Static and Dynamic Analysis

In static analysis, there is no effect of mass (inertia) or of damping. In dynamic analysis, nodal forces associated with mass/inertia and damping are included. Static analysis is done using an implicit solver in LS-DYNA. Dynamic analysis can be done via the explicit solver or the implicit solver. In nonlinear implicit analysis, solution of each step requires a series of trial solutions (iterations) to establish equilibrium within a certain tolerance. In explicit analysis, no iteration is required as the nodal accelerations are solved directly. The time step in explicit analysis must be less than the Courant time step (time it takes a sound wave to travel across an element). Implicit transient analysis has no inherent limit on the size of the time step.

As such, implicit time steps are generally several orders of magnitude larger than explicit time steps. Implicit analysis requires a numerical solver to invert the stiffness matrix once or even several times over the course of a load/time step. This matrix inversion is an expensive operation, especially for large models. Explicit doesn'tm require this step. Explicit analysis handles nonlinearities with relative ease as compared to implicit analysis. This would include treatment of contact and material nonlinearities. In explicit dynamic analysis, nodal accelerations are solved directly (not iteratively) as the inverse of the diagonal mass matrix times the net nodal force vector where net nodal force includes contributions from exterior sources (body forces, applied pressure, contact, etc.), element stress, damping, bulk viscosity, and hourglass control.

Once accelerations are known at time n, velocities are calculated at time n+1/2, and displacements at time n+1. From displacements comes strain. From strain comes stress and the cycle is repeated (LS-Dyna Support.com, n.d.). (Hua Song et.al), (Jian Yang et.al) looked at the differences between application of FEA methods by Implicit-Explicit and the Explicit-Explicit techniques. It was reported that the Explicit-Explicit method exhibited the same level of accuracy as the common Implicit-Explicit method.

The Explicit-Explicit method had however, a faster solver which performed better than that in the implicit-explicit FEA method. Other researchers have tried analytical methods, (Mehmet Ali Arslan, 2011) documented that analytical methods describing the physics of the Rail–Wheel contact phenomenon were only defined for certain types of simple contact geometries. For complex geometries it was stated that, analytical models utilising closed formulations remained elusive. (Mehmet Ali Arslan, 2011) performed a static FEA analysis using Ansys on a section of a rail track and wheel profile to evaluate the stresses.