Post-buckling of simply supported column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2012-06, Vol.92 (6), p.479-489
• Main Authors: Saetiew, W., Chucheepsakul, S.
• Format: Article
• Language: English
• Subjects: generalized Ludwick constitutive law; hysteresis loop; limit load point; nonlinear elastic material; Post-buckling; shooting method; snap-through phenomenon
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201100081

In this article, the post‐buckling behavior of a simply supported column made of nonlinear elastic materials subjected to an end axial force is investigated. The column has a uniform rectangular cross‐section in which the stress–strain relationship of such materials is represented by the generalized Ludwick constitutive law. To derive the governing equations, both geometrical and material nonlinearities have been considered. Further, a set of highly nonlinear simultaneous first‐order differential equations with boundary conditions is established and numerically solved by the shooting method. Several numerical results are carried out and discussed highlighting the significant influences of the material nonlinearity parameter n on the equilibrium configurations and the equilibrium paths. From the results, there are many interesting features associated with the nonlinear hardening column such as a non‐monotonic bifurcation curve, the limit load point, snap‐through phenomenon, and hysteresis loop. Furthermore, the numerical results are compared with previous studies in order to test the validity and accuracy of the present method. The post‐buckling behavior of a simply supported column made of nonlinear elastic materials subjected to an end axial force is investigated. The column has a uniform rectangular cross‐ section in which the stress–strain relationship of such materials is represented by the generalized Ludwick constitutive law. To derive the governing equations, both geometrical and material nonlinearities have been considered. Further, a set of highly nonlinear simultaneous first‐order differential equations with boundary conditions is established and numerically solved by the shooting method. Several numerical results are carried out and discussed highlighting the significant influences of the material nonlinearity parameter n on the equilibrium configurations and the equilibrium paths. From the results, there are many interesting features associated with the nonlinear hardening column such as a non‐monotonic bifurcation curve, the limit load point, snap‐through phenomenon, and hysteresis loop. Furthermore, the numerical results are compared with previous studies in order to test the validity and accuracy of the present method.