Composite Structures 303 (2023) 116270 Available online 4 October 2022 0263-8223/© 2022 Elsevier Ltd. All rights reserved. Stability analysis of shear deformable cross-ply laminated composite beam-type structures Damjan Bani´ c * , Goran Turkalj , Domagoj Lanc Department of Engineering Mechanics Faculty of Engineering, University of Rijeka, Vukovarska 58, HR-51000 Rijeka, Croatia A R T I C L E INFO Keywords: Thin-walled composite cross-section Cross-ply laminates Shear deformations Shear coupling effects Beam model Buckling analysis ABSTRACT This paper presents a shear deformable beam model for the nonlinear stability analysis of composite beam-type structures. Each wall of the cross-section is stacked in the cross-ply scheme. The incremental equilibrium equations are derived in the framework of an updated Lagrangian formulation. Hooke’s law is assumed to be valid. The nonlinear displacement feld of the composite cross-section accounts for the restrained warping and the large rotation effects. The shear deformation effects are included through Timoshenko’s bending theory and modifed Vlasov’s torsion theory. Additional shear correction factors due to the bending-torsion coupling occurring at asymmetric cross-sections are introduced in the analysis. The accuracy and reliability of proposed numerical mode are verifed on benchmark examples, and the obtained results confrm that it can be classifed as a shear locking-free model. 1. Introduction As load-bearing composite structures generally contain slender beam structural elements of thin-walled cross-section, the response of such optimized structures to the effect of external loading is much more complex and their increased tendency to lose the stability of the defor- mation form and the appearance of buckling is particularly pronounced [1–9]. The occurrence of instability in beam structures can be man- ifested in the pure fexural, pure torsional, torsional-fexural or lateral deformation form. All mentioned deformation forms are global insta- bility forms, or global buckling forms. Thin-walled frames are also sus- ceptible to local instability forms, where signifcant distortion of the cross-section occurs because the initial cross-sectional shape becomes unstable. This can lead to the collapse of the structure even before the global instability form occurs [1,2,4–6,9]. Therefore, in the optimal design of the structure, special attention should be paid to the exact determination of the limit state of stability of deformation forms, that is, the buckling strength. Analytical solutions are only available for simpler cases [10–15], and therefore the development and application of nu- merical solutions is imposed as a necessity [1–9]. Although the introduction of composites further complicates the design process, it is the right way to achieve optimal solutions in terms of weight, load bearing capacity, functionality, construction cost, energy effciency and resistance of the structure to chemical processes [16,17]. Shear deformations have a signifcant effect on the transverse dis- placements, natural vibration frequencies and critical buckling loads of composite structures. Analyses of composite beam structures based on Euler-Bernoulli assumption can lead to signifcant errors in the analysis results [12,18–20]. Geometric nonlinear analyses of composite beam structures with the infuence of shear deformations are presented in [1–9,21–24]. In Refs. [21–24] the authors also include bending-torsion coupling effects occurring for the asymmetric cross-section where the principal bending and principal shear axes do not coincide [25]. In the authors’ last paper [24] composite frames with semi-rigid connections are presented, where geometrically nonlinear beam model and shear deformation effects were presented. In that paper unidirec- tional orthotropic composite structures were considered and the shear deformation coupling effects are accounted in the virtual elastic strain energy, while in the force-strain relationships such effects were ignored. In the present study, the shear coupling effects occurring due to non- symmetry of the cross-section are introduced even in the force-strain relationships and modelling of general orthotropic cross-sections is enabled. Axial forces and bending moments applied in the ply directions do not cause shear or twist of the cross-section. It is also assumed that the cross-section is not deformed in its own plane, and the material obeys Hooke’s law. Shear deformation effects are included by the use of improved shear-deformable beam formulation which includes the bending-torsion coupling effects [21–24]. The beam member is assumed * Corresponding author. E-mail address: dbanic@riteh.hr (D. Bani´ c). Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct https://doi.org/10.1016/j.compstruct.2022.116270 Received 14 April 2022; Received in revised form 11 July 2022; Accepted 25 September 2022