A finite element based large increment method for nonlinear structural dynamic analysis

For structural dynamic analysis with nonlinear materials, the displacement-based approach is widely used. In this method, in order to quickly reach convergence, Δt must be kept sufficiently small to control the accumulation of error and to avoid possible divergence of Newton-Raphson iterations. Thus, one can imagine the computational effort needed in each time step for each element, in each iteration, to reach a converged solution. The traditional displacement-based approach is obviously quite cumbersome. Thus the FE displacement approach may be associated with a lack of efficiency and computational speed. This paper presents a new force-based approach in an attempt to create robust and fast computational algorithms for nonlinear structural dynamics. The proposed algorithm is based on the developed flexibility-based large increment method (LIM) previously investigated by the present authors under quasistatic conditions. Unlike the displacement-based approach, LIM shows excellent computational benefits when used in nonlinear quasistatic analysis which can be summarized by large solution time steps, less number of iterations, and significantly fewer elements. Thus, this paper aims to present a framework to merge knowledge gained in the development of LIM for nonlinear structural analysis along with developments in mathematics ultimately to solve large and complex nonlinear structural dynamic problems in an efficient manner.