Nonlinear Analysis of Space Trusses Using Modified Normal Flow Algorithm

In order to evaluate the structures’ behavior accurately, a suitable mathematical algorithm and a set of appropriate assumptions concerning the structures’ behavior must be adopted. The more accurate the algorithm and the assumptions adopted the more real behavior of the structures is determined. In the case of nonlinear analysis, the evaluation process is complex and cost effective. Therefore, for this aim, the researchers have presented simple relationships ignoring the effect of several factors. In the proposed method, in the case of nonlinear analysis, linear analysis is directly used first, and then by implementing simple or advanced iterative methods convergence is achieved in the equilibrium path. Using these methods, after passing limit points, the structure behavior is defined and so accurate design of the structure is possible. In the present study, for passing the equilibrium path of the space trusses, the Newton–Raphson iterative algorithm is used along the flow path perpendicular to the Davidenko curves with modified convergence rate. Contrary to the previous methods, this algorithm uses the homotopy approach, is based upon the new mathematical concepts, and has great ability for developing complex load-displacement paths of the structures with multidegrees of freedom. At the end, through three numerical examples, three structures have been analyzed using the algorithm presented in this paper and the results are compared with the previous advanced iterative methods that have been used for nonlinear analysis of those structures. The ability of the proposed method, particularly for passing the limit points, has been indicated by those numerical examples.