Search

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture . This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes . For elastic fracture in the X-VEM, the standard virtual element space is augmented by additional basis functions that are constructed by multiplying standard virtual basis functions by suitable enrichment fields, such as asymptotic mixed-mode crack-tip solutions. The design of the X-VEM requires an extended projector that maps functions lying in the extended virtual element space onto a set spanned by linear polynomials and the enrichment fields. An efficient scheme to compute the mixed-mode stress intensity factors using the domain form of the interaction integral is described. The formulation permits integration of weakly singular functions to be performed over the boundary edges of the element. Numerical experiments are conducted on benchmark mixed-mode linear elastic fracture problems that demonstrate the sound accuracy and optimal convergence in energy of the proposed formulation.

Within the student competition that took place during the 10th International Masonry Conference (10th IMC, 9–11 July 2018, Technical University of Milan, Milan, Italy), a set of tilting plane tests on dry joint masonry shear panels were carried out. Several tests were conducted by means of a tilting table: in-scale models of different perforated masonry shear walls were inclined until the activation of a global collapse mechanism. The ultimate inclination angle is always representative of the maximum shear force that the structure can bear. A total of 7 wall designs WDs, each one proposed by a student team according to some imposed geometrical criteria (8 bricks length, 27 bricks height, 30% minimum percentage of openings), was tested. In this work, numerical simulations aimed at reproducing experimental results obtained during the competition are presented. The problem is studied both in terms of rigid body structures subjected to a finite base rotational settlement and by means of traditional limit analysis. The finite settlement problem is treated incrementally, i.e. by increasing through a small amount the base rotational settlement at each step. On the other hand, limit analysis is performed assuming both associative and non-associative behavior for the masonry material. Finally, in order to better represent the actual behavior of walls during experiments, some simple strategies aimed at including within the numerical models some geometrical imperfections of the bricks and installation defects are devised and their effects are evaluated by means of sensitivity analyses.

We propose a new adaptive NURBS upper-bound limit analysis approach for the assessment of general three-dimensional curved masonry structures, based on different meta-heuristic mesh adaptation schemes. The method, which can easily be integrated within CAD modeling environments, allows to establish the actual failure mechanism and load bearing capacity of a masonry structure by iteratively adjusting a tentative pattern of yield lines, defined upon a suitable initial mesh of NURBS rigid elements, by means of a suitable meta-heuristic algorithm which searches for the minimum collapse load multiplier, thus enforcing the upper-bound theorem of limit analysis. In particular, we investigate and discuss the efficiency of several meta-heuristic algorithms in delivering the optimal solution: a specifically devised Prey Predator Algorithm (PPA) is compared with the Particle Swarm Optimization (PSO) Algorithm, the Firefly Algorithm (FA) and a suitable Genetic Algorithm (GA). Four masonry vaults have been chosen as case studies. In particular, the modified PPA proves to be the most efficient mesh-adjustment scheme for the proposed adaptive NURBS-based limit analysis procedure.