Buckling, post-buckling and geometrically nonlinear analysis of thin-walled beams using a hypothetical layered composite cross-sectional model

• Published in: Acta mechanica Vol. 232; no. 7; pp. 2733 - 2750
• Main Authors: Einafshar, N., Lezgy-Nazargah, M., Beheshti-Aval, S. B.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.07.2021; Springer; Springer Nature B.V
• Subjects: Aerospace engineering; Algorithms; Analysis; Civil engineering; Classical and Continuum Physics; Composite materials; Control; Cross-sections; Deformation; Design; Differential equations; Differential geometry; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Equivalence; Finite element method; Heat and Mass Transfer; Laminates; Mathematical models; Multilayers; Nonlinear analysis; Nonlinear equations; Original Paper; Postbuckling; Shear deformation; Solid Mechanics; Stability analysis; Stiffness; Theoretical and Applied Mechanics; Variables; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-021-02936-3

In this study, an efficient 1D finite element model (FEM) is presented for the axial–flexural buckling, post-buckling and geometrically nonlinear analyses of thin-walled beams. The non-classical effects like transverse shear and normal flexibilities are incorporated in the formulation by adopting a new structural concept called equivalent layered composite cross-sectional (ELCS) modeling. In the framework of ELCS, the original cross section of the thin-walled beam is replaced with a layered composite cross section with equivalent stiffness. A layered global–local shear deformation theory is employed for representing the displacement fields of the beam. A full Green–Lagrange type of geometrically nonlinear FEM is developed to formulate the governing differential equations. The Newton–Raphson linearization approach is adopted for solving the nonlinear equations. The proposed FEM avoids the use of a shear correction factor and has a low number of degrees of freedom (DOFs). For the validation of the proposed model, various buckling, post-buckling and nonlinear bending tests are carried out and the obtained results are compared with the results of classical beam theories and 2D/3D finite element results. Comparisons of the results prove the efficiency and accuracy of the suggested formulation for stability and geometrically nonlinear analysis of thin-walled beams.