Implicit and Explicit Time Integration Methods for Nonlinear Structural Dynamics

Computational algorithms and solution techniques for dynamic analysis of structural systems have indeed matured over the decades. In general, there are two basic categories of step by step integration methods;explicit method and implicit method.A method is explicit if the equation of motion of the thstep and previous is used in determining the (step displacement. For very highly non-linear motion of the (i+1)th step is used in determining the (step displacement. For very highly non linearstructural dynamic analysis, the explicit central difference method is often used as the time integration algorithms. However, the conditional stability of the central difference method put a limit value on its time step. On the other hand, the implicit time integration algorithms are also typical choices of someanalysis, but require non-linear Newton–Raphson type iterations during each time step which may become time consuming. Many implicit time stepping algorithms have been proposed, some of which relies on Newton iterations algorithms to satisfy the equations of motion In the present work, comparison is made between explicit and implicit methods of computational analysis of structural dynamics under periodic loading. The material is assumed to be linear while large displacement is considered in 2D finite elements simulation.

Keywords:

Computational algorithms , structural dynamic implicit method , explicit method