A numerical procedure is developed for the contact-impact analysis in deformable multibody systems. The variational method is used for the derivation of the equations of motion of constrained multibody systems. Elastic deformation is described by finite element method. Contact conditions for node to non-node contact are derived. Frictional effect based on Coulomb's friction law is included. The checking of contact status is separately made depending on the satisfaction of approximate conditions such as normal distance, stick or slip, and so on. The contacting point in the target is obtained by a linear interpolation scheme. The idea of constraint addition-deletion is used for the treatment of contact state.
A computer program has been developed based on the proposed algorithm to solve two dimensional or axisymmetric contact-impact problems. It is utilized to simulate the contact-impact of simple bodies. The results are used to study coefficients of restitution. The classical definition is shown to be rather ambiguous to be used for deformable bodies. New definitions are proposed and comparisons made.
Several examples are taken to test the method developed here. A sphere impacting against a rigid wall is simulated and the results are compared with the Hertz solution. Not much difference is shown in this case. A model of television bulb impact-test is simulated. The energy transfer between the impacting bodies is clearly shown. As an application of the method for the contact-impact analysis in deformable multibody systems, a flexible slider-crank mechanism is selected. The flexible connecting rod is discretized using four beam elements and slider and impacting cylinders are assumed axisymmetric. Dynamic stress histories and elastic deformations of the connecting rod are obtained and general trend discussed.
Through these examples, although very computation intensive, the algorithm is shown capable of producing reasonable numerical solutions for the local behavior of contact-impact.
