Nonlinear dynamics

As mentioned earlier, the modal dynamics procedure is suitable only for linear problems. When nonlinear dynamic response is of interest, the equations of motion must be integrated directly. The direct-integration of the equations of motion is performed in Abaqus/Standard using an implicit dynamics procedure. When this procedure is used, the mass, damping, and stiffness matrices are assembled and the equation of dynamic equilibrium is solved at each point in time. Since these operations are computationally intensive, direct-integration dynamics is more expensive than the modal methods.

Since the nonlinear dynamic procedure in Abaqus/Standard uses implicit time integration, it is suitable for nonlinear structural dynamics problems, for example, in which a sudden event initiates the dynamic response, such as an impact, or when the structural response involves large amounts of energy being dissipated by plasticity or viscous damping. In such studies the high frequency response, which is important initially, is damped out rapidly by the dissipative mechanisms in the model.

An alternative for nonlinear dynamic analyses is the explicit dynamics procedure available in Abaqus/Explicit. As discussed in Abaqus Basics, the explicit algorithm propagates the solution as a stress wave through the model, one element at a time. Thus, it is most suitable for applications in which stress wave effects are important and in which the event time being simulated is short (typically less than one second).

Another advantage associated with the explicit algorithm is that it can model discontinuous nonlinearities such as contact and failure more easily than Abaqus/Standard. Large, highly discontinuous problems are often more easily modeled with Abaqus/Explicit, even if the response is quasi-static. Explicit dynamic analyses are discussed further in Nonlinear Explicit Dynamics.