The α-generalized implicit method associated with Potra–Pták iteration for solving non-linear dynamic problems

Abstract

Generally, direct time integration procedures are used for solving the equations of motion in transient analysis of structures with large displacements. In this context, we propose an algorithm that combines the α-Generalized implicit integration method with the Potra–Pták two-step iterative scheme. The free Scilab program develops a computer code for the non-linear dynamic analysis of plane frames with large displacements and rotations. The FEM corotational formulation discretizes the structures considering the Euler-Bernoulli beam theory. The null-length connection element described by the axial, translational and rotational stiffnesses simulate the behavior of the beam-column connection. Jacobi’s method and the Scilab’s spec function determine the natural frequencies. The developed program is used for modal and transient dynamic analyses of frame problems available in the literature. The numerical results show that the Potra-Pták scheme obtains approximate solutions with fewer cumulative iterations until convergence and shorter processing time compared to the standard Newton-Raphson scheme. Further-more, the results show that the type of beam-column connection affects the vibratory behavior of the structure as well as the values of its natural frequencies.