An inflation load of 200 kPa is applied in the axisymmetric half-tire model
contained in
substructtire_axi_half.inp.
This is followed by a footprint load of 1650 N applied to the three-dimensional
half-tire model given in
substructtire_symmetric.inp;
and, subsequently, results are transferred to the full tire model with the
complete footprint load of 3300 N. All of these steps are run with the NLGEOM=YES parameter, so all preload effects including stress stiffening
are taken into account when the substructure is generated.
To retain degrees of freedom that are involved in contact constraints at the
footprint, it is necessary to replace the contact constraints with boundary
conditions. This is done once the footprint solution is obtained by fixing the
retained nodes in the deformed state and removing the contact pair between the
footprint patch and the road surface. Without this change, the contact
constraints produce large stiffness terms in the substructure stiffness that
can produce non-physical behavior at the usage level. The mechanical response
of the substructure is unchanged because the tire is held in its deformed state
by a fixed boundary condition. These boundary conditions on the retained
degrees of freedom are then released in the substructure generation step, in
which they are replaced with concentrated loads. To carry out these steps, it
is necessary to obtain the list of nodes in contact with the road. Hence, the
substructure is generated in a restart analysis following the analysis with the
preloads. This makes it possible to construct the list of nodes that are
involved in contact with the road at the end of the preloading. It is necessary
to activate element removal in the analysis prior to substructure generation to
enable the removal of the contact constraints.
To enhance the dynamic response of the substructure, several restrained
eigenmodes are included as generalized degrees of freedom. These restrained
eigenmodes are obtained from an eigenfrequency extraction step with all the
retained degrees of freedom restrained. In this example the first 20
eigenmodes, corresponding to a frequency range of 50 to 134 Hz, are computed.
With 67 nodes in the footprint, one rim node with six degrees of freedom, and
20 generalized degrees of freedom, the substructure has 227 degrees of freedom.
At the usage level the nodes that form the footprint patch in the tire model
are restrained to a single node. The steady-state response of the substructure
to harmonic footprint loading is analyzed over a range of frequencies from 40
to 130 Hz.
