Hencky bar-chain model for optimal circular arches against buckling

This paper is concerned with the formulation of the Hencky bar-chain model (HBM) for shape optimization of pinned-pinned circular arches under uniform radial pressure for maximum buckling capacity. The so-called HBM is a discrete model which comprises a finite number of rigid curved segments connected by frictionless hinges and elastic rotational springs. The different rotational spring stiffnesses along the arch represent the varying cross-section of the arch. Therefore, the optimization of the rotational spring stiffnesses of a HBM leads to the optimal shape of a circular arch. With a sufficiently large number of springs, one may obtain the optimal continuous shape of the arch. HBM has a great advantage over other numerical methods in seeking the optimal solution because it allows one to obtain the analytical optimality conditions in a set of recursive equations that requires minimal computational effort to solve the problem. Although HBM has been used by Krishna and Ram [1] and Zhang et al. [2] for column shape optimization, this is the first time that HBM is developed for arch optimization.