Since the introduction of space elevators by Tsiolkovsky in 1895, many researchers, engineers, and designers stepped forward to suggest theories for the construction of space elevators. Based on the investigations made by many authors for building space elevators, Earth-to-space, Lunar space, and Mars-to-space elevators can contribute for future space exploration and colonization. In the presented study, the aim is to review the previous studies regarding the design and construction of space elevators with appropriate materials and to predict the thermal fatigue life of space elevators for the first time as it is one of the concerns in space environment because space elevators are exposed to thermal cycles. For this purpose, Extended Convex Curves Method is used. The results have shown that the thermal fatigue life of lunar space elevator is less than that for Earth-to-space and Mars-to-space elevators due to the lack of atmosphere on the Moon. This contribution can help to design and construct the space elevators with higher safety against the thermal fatigue failure with the selection of appropriate materials for the space elevator structure.
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