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

Giuseppe Cocchetti and Egidio Rizzi ()
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Giuseppe Cocchetti: Politecnico di Milano, Dipartimento di Ingegneria Civile e Ambientale
Egidio Rizzi: Università degli studi di Bergamo, Dipartimento di Ingegneria e Scienze Applicate

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 3, No 6, 707-757

Abstract: Abstract 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.

Keywords: Symmetric circular masonry arches; Couplet–Heyman problem; Minimum thickness; Structural form optimization; Purely rotational collapse mode (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01772-0

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