Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article An analytical and numerical study on the buckling of cracked cylindrical shells V. Akrami a , S. Erfani b, ⁎ a Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran b Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran ARTICLE INFO Keywords: Cracked cylindrical shell Buckling load Beam on elastic foundation Finite element method Eigenvalue analysis ABSTRACT Presence of flaws or cracks may cause substantial decrease in the strength of a component or structure. This kind of structural damage will accumulate over time, leading to significant decrease in ultimate load carrying ca- pacity of structural members and premature brittle failure. In this paper, a coupled analytical and numerical study is implemented in order to evaluate buckling load of cracked cylindrical shells which is often encountered in the fields of civil engineering, offshore engineering and mechanic engineering. In the first phase of the study, buckling load of cylindrical shells with circumferential crack is investigated by treating the symmetric model as a cracked rectangular beam-column on an elastic foundation. The cracked beam-column is modelled as two beam elements on elastic foundation connected by an equivalent rotational spring and governing characteristic equation is obtained. Finite element models are used to verify analytical results and assess their accuracy, based on which good agreement is observed between analytical and numerical results. Effect of different parameters such as the length of cylinder, radial stiffness of cylinder, crack location and crack severity is studied on the axial load carrying capacity of such members. A simplified equation is proposed in order to calculate buckling load of tall cylindrical shells with a circumferential crack. In the second phase, the buckling load of cylindrical shells with a partial crack is studied using the results of finite element analysis on models with varying crack length. Based on the results of numerical analysis, an empirical equation is proposed to interpolate buckling load of these members between two limiting values, namely the buckling loads of same uncracked cylinder and the cylinder with circumferential crack. 1. Introduction The strength of a compression member may be reduced significantly by the presence of defects. The most common type of these defects is due to the presence of small initial cracks which will grow under fatigue loads. The awareness of this phenomenon in metallic structures started in the mid-19th century with the occurrence of fatigue failures in the railway industry [1]. Presence of cracks in a compressive cylindrical shell can decrease buckling load of the member and cause premature brittle failure. This phenomenon is one of the major failure modes in columns of highway and railway bridges, cranes, offshore structures, containers, machine elements, etc. Buckling behaviour of cracked cylindrical shells has been studied by several researchers. Among the rest, Hutchinson et al. [2] conducted a joint theoretical and experimental investigation on the effects of certain types of local axisymmetric imperfections on the buckling of cylindrical shells. Considering the analogy between the strut on an elastic foun- dation and the axisymmetric cylinder El Naschie [3] presented a closed form solution for the post buckling path of an infinitely long cylindrical shell with a free edge. It is stated that the presented solution could relate to the buckling of a compressed concrete cylinder containing a circumferential crack. Vafai et al. [4] computed the free vibration fre- quencies and the corresponding mode shapes of a simply supported rectangular plate with a crack emanating from one edge. Once the vi- bration frequencies and mode shapes were found they were used to establish regions of instability and compute buckling loads of the plate. Hampton and Nelson [5] conducted a numerical and experimental study on the crack growth in thin plates and cylinders and showed that the buckling effects must be included in the finite element analysis to have a good agreement between numerical and experimental results. In an attempt to study more general case, Brighenti [6,7] studied rectan- gular elastic thin-plates a through thickness crack and assessed the ef- fect of crack length, crack orientation and boundary conditions of the plate on the buckling loads. Most of the recent studies in this filed are focused on finite element (FE) modelling to investigate effect of dif- ferent parameters (e.g. crack length, crack angle, loading condition, http://dx.doi.org/10.1016/j.tws.2017.06.023 Received 20 December 2016; Received in revised form 13 June 2017; Accepted 20 June 2017 ⁎ Corresponding author. E-mail addresses: v.akrami@uma.ac.ir (V. Akrami), sderfani@aut.ac.ir (S. Erfani). Thin-Walled Structures 119 (2017) 457–469 0263-8231/ © 2017 Elsevier Ltd. All rights reserved. MARK