Post-buckling behavior of two elastica columns linked with a rotational spring

The post-buckling problem of a fixed-free column composed of two segments connected by a linear rotational spring with different flexural stiffness and lengths is studied. A semi-analytical solution is derived and the results are checked using two different numerical approaches. In the first approach, the problem is solved using numerical integration technique, while in the second approach, the problem is solved using large displacement finite element analysis of NASTRAN program. Excellent agreements have been obtained between the semi-analytical and the numerical approaches. Furthermore, a regression analysis has been made for the parameters covered in this study and a regression function has been obtained which relates to the tip axial horizontal displacement (beta) as a function of load parameter (alpha) and fixity ratio (f). From this function, the stored strain energy (U) is obtained and plotted to be used as a design chart for engineers to obtain the required fixity ratio for a given stored strain energy and load parameter. (C) 2004 Elsevier Ltd. All rights reserved.