# In-Plane Structural Analysis of Coated Masonry Walls via a Homogenized Model
## 6 Conclusions  
The in-plane behavior of coated masonry walls has been analyzed via a homogenized orthotropic model, based on suitable designed assemblies of in-parallel springs. Accordingly, the stresses distributed between masonry and reinforcement coatings have been evaluated analytically, once the average stress acting on the homogeneous medium has been determined. Static and dynamic numerical analyses have been carried out on both non-homogeneous and homogeneous FE models of two sample systems. Parametric analyses have been also performed to investigate the reinforcement influence on the global behavior of the system.  
The following main conclusions are drawn:  
* Homogenized FE models of coated wall systems enable structural analysis to be performed with a significantly reduced computational burden. This is especially true when much coarser 2D homogeneous models are used, while still achieving excellent results. This outcome, which was recently discovered in [30] based on a few preliminary structural analyses on scale models, has been corroborated here. For instance, concerning Sample System 1, the calculation time of the refined model (3 LM) is found to be 236 times greater than that of the homogenized one (1 LM-2D).
* The homogeneous model is able to accurately describe the local displacement field of the non-homogeneous model, while it fits _on average_ the stress fields, due to the fast changes occurring across the constituent boundaries. However, when the average stress is partitioned between masonry and reinforcement via closed-form formulae, the stress peaks in each element are captured, in spite of the fact the homogeneous model is aimed at describing global, and not local, behavior. The effect of a self-stress state in the elements, triggered by the Poisson effect, is also considered. It has been found to be significant mainly at the reinforcement layers. These results are of particular importance in structural field, since: (i) local analyses are aimed at strength verification of each component (i.e., masonry and reinforcement), to asses the effectiveness of SFRM application; (ii) global analyses, on the other hand, allow for estimating how the reinforcement modifies the overall mechanical behavior.  
Figure 16: Natural frequencies of the non-homogeneous model vs. coating-to-wall thickness ratio, for the Sample System 1; numerical results (black dots) and interpolating laws (solid black lines).  
Figure 15: Natural frequencies of the non-homogeneous model vs. reinforced-to-unreinforced wall modulus ratio, for the Sample System 1; numerical results (black dots) and interpolating laws (solid black lines).  
As evidenced by parametric analyses (within the explored range of parameters), it has been observed that increasing the elastic moduli or the thickness of the reinforcement results in an increase in the natural frequencies of a given structural system, due to the application of reinforcement. This increase can be up to approximately 50%, depending on the elastic moduli of the reinforcement. On the other hand, the thickness of the coating has a less significant impact on the system dynamics, as it leads to frequency increments of up to 10%.  
A future prospect of the work could involve performing experimental tests and more extensive numerical simulations to enhance confidence in analytical predictions and highlight the advantages of homogenization. For instance, this could include estimating the reduction in calculation time for a real-size building.  
Conceptualization, A.L.; Methodology, S.D.N. and A.L.; Software, S.D.N.; Validation, S.D.N.; Formal analysis, S.D.N.; Writing--original draft, S.D.N.; Writing--review & editing, S.D.N. and A.L.; Supervision, A.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data availability Statement: Data are contained within the article. The authors declare no conflict of interest.