Eroglu, UgurcanRuta G.Paolone A.Tüfekci E.2023-06-162023-06-16202197811198318919781786307149https://doi.org/10.1002/9781119831891.ch6https://hdl.handle.net/20.500.14365/3346Most studies on cracked one-dimensional structural elements deal with their statics and free dynamics, while their stability is only given marginal consideration, especially arches. This chapter investigates buckling and post-buckling of parabolic arches with crack-like damages. The environment acts on the arch by: a vector force field, power dual of the incremental displacement of the axis; and a skew-symmetric tensor couple field, power dual of the incremental rotation of the cross-sections. The chapter presents two perturbation expansions of the finite governing equations for arches modeled as curved beams, in order to investigate their non-trivial fundamental path and their post-buckling path. Kinematics is finite, balance is in the actual configuration and only constitutive equations are supposed linear elastic. Future investigations will be about the quality of the post-buckling path and on linear vibration about non-trivial pre-stressed states, in order to detect the effect of local damages for monitoring purposes. © ISTE Ltd 2021.eninfo:eu-repo/semantics/closedAccessBuckling modesCrack-like damagesLinear vibrationParabolic archesPost-bucklingBook Part10.1002/9781119831891.ch62-s2.0-85136081417