Keywords: masonry structures, fiber-reinforcement, topology optimization, stress-constrained optimization.

Masonry exhibits a low tensile strength, which is often responsible for the undesired brittle collapse of existing constructions. Externally bonded fibre reinforced polymer (FRP) systems may be conveniently adopted to improve the performance of masonry structures, both in terms of strength and ductility. The layout of the fibre-reinforcement is generally designed according to code rules [1], or to methods based on the experience gained from experimental programmes. These procedures cope with standard masonry panels, but are not conceived for a straightforward extension to more complex geometries that frequently occur in practice.

In this paper, a novel approach for the optimal placement of fibre reinforcement in masonry structures is presented, with the aim of providing the designer with an automatic and general method to address this task. The theoretical tool employed is topology optimization [2], with the aim of distributing the minimum amount of reinforcing material such as to keep the stress at any point in the masonry region below a prescribed threshold. The stiffness matrix of any finite element into which the design domain is discretized consists of two contributions related to masonry and to the fibre-reinforcement; the latter one is penalized according to a classical SIMP-law [2]. At the initial step of the optimization procedure, all the elements are assumed to be strengthened by a layer of FRP. Standard methods of mathematical programming are adopted to remove reinforcement regions that are unnecessary for the control of the stress in the masonry element.

An anisotropic Cauchy continuum model is employed to describe the macroscopic elastic behaviour of masonry. The strength criterion employed for masonry was recently formulated according to a lower bound limit analysis homogenization model [3], relying upon the discretization of a quarter of any unit cell by six CST elements. As a result of the limited number of variables involved, closed form solutions for the masonry macroscopic strength domain can be obtained. The reinforcement is supposed to consist of unidirectional FRPs, endowed with stiffness only along the fibre direction. The local orientation of the fibres and the local reinforcement densities in any finite element are the design variables.

This paper discusses preliminary results addressing the fibre-reinforcement of a benchmark masonry wall. The numerical FRP distributions achieved are compared with standard reinforcement layouts suggested by design codes.

1

CNR-DT 200, "Guide for the design and construction of externally bonded FRP systems for strengthening existing structures", C.N.R. National Research Council, Italy, 2004.

2

M. Bendsøe, N. Kikuchi, "Generating optimal topologies in structural design using a homogenization method", Comp. Meth. Appl. Mech. Eng., 71, 197-224, 1988. doi:10.1016/0045-7825(88)90086-2

3

G. Milani, "Simple homogenization model for the non-linear analysis of in-plane loaded masonry walls", Comput. Struct., 89, 1586-1601, 2011. doi:10.1016/j.compstruc.2011.05.004

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