Semismooth Newton solver for periodically-forced solutions to a unilateral contact formulation

Abstract eng:
The vibratory response of a periodically-forced generic mechanical system undergoing a unilateral contact condition is addressed. The unilateral contact constraint is reformulated as a nonsmooth Lipschitz continuous function. This allows the use of the so-called semismooth Newton method capable of solving the equations governing the dynamics and the unilateral contact constraints simultaneously. The assumed periodic solution and the contact force are approximated by truncated Fourier series before being incorporated in the solver after projection of the equations on the Fourier basis. Continuation of the solution harmonics with respect to the forcing frequency is performed. For a medium size system of 20 degrees-of-freedom, it it shown that convergence is achieved by comparing with the “reference” time-marching solution.

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