## 4 Conclusions and Future Steps  
In this work, attention was paid to estimating the actuation produced by piezoelectric patches bonded on curved beam elements made of PVC material, in view of ice protection applications on different parts, such as the piping and windshield. The peculiarity of these applications is represented by the stiffness of the protected structure, which is 1 order of magnitude lower than the piezoelectric patch. The aim of the work was to find a parametric relation among certain geometric features of the system (e.g., the curvature, location, and extension of the piezo patch; the thickness and strength of the bonding) and the force transmitted. In this sense, two configurations were investigated--one constituted by a curved structure with a piezo patch bonded and expanding under the effect of a unitary thermal load (representative of the voltage when a fictious thermal coefficient is assigned to the material of the piezo patch) and another one constituted by the structure alone subjected to unitary tangential pin forces and balanced radial components, reproducing the action of the piezoelectric patch. At first, a comparison was organised with models from the literature; although these theoretical schemes refer to flat applications, a good agreement was found in terms of the transmission factor, especially when the strain profile was assumed linearly to the thickness of the piezo patch. After having proven the consistency of the proposed model, the parameterization was carried out, whereby the ratio between the displacements for the two configurations and the ratio between the unitary pin force and the load generated by the solver and equivalent to the unitary thermal were computed. These two ratios, in fact, play a critical role in two aspects--the modeling of curved plates under the action of pin forces representing piezoelectric actions in static configuration and the computation of the strain transmission. The work herein presented is just a step towards the comprehension of the strain actuation of piezoelectric patches integrated onto curved soft structures. The results provide operational guidelines for designers in the static field; that is to say, far from resonance phenomena. Notwithstanding the typical applications of the piezoelectric actuators, which rely upon the resonance effect, the next step of the research will be the extension of the results to the dynamic responses. Figure 30: Structural solicitation and ice interface stress level compared with material yield strength and detachment threshold (**top**) and structure safety factor (**bottom**) vs. frequency. **Author Contributions:** Conceptualization, A.C. ([PERSON]); specifications, A.C. ([PERSON]); specifications of the actuation systems, A.C. ([PERSON]); methodology, A.S.P., A.V. ; validation, A.V. ; formal analysis, S.A.; visualization, A.S.P., S.A., A.C. ([PERSON]); supervision, L.C., A.C. ([PERSON]); writing, all authors; original draft preparation, A.S.P., A.V., S.A.; project administration, L.C. All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Data Availability Statement:** Data available on request due to restrictions. **Conflicts of Interest:** The authors declare no conflict of interest. **Acronyms and Symbols**