This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi–Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.
The paper presents a failure analysis of the bell tower of the church of St. Francis of Assisi on Kaptol in Zagreb subjected to seismic activity using the finite-discrete element method—FDEM. The bell tower is a masonry building, and throughout history it has undergone multiple damages and reconstructions. It was significantly damaged during the earthquake in Zagreb which occurred on 22 March 2020 with a magnitude of 5.5. The analysis was performed on a simplified FDEM 2D numerical model which corresponds to the structure in its current pre-disaster state and the structure after the proposed post-disaster reconstruction. The obtained results showed a good agreement of the crack pattern in the numerical model and the cracks that occurred due to these earthquakes. In addition, the conclusions based on the conducted analysis can provide a better insight into the behaviour and serve as guidelines to engineers for the design of such and similar structures.
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