Abstract
For thousands of years, arches have been used as durable structures that are easy to build and that rely on gravity for their inherent stability. Since then, many researchers and engineers have studied their stability either when subjected to gravity or inertial loading. Currently, given the Insight mission to Mars and the ambitious Artemis program to the Moon, it has become apparent that there will soon be the need to design and build the first resilient extraterrestrial structures and arches represent an ideal option for such structures. This paper focuses on the stability of parabolic arches with different embrace angles subjected to different levels of equivalent inertial loading in low-gravity conditions. The results are contrasted with the well-studied circular arches. More specifically, this investigation employs variational principles to identify the imminent mechanisms and numerical methods based on the limit thrust line concept in order to estimate the minimum required thickness of parabolic arches for a given loading and in different gravitational fields. The paper shows that although parabolic arches can be much more efficient than their circular counterparts for gravitational-only loading, this is not the case for different combinations of inertial loading and embrace angles where the opposite can be true. It highlights the dominant effect of low-gravity conditions on the minimum thickness requirements for both types of arches and considers the effect of a potential additional infill for radiation shielding. Furthermore, this study reveals a self-similar behaviour, introduces a “universal” inertial loading and showcases, through the use of master curves, the areas where the parabolic arches are more efficient than their circular counterparts and those where the opposite is true. These areas can be used for the preliminary design of such structures. Additionally, the paper identifies hidden patterns associated with the developed mechanisms between the two different geometries for the different gravitational fields. Finally, it presents a case study where the need to optimise the structural form of extraterrestrial structures becomes evident.
Highlights
Nowadays, following the new space era towards the exploration and potential human settlement in other planetary bodies, various space agencies (NASA, ESA, ISRO, etc) and private firms (SpaceX, Virgin Galactic, Blue Origin, etc) are investing in ambitious missions such as “Artemis” amongst others
It is observed that the collapse mech anisms are exactly opposite; in the case of the semi-circular arch, the thrust line starts at the extrados at the base, it touches the intrados at 35.52o and the extrados at the crown, while for the parabolic arches the limit thrust line starts at the intrados, at the base, touches the extrados at43.81o and the intrados at the crown
The numbering adopted for the rupture angles is different between the circular and parabolic arches to facilitate comparison; this will become evident when ac counting for inertial loading
Summary
Nowadays, following the new space era towards the exploration and potential human settlement in other planetary bodies, various space agencies (NASA, ESA, ISRO, etc) and private firms (SpaceX, Virgin Galactic, Blue Origin, etc) are investing in ambitious missions such as “Artemis” amongst others. There have been many concepts and ideas proposed in the past, as summarised by Kalapodis et al [24], but the most prevalent is the need for an external resilient shielding structure that would protect valuable assets (energy fuel tanks, robotic elements, future inflatable modules, etc) from extreme radiation [38] and temperature fluctuations [5,23] Ricci et al [39] proceeded with a thorough analytical calculation of the thrust line of a semicircular arch subjected to both vertical and inertial loading and the numerical esti mation, through Point Collocation Method [21] and constrained opti misation, of the upper and lower limits of semicircular, parabolic and pointed (statically determinate) arches
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