Dynamic contact of deformable bodies

The objective of this thesis is to develop a new incremental finite elementmodel with neither a need for special artificial elements nor requiring thedetermination of flexibility matrices and/or the introduction of extraneous orartificial variables to simulate the dynamic behavior of elastic bodies in contact.The proposed model exploits the direct simulation method previously reported forthe treatment of static problems for the solution of frictionless elasto-dynamicbehavior of contact bodies. The mathematical model is based upon a dynamicequilibrium formulation which is piece wise linear over time intervals betweencontact and separation events. The differential equations of motion can either bedirectly integrated over time or indirectly integrated using modal analysis andeigenmode expansion. The theoretical formulation of the undamped dynamiccontact problem as well as a complete algorithm are given. The method is firstapplied to the undamped, unilateral response of beams and plates on masslessspring foundations. The direct simulation procedure is used next to solve two-body problems whose impact conditions are either elastic or inelastic. Thenumerical treatment includes two identical and two dissimilar elastic bars.Numerical results for a dynamic Hertz problem concerning identical anddissimilar cylinders are also given. The results include contact time, contactforce, displacement and velocity histories, stress histories, deflections anddeformations. These are plotted and discussed. The results provide new insightinto the physics as well as the computaional aspects of dynamic simulation.