, a masonry plate is discretized into infinitely resistant hexahedrons and quadrilateral interfaces where all plastic dissipation occurs. Three internal static variables act on interfaces, namely bending moment, out-of-plane Kirchhoff shear and torque. Equilibrium is imposed on hexahedrons, whereas admissibility is enforced exclusively on interfaces between adjoining elements. The admissibility of the internal actions on masonry interfaces is imposed with a strength domain obtained by means of an already existing LB homogenization technique where joints are reduced to interfaces. The resultant Linear Programming (LP) problem - which allows to estimate collapse loads and distribution of internal actions at collapse - is characterized by a number of variables and constraints relatively limited, which requires little computational burden to be solved through standard interior point LP software. Failure mechanisms are obtained solving the dual LP problem. The procedure is validated against two existing experimental datasets of walls in two-way bending, namely three series of panels with and without perforations tested at collapse at the University of Adelaide Australia and four series of solid and perforated panels tested at the University of Plymouth UK. Comparing the results in terms of collapse loads, active failure mechanisms and distribution of internal actions with both experimental evidence and previously presented numerical models, excellent results are found, an outcome showing the reliability of the procedure proposed.