# Multi-Objective Pareto Optimization of Tensile Membrane Architecture for Energy Harvesting
## 5 Conclusions  
In this study, the previous research of [PERSON] and [PERSON] [12] was extended, and the TMA was optimized with two objectives--power generation and stability--for the environments of Inner Mongolia and Texas. A total of 18 Pareto optimal graphs were visualized, and 54 selected Pareto-front solutions were proposed. When designing an energy-harvesting TMA, designers can determine appropriate tradeoffs through Pareto-optimal solutions and the correlation between the material stiffness and the electricity generation. Some designers may sacrifice energy efficiency to achieve the required stability whereas others may select the Pareto solution with the largest amount of electricity generation for enhancing the sustainability. Regardless of the design objectives, TMA designers can consider green energy in the future, and the TMA can be useful to designers considering green energy buildings. The novelty of this paper stems from the regional wind pattern and the TMA orientation. TMA designers have focused on TMA designs that do not fail and the elastic constants were mainly used as assistance for biaxial data and stress-strain data. Unlike the present, when designers put values in the feasible zone and end the investigation, after an introduction to a new research area--energy harvestable TMA--designers could adjust the elastic constants--push the parameters to the limit just before failure to maximize the electric generation. An important finding is that high wind frequency does not ensure high energy efficiency. Frequent changes in the wind speed do not necessarily improve the vibration of the harvesters on the membrane. Therefore, a detailed wind-pattern analysis is needed to construct an efficient energy-harvesting TMA. To the best of our knowledge, this was the first study in which the TMA was optimized with regard to the building shape, orientation, material, and vibration-based energy harvesting. According to the experimental results, it is recommended that designers select materials with a high stiffness with consideration of the effect of stability on efficiency when choosing materials for conic or barrel-vault structures. However, for hypar structures, it is recommended that designers choose materials according to the energy efficiency. The shapes of the Pareto front solutions did not differ significantly between Texas and Inner Mongolia, but in the case of the hypar shape, the design variable range is wider due to differences in optimized shapes between the two regions. For the conic and barrel-vault shapes, the specific shape suggested in the Pareto solution is expected to have the highest energy efficiency even in other wind environments. To overcome and supplement the limitations of computational simulation, an actual scale model of the TMA can be developed. Additionally, in this study, the [PERSON]'s ratios and shear moduli, which are used to evaluate the stability of TMAs, were neglected in order to focus on the material stiffness of each material type. The use of these properties together with the material stiffness (Young's modulus) will enhance future simulations. Fluid-structure interaction programs that can consider the movements of the membrane due to wind will be useful for the development of a more sophisticated urban wind environment.  
Conceptualization, (K.H.H.); Data curation, (H.M.); Formal analysis, (H.M.); Funding acquisition, (K.H.H.); Investigation, (H.M.); Methodology, (H.M.); Project administration, (K.H.H.); Resources, (K.H.H.); Supervision, (K.H.H.); Validation, (H.M.); Visualization, (H.M.); Writing--original draft,(H.M.) and (K.H.H.); Writing--review & editing, (H.M.) and (K.H.H.). All authors have read and agreed to the published version of the manuscript.  
The National Research Foundation of Korea (NRF-2020R1C1C1011974) supported this work.  
The authors declare no conflict of interest.