## Static Nonlinear Solver (B2000++ Pro)

The static nonlinear solver allows for solving incremental static (stationary) nonlinear problems, i.e. static nonlinear problems that depend on an increment control parameter denoted λ .

The static nonlinear solver allows for solving static (stationary) non-linear problems. It is invoked by the MDL command analysis nonlinear; this command must be specified in the case block.

## 1. Applications

The static solver is most commonly used for stress analysis involving geometric, material, or boundary nonlinearity, and for heat transfer analysis involving nonlinear material or boundary behaviour.

Note For load-controlled quasi-static stress analysis with artificial damping, an alternative exists in the dynamic nonlinear solver, which can also be used for quasi-static stress analysis when specifying the MDL commands analysis dynamic_nonlinear residue_function_type artificial_damping Due to its predictor and its mechanism to control the time increment by means of an error estimator, the dynamic nonlinear solver may be - depending on the problem and depending on the solution parameters - more effective than the static nonlinear solver.

The static solver can also steer a weakly-coupled multi-disciplinary analysis, this is briefly explained for the case of steady-state aero-elasticity: The spatial coupling, CFD mesh deformation, and CFD solver are wrapped inside a specially-designed and implemented nonlinear natural boundary condition object. For each Newton iteration, the static solver evaluates the natural boundary condition for the solution field; in this case, the boundary condition returns the spatially mapped aerodynamic forces that were calculated from the deformed configuration.