Issue 51

M. Pepe et alii, Frattura ed Integrità Strutturale, 51 (2020) 504-516; DOI: 10.3221/IGF-ESIS.51.38 512 (a) (b) (c) Figure 8 : Collapse mechanism for Example 5, horizontal live load: ( a ) ALMA 2.0, ( ) FEM/DEM, ( ) FEM (a) (b) (c) Figure 9 : Collapse mechanism for Example 6, horizontal live load: ( a ) ALMA 2.0, ( ) FEM/DEM, ( ) FEM Fig. 7 refers to results obtained for Example 4, characterized by the presence of two openings. Results are in this case similar to those obtained for the panel with only one windows. In particular, all the models provide a hinging collapse with rotation around the lower right corner of the wall and the formation of ‘stair-stepped’ cracks. In this case FEM/DEM provide a hinge positioned at ground level while Limit Analysis and FEM consider the hinge upon the first row of blocks. On the contrary Limit Analysis and FEM/DEM reveals also a little rotation of the part of the panel to the left of the first window while FEM, as for the previous case, considers this portion of the panel stable. Fig. 8 refers to results obtained for the slender panel of Example 5. For this case the results of the three different approaches are almost the same, with a hinging collapse due to the formation of several cracks, positioned at correspondence of openings, which divide the panel into several macro-blocks. The more evident difference is noticed for FEM/DEM which compute the hinge at the lower right corner of the wall at ground level, while for Limit Analysis and FEM it is positioned upon the first row of blocks. Fig. 9 refers to results obtained for Example 6, characterized by the presence of four openings. The collapse of the panel is due to a hinging behavior with the formation of several diagonal cracks which divide the structure into various macro- blocks. About the position of the cracks, the models provide results slightly different, except for those that identify the macro-blocks positioned to the right of the panel. Another difference is observed for FEM that compute the left part of the panel as stable, while Limit Analysis and FEM/DEM reveal in that portion different cracks and rotating macro-blocks. The collapse multiplier obtained with Limit Analysis, FEM/DEM and FEM has been compared with the results related to the associative (LP) and non-associative (Mixed Complementarity Problem MCP and Mathematical Program with Equilibrium Constraints MPEC) problems solved by Ferris and Tin-Loi [42]. As expected, results obtained with ALMA2.0 are very close to the one obtained with the associative case.