RIGIDBODY_TimeIntegrationVersion

If the MOVE statement of a geometrical unit / body is %MOVE_rigid% (see there) or %MOVE_MassSpringDashpot% , then the time integration of the equations of motion is solved explicitly. Version 2 mainly allows also body-body and body-boundary collisions. For this, the time integration of the rotation has to be reduced from quasi-analytical to first/second order in time. Default: RIGIDBODY_TimeIntegrationVersion = 1 The collision model (see RIGIDBODY_UseCollisionModel ) can only be chosen with version 2. Default settings for version 2 are : RIGIDBODY_TimeIntegrationVersion = [ 2.0, 0.0, 0.0, 0.0, 0.5, 1e5 ] Optional arguments:

• N_sub: define the permissible number of sub-iterations for the RIGIDBODY structure per MESHFREE time cycle, so the numerical time step size for the RIGIDBODY structure (RB) would be \( \Delta t_\text{sub}=\frac{\Delta t_\text{MESHFREE}}{N_\text{sub}}\)
• dt_fix: define numerical time step size for the RIGIDBODY structure
• extrapolationRigidBodyForces: extrapolate the forces/moments acting on the COG of a %MOVE_RigidBody% a little bit into the future: \( \mathbf{F}_{applied}^{n} = (1+\alpha) \cdot \mathbf{F}^n - \alpha \cdot \mathbf{F}^{n-1}\) where the dynamics of the RIGIDBODY is updated by \( \mathbf{v}^{n+1} = \mathbf{v}^n + \frac{\nabla t}{m} \mathbf{F}_{applied}^{n}\) Similarly, we treat an applied moment for the rotation of the body. Remark: choosing \( \alpha=0.5\) would result in a second order ansatz for the forces / moments. might be very precise, but maybe unstable.
• extrapolationSpringSashpotForces: similar like above, the forces for a %MOVE_MassSpringDashpot% element are extrapolated .
• MaxNiterAbort : A maximum upperlimit added for the number of sub-iterations above which the simulation will be aborted. Typically, during collisions or computing contact forces RIGIDBODY sub-timestep falls below the user-prescribed dt_fix: . This may create extremely small timsteps and result in a non-converging solution. With this value you can provide an upper limit to abort the simulation. Default is : 1e5, i.e. for each MF timestep the maximum number of sub-iterations can be 1e5. REMARK: by putting a minus sign in front, the user suppresses the abort of the running simulation, if the MaxNiterAbort is triggered. Insted, the simulation continues with the hope, that the next time step behave in a more regular fashion.

Taking into account the optional arguments, the numerical time step size for the RIGIDBODY structure is \( \Delta t_\text{RB} = \min \left( \Delta t_\text{sub} , \Delta t_\text{fix} \right)\)

• Version 1: second order for the velocity, but quasianalytical for the rotation (exact integration of the Euler equation for rotation)
• Version 2: second order for velocity and rotation (in this way, implicit collision and joint/link forces can be taken into account)

See also RIGIDBODY.