Computers and Structures 301 (2024) 107427 Available online 1 June 2024 0045-7949/© 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies. A geometrically nonlinear finite element formulation for buckling analysis of shear deformable angle-ply 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: Composite beam-type structures Buckling analysis Thin-walled cross-section Angle-ply laminates Shear deformability Shear coupling effects Beam element Large rotations ABSTRACT This paper introduces an improved shear-deformable beam formulation for nonlinear buckling analysis of laminated composite beam-type structures with thin-walled cross-sections. Each wall of a cross-section is assumed to be a thin symmetric and balanced angle-ply laminate. The incremental equilibrium equations of a straight beam element are derived by applying the virtual work principle within the framework of updated Lagrangian formulation, Hooke’s law and the nonlinear displacement field of a thin-walled cross-section, which takes into account restrained warping and large rotation effects. Incremental stress resultants are calculated by the Timoshenko–Ehrenfest beam theory for bending and the modified Vlasov theories for torsion. Shear coupling problems occurring at non-symmetric thin-walled cross-sections and arising from the shear forces-warping tor- sion moment couplings are considered. As a result, new shear-correction factors for a cross-section composed of thin angle-ply laminates are derived. Force recovering is performed according to the conventional procedure based on the concept of semitangential rotations. The shear-locking occurrence is prevented by applying the Hermitian cubic interpolation functions for deflections and twist rotation, and the associated quadratic functions for slopes and warping. The effectiveness of the proposed geometrically nonlinear shear-deformable beam formulation is validated through the test problems. 1. Introduction Load-bearing composite structures typically incorporate slender beam structural elements with thin-walled cross-sections. The response of these optimized structures to external loads is more intricate compared to traditional structures, exhibiting an increased susceptibil- ity to occurring of buckling [1–5]. Buckling in beam structures can manifest in various deformation forms, such as pure flexural, pure torsional, torsional-flexural, or lateral deformation. Determining the limit state of stability, particularly the buckling strength for different deformation forms, is crucial for the optimal design of composite structures. While analytical solutions are available for simpler cases [6–9], the need for numerical solutions arises in more complex scenarios [1–5,10]. The introduction of composites in structural design adds complexity to the process but presents the potential for achieving optimal solutions in terms of weight, load-bearing capacity, functionality, construction cost, energy efficiency, and resistance to chemical processes [11–14]. However, shear deformations significantly impact the transverse displacements, natural vibration frequencies, and critical buckling loads of composite structures. Traditional analyses based on the Euler- Bernoulli assumption may lead to significant errors without proper consideration of shear deformations [8,15,16]. To address these challenges, researchers have introduced geometric nonlinear analyses of composite beam structures considering shear de- formations [2,4,17–26]. Some studies also incorporate bending-torsion coupling effects, particularly for asymmetric cross-sections where the principal bending and shear axes do not coincide [27]. In authors’s recent study [25], a geometrically nonlinear beam model for buckling analysis of shear-deformable cross-ply laminated beam-type structure was presented. In this work, an improved beam model capable of modelling angle-ply composites is introduced. The assumption that each wall of a thin-walled cross-section is balanced and symmetrical composites is retained in this study as well, and the issues that arise when using unbalanced and nonsymmetrical composites will be the main topic of our future research. Shear coupling effects due to the non-symmetry of a cross-section are considered and the improved shear-deformable beam formulation, considering bending-torsion * Corresponding author. E-mail address: goran.turkalj@uniri.hr (G. Turkalj). Contents lists available at ScienceDirect Computers and Structures journal homepage: www.elsevier.com/locate/compstruc https://doi.org/10.1016/j.compstruc.2024.107427 Received 1 February 2024; Accepted 24 May 2024