Author:
El-Borhamy Mohamed,Dabaon Mohamed A.
Abstract
AbstractThis work tackles the mathematical modeling of buckling problem to obtain their critical loads in tapered columns subjected to concentrated and axial distributed loads. The governing model is a general eigenvalue problem that has no exact solution due to some new terms included. A semi-analytical technique satisfying the boundary conditions is proposed for the solution procedure. The minimum residual Galerkin’s method is suggested due to its effectiveness as a semi-analytical tool for the buckling problem to obtain the buckling shape modes by using admissible periodic functions. The study investigates the buckling instability and the responses of tapered columns with different periodic trial shape functions as approximations to the exact solutions. Based on the eigenvalue problem, Galerkin’s method is employed to obtain the transition curves to represent the critical loads. The stability charts (Ince–Strutt diagrams) among the parameters of the problem are proposed to explain the elastic stability of different tapered columns subjected to different shapes of cross sections and distributed weights. Consequently, the influences of the included parameters on the critical buckling loads are discussed. Among the different tapered columns presented, some parameters in the proposed distributions have a big influence on the critical buckling load and the creation of the instability regions in the chart for the clamped-clamped boundary conditions. The results are verified using the analytical solutions for some specific known problems.
Publisher
Springer Science and Business Media LLC
Reference37 articles.
1. Abdel-Latif TH, Dabaon M, Abdel-Moez OM, Salama MI. Buckling of columns with sudden change in cross section. In: Mansoura third international engineering conference, Mansoura; 2000. pp. 11–3.
2. Abdel-Latif TH, Dabaon M, Abdel-Moez OM, Salama MI. Buckling loads of columns with gradually changing cross-section subjected to combined axial loading. In: Fourth Alexandria international conference on structure and geotechnical engineering, Alexandria; 2001. pp. 2–4.
3. Agarwal RP, O’Regan D. Ordinary and partial differential equations with special functions, Fourier series, and boundary value problems. Springer; 2009. E. ISSN 2191-6675.
4. Arbabei F, Li F. Buckling of variable cross-section columns. Integral-equation approach. J Struct Eng. 1991;117(8):2426–41. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:8(2426).
5. Ceballes S, Abdelkefi A. Applicability and efficacy of Galerkin based approximation for solving the buckling and dynamics of nanobeams with higher order boundary conditions. Eur J Mech A/Solids. 2022;94:104596. https://doi.org/10.1016/j.euromechsol.2022.104596.