Catenary arch of finite thickness as the optimal arch shape

Nikolić, Dimitrije

doi:10.1007/s00158-019-02304-9

Cited by 21 publications

(9 citation statements)

References 17 publications

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“…Except of the case of semicircular arches, various researchers dealt with the investigation of other arch geometries such as parabolic [20,28], elliptical [21], pointed/gothic [20,22,23] and catenary arches [23,24]. Most of the works mentioned above, are referred to the static behaviour and stability of the arches through determining their corresponding upper and lower bound thrust lines.…”

Section: Background Of the Problemmentioning

confidence: 99%

“…After Hooke [2], the catenary shape symbolised the perfect arch shape as it represented the optimal thrust line. [24] Highlighted the deviation of the resulting thrust line from the catenary centerline of a catenary arch, although he admitted that there is no minimum thickness for a two-dimensional catenary arch under self-weight. The justification is that, as the thickness of a catenary arch tends to zero (one-dimensional arch), the thrust line tends to follow a purely catenary shape and hence, it will always be confined within the arch's geometry (intrados and extrados).…”

Section: Background Of the Problemmentioning

confidence: 99%

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Comparison of the Efficiency of Minimum-Thickness Circular and Parabolic Arches for Various Gravity Conditions

Kalapodis¹,

Kampas²,

McLean³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Arches are structural forms that have been used for thousands of years and rely on gravity for their inherent stability. Currently, given the space race for lunar and martian exploration, it has become apparent that soon enough, there will be a need to design and build the first resilient shielding structures on the Moon and Mars against extreme radiation. Arches represent an ideal option for such structures given that they are durable and can be easily built. This paper is based on previous work of the authors and focuses on the stability of circular and parabolic arches with different embrace angles subjected to different levels of equivalent inertial loading in low-gravity conditions. More specifically, it reveals that although parabolic arches can be much more efficient than the corresponding circular 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 behavior and introduces a "universal" inertial loading.

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Section: Background Of the Problemmentioning

confidence: 99%

Section: Background Of the Problemmentioning

confidence: 99%

Comparison of the Efficiency of Minimum-Thickness Circular and Parabolic Arches for Various Gravity Conditions

Kalapodis¹,

Kampas²,

McLean³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…Similarly, Eqs. (48) and (49) could be used as well for a recursive determination of η and h, with above comments applying in the same way. However, recall that the role of η is inverted, as opposed to that of A and h, since the triplets have to be sorted out in orders (A + ,η − , h + ) and (A − ,η + , h − ).…”

Section: Ccr Solutionmentioning

confidence: 99%

“…Specifically, in the least-thickness collapse evaluation, classical Heyman solution [3] is shown to constitute a sort of approximation of the true solution (here labelled as "CCR" [7]), in Heyman assumption of self-weight distribution along the geometrical centreline of the arch, while Milankovitch solution [43][44][45], as a cornerstone of thrust-line-like analysis, in view of form optimization [46][47][48][49][50][51][52], may as well be derived, in the consideration of the real self-weight distribution along the arch, though at the price of a recorded increasing complexity in the explicit analytical handling of the governing equations (now analytically resolved to a very end in [14]).…”

Section: Introductionmentioning

confidence: 99%

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

Cocchetti

Rizzi

2020

J Optim Theory Appl

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This paper re-considers a recent analysis on the so-called Couplet–Heyman problem of least-thickness circular masonry arch structural form optimization and provides complementary and novel information and perspectives, specifically in terms of the optimization problem, and its implications in the general understanding of the Mechanics (statics) of masonry arches. First, typical underlying solutions are independently re-derived, by a static upper/lower horizontal thrust and a kinematic work balance, stationary approaches, based on a complete analytical treatment; then, illustrated and commented. Subsequently, a separate numerical validation treatment is developed, by the deployment of an original recursive solution strategy, the adoption of a discontinuous deformation analysis simulation tool and the operation of a new self-implemented Complementarity Problem/Mathematical Programming formulation, with a full matching of the achieved results, on all the arch characteristics in the critical condition of minimum thickness.

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“…Moreover, Milankowitch 4 and Makris and Alexakis 5 demonstrated that, apart from 1D arches, admissible thrust‐lines cannot be of catenary shape, hence an arch of finite thickness that resembles a catenary can not be automatically assumed to be optimal. Past studies have mostly examined the stability of arches of classical form under static loads focussing on arches of classical form like semicircular, 1,4–7 parabolic, 8,9 elliptical 10 and catenary arches 3,11 …”

Section: Introductionmentioning

confidence: 99%

Optimal arch forms under in‐plane seismic loading in different gravitational environments

Mariotti

McLean

Kalapodis

et al. 2022

Earthq Engng Struct Dyn

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This paper is motivated by the renewed interest in space exploration and the need to provide structurally sound and resource‐efficient shielding solutions for valuable assets and future habitable modules. We present, implement and test a methodology for the preliminary design and assessment of optimal arch forms subjected to self‐weight as well as seismically induced loads. The numerical framework, built around a limit thrust‐line analysis, previously published by the authors, is summarized first. This is followed by a detailed account of the form‐finding algorithm for arches of variable thickness. Special attention is placed on the physical feasibility of our assumptions and the justification of the engineering inputs adopted. The newly form‐found arches achieve material efficiencies between 10% and 50% in comparison with their constant minimum‐thickness circular or elliptical counterparts, depending on the relative intensity of the seismic action. The influence of the initial input geometry and the stabilising presence of additional shielding material against extreme radiation are also evaluated with emphasis on the effects of low‐gravity conditions. Finally, a case study is presented and Discrete Element Models of constant and varying thickness arches (VTAs) are assessed under a set of representative ground‐motions on a lunar setting. The significant over‐conservatism of constant thickness arches (CTAs) is made manifest and potential improvements of the optimally found arch shape are highlighted. Although developed with extraterrestrial applications in mind, the results and methods we present herein are also applicable to terrestrial conditions when material efficiency is of utmost concern.

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Catenary arch of finite thickness as the optimal arch shape

Cited by 21 publications

References 17 publications

Comparison of the Efficiency of Minimum-Thickness Circular and Parabolic Arches for Various Gravity Conditions

Comparison of the Efficiency of Minimum-Thickness Circular and Parabolic Arches for Various Gravity Conditions

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

Optimal arch forms under in‐plane seismic loading in different gravitational environments

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