Appendix A: Theory Description

The Adams nonlinear flexible body employs a method that allows material, geometry, and contact nonlinearities that are available in a nonlinear finite element (FE) solver to be accounted for in Multi-Body System (MBS) simulations.

This method converts the equations of motion in nonlinear FE domain into phase-space form and discretizes them in time according to the MBS integrator settings. The resulting linearized FE equations have dynamic matrices on the left hand side and residual forces on the right hand side. The coupling of the MBS and FE equations is achieved through the interface connection grids that have states defined in both domains and constraint equations defined to enforce kinematic compatibility between the states. Condensation of the dynamic matrices and residual vector reduces the FE equations to the states on the connecting grids and produces terms from nonlinear FE parts that contributed to the physical and kinematic terms of the residual, and physical, kinematic and constraint terms of the Jacobian. These condensed terms from FE domain are of size significantly smaller than the original FE matrices and vectors so that they can be readily assembled in and solved by the MBS solver. The states of the interior FE grids are recovered from the states of the connecting grids by the nonlinear FE solve at each time step.

Data exchanges between the MBS and FE domain and the control of solution flow are implemented in a Simulation Component Architecture (SCA) framework with the nonlinear FE solver implemented as a Non-Linear Finite Element (NLFE) service. This method allows nearly all transient dynamic analysis capabilities, including the support of material nonlinearity, large displacement analysis, and self-contact to be available in the simulation of MBS. In addition, it allows multiple nonlinear FE parts to be included in a fully coupled simulation efficiently, with matrices and vectors from each FE part processed and condensed by separate computing resources, leveraging existing HPC methods for faster solve times.