Dynamic Nonlinear Solver (B2000++ Pro)

The dynamic nonlinear solver adopts for the implicit time integration the backward differential formula (BDF) method which is well suited for stiff ordinary differential equations [Shampine79] like the ones encountered in stress analysis. The second-order BDF is applied by default, giving unconditional nonlinear stability. For computational efficiency, the time step size is adapted during the analysis using the Nordsieck transformation method [Nordsieck62]. For stability and accuracy of the time integration method, the rate of increment of the step size is limited [Calvo87] and the step size is controlled using Milne's device error estimator [Milne70].

The solver is invoked by the MDL command analysis dynamic_nonlinear; this command must be specified in the case block.

In general, the analysis duration is not 1 (second), and an analysis stage must be defined in the case definition, scaled by the duration. Refer to the first of the examples below for details.

1. Applications

In stress analysis, the dynamic solver can be applied to problems involving inertia forces or viscous forces. Like the static nonlinear solver, the problem to be solved may involve any kind of geometric, material, or boundary nonlinearities. Typical uses are:

  • Relaxation and creep analysis, in conjunction with visco-elastic materials

  • Dynamic buckling analysis with or without artificial damping

  • Quasi-static buckling analysis with artificial damping

In heat-transfer analysis, typical applications are nonlinear loading (e.g. cyclic loading) and predicting the non-stationary behaviour (i.e. the evolution of the temperature field). Like the static nonlinear solver, the problem to be solved may involve any kind of material or boundary nonlinearity.