A short note for numerical analysis of dynamic contact considering impact and a very stiff spring-damper constraint on the contact point
By extending the numerical technique suggested by the author for the dynamic contact problem having a very stiff spring on the contact point, it is shown that the dynamic contact problem having a very stiff damper as well as a spring on the contact point can be time integrated without instability by imposing the time-differentiated constraints with the unconditionally stable Newmark time integration rule. It is also shown that the dynamic contact involving the repeated impacts and separations can be solved without instability by using the same time-differentiated constraints, and that the spring-damper deformation (i.e., penetration) on the contact point at the time of impact (i.e., at the first time step of contact) can be most reasonably determined by the displacement contact constraint. The special features of the present technique to solve the impact problem having a very stiff spring-damper on the contact point are that the equation of motion may be time integrated with any convenient ODE technique, and that the time step size reduction or the penetration threshold need not be considered at the time of impact.
KeywordsDynamic contact Impact Spring-damper Stiff constraint Multibody dynamics
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