DYNAMIC BOUNDARY INTEGRAL-EQUATION METHOD FOR UNILATERAL CONTACT PROBLEMS

The aim of the present paper is the extension of the method of boundary integral equations (B.I.E.) to dynamic unilateral contact problems. Using semidiscretization, with respect to time, and then the inequality constrained principle of minimum potential and the equivalent variational inequality formulation, we derive saddle point formulations for the problems using appropriate Langrangian functions. An elimination technique gives rise to a minimum 'principle' on the boundary with respect to the unknown normal displacements of the contact region, which has as parameters the velocities etc. of the previous time steps. It is also shown that the minimum problem is equivalent to a multivalued boundary integral equations problem involving symmetric operators. The theory is illustrated by numerical examples, which also treat the case of impact of the structure with its support. In order to achieve this last task, an appropriate time discretization scheme has been chosen. Numerical examples dealing with the seismic behaviour of two-dimensional structures supported by the ground are presented to illustrate the method.