NURBS-based kinematic limit analysis of FRP-reinforced masonry walls with out-of-plane loading

A three-dimensional (3D) general upper-bound limit analysis procedure for the determination of the collapse load of out-of-plane loaded masonry walls with Fiber Reinforced Polymer (FRP) reinforcement strips is presented. The geometry of a given FRP reinforced masonry wall of arbitrary shape is represented by its Non-Uniform Rational B-Spline (NURBS) description in the three-dimensional Euclidean space. The NURBS parameter space is partitioned by means of a number of possible fracture lines and the original reinforced wall geometry is subdivided into an initial set of rigid elements, accordingly. An upper-bound limit analysis formulation, accounting for the main characteristics of both masonry material and FRP reinforcement by means of homogenization techniques, is deduced. Internal dissipation is allowed along element edges only and the effect of vertical loads and membrane stresses is considered as well. Numerical experiments show that a good estimate of the load bearing capacity is obtained provided that the initial arrangement of yield lines is adjusted by means of a suitable Genetic Algorithm (GA).