Algorithms for Nonlinear Structural Dynamics

Several competitive numerical integration techniques for nonlinear dynamic analysis of structures by the finite element method are examined and compared for a plane stress problem. Both material and geometric nonlinearities are included in the finite element formulation. Three explicit methods are investigated: (1)Central difference predictor; (2)two-cycle iteration with the trapezoidal rule; and (3)fourth-order Runge-Kutta method. A nodewise solution technique is generated at any state in the analysis. Three implicit methods also are studied: Newmark-Beta method, Houbolt method, and Park's stiffly-stable method. Among the three explicit methods, it is concluded that the central difference predictor is the best, whereas the performances of the other two methods are about equal. The three implicit approaches are nearly equal, but Park's stiffly-stable method is somewhat better than the Newmark-Beta method, and Houbolt's procedure must be rated third.