11 APRIL 2019

As mentioned in our previous article “Roll Over Protective Structure (ROPS) simulation: an opportunity to evaluate explicit solver performance in quasi-static phenomena”, NOVA demonstrates, thanks to its solid FEA analysis experience that quasi-static simulation can be solved via explicit time integration solving scheme.

When running any FEA analysis, the target is to reach the best compromise, both in terms of result accuracy and convergence speed. It has been proven that if correctly set up, an explicit solver can provide very precise solutions with high convergence speed if compared with real in field tests. The result reliability is strongly affected by the energy error percentage; if the error is negative it means some energy has been dissipated, while if positive there is an energy creation.

Considering RADIOSS explicit solver, the energy error percentage depends on translational and rotational kinetic energy, internal energy, work of external forces and energy at the beginning of the run.

Figure 1: Available energy forms in RADIOSS output

In case of using QEPH shell formulation or fully integrated elements, the energy error percentage can be slightly positive since no hourglass is involved and its computation is much more accurate (%E=1÷2%). In case of a more important positive energy, the source of this energy must be identified as related to incompatible kinematic conditions.

Therefore, explicit analysis should be prepared by managing and reducing most critical problems related to the undesired dynamic phenomena such as the stabilization of the kinetic energy. An explicit solver, such as RADIOSS, can handle the capability of stabilizing the energy during the whole duration of the simulation. To reduce the dynamic effect, both dynamic and kinetic energy relaxation can be used by activating /DYREL & /KEREL control cards in the engine file. The concept of dynamic relaxation was first introduced by Otter and has been used in several hydrodynamic codes.

The effect of the dynamic relaxation is to speed up converge through static solution by introducing a diagonal damping matrix proportional to the mass matrix as a function of the period to be damped. The main parameters that must be set while handling with dynamic relaxation are relaxation factor β and the period to be damped Τ, that must be less than or equal to the largest period of the system. While relaxation factor β value is usually recommended, the value of the period to be damped Τ must be set by launching iterative simulation analysis to detect the first oscillation period of the system to be diagnosed. Using an explicit code, application of the dashpot force reduces the velocity equation modification according to (Eq.1).

Kinetic equations with relaxation are considered under the basic assumption of two collision invariants, namely mass and energy. This empirical methodology consists in setting to zero the nodal velocities each time the kinetic energy reaches a maximum.

Figure 2: Kinetic relaxation method with the /KEREL option (also named energy discrete relaxation)

The following article demonstrates once more the flexibility of explicit solvers, highlighting their power in solving as well static non-linear analysis. Thanks to the comprehensive experience acquired in performing static non-linear analysis with explicit solvers, NOVA has expanded its' knowledge on setting relaxation parameters to keep error energy percentage under control for the whole duration of the analysis. These results in the capability of obtaining numerical models that completely fulfill costumers’ requirements in terms of both accuracy and promptness of the results with respect to real in-field tests.

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11 APRIL 2019

As mentioned in our previous article “Roll Over Protective Structure (ROPS) simulation: an opportunity to evaluate explicit solver performance in quasi-static phenomena”, NOVA demonstrates, thanks to its solid FEA analysis experience that quasi-static simulation can be solved via explicit time integration solving scheme.

When running any FEA analysis, the target is to reach the best compromise, both in terms of result accuracy and convergence speed. It has been proven that if correctly set up, an explicit solver can provide very precise solutions with high convergence speed if compared with real in field tests. The result reliability is strongly affected by the energy error percentage; if the error is negative it means some energy has been dissipated, while if positive there is an energy creation.

Considering RADIOSS explicit solver, the energy error percentage depends on translational and rotational kinetic energy, internal energy, work of external forces and energy at the beginning of the run.

In case of using QEPH shell formulation or fully integrated elements, the energy error percentage can be slightly positive since no hourglass is involved and its computation is much more accurate (%E=1÷2%). In case of a more important positive energy, the source of this energy must be identified as related to incompatible kinematic conditions.

Therefore, explicit analysis should be prepared by managing and reducing most critical problems related to the undesired dynamic phenomena such as the stabilization of the kinetic energy. An explicit solver, such as RADIOSS, can handle the capability of stabilizing the energy during the whole duration of the simulation. To reduce the dynamic effect, both dynamic and kinetic energy relaxation can be used by activating /DYREL & /KEREL control cards in the engine file. The concept of dynamic relaxation was first introduced by Otter and has been used in several hydrodynamic codes.

The effect of the dynamic relaxation is to speed up converge through static solution by introducing a diagonal damping matrix proportional to the mass matrix as a function of the period to be damped. The main parameters that must be set while handling with dynamic relaxation are relaxation factor β and the period to be damped Τ, that must be less than or equal to the largest period of the system. While relaxation factor β value is usually recommended, the value of the period to be damped Τ must be set by launching iterative simulation analysis to detect the first oscillation period of the system to be diagnosed. Using an explicit code, application of the dashpot force reduces the velocity equation modification according to (Eq.1).