A Strut-and-Tie Topology Optimization Model for the Pushover Analysis of In-Plane Loaded Masonry Walls

This paper presents a rigid triangular finite element macro-model for the pushover analysis of in plane loaded masonry walls. The shape and position of rigid triangular elements are paramount parameters for a correct evaluation of the failure modes of piers and spandrels. Such parameters are here evaluated by means of a topology optimization approach where masonry is treated by means of a quasi no-tension material. In order to tackle elastic and inelastic deformations, interfaces between adjoining triangles are assumed to behave as elasto-plastically with softening in both tension and compression, with peak tensile strength almost vanishing. The two-step procedure competes favorably with classic equivalent frame approaches because it does not require a-priori assumptions on the position of the triangular elements and on the length of the rigid offsets. Furthermore, excellent stability of the algorithm and numerical efficiency are experienced. An example of technical relevance is discussed, exhibiting promising comparisons with results obtained with different equivalent frame procedures.