22nd Congress of International Council of the Aeronautical Sciences, Harrogate, UK, 28 August - 1st September, 2000
Paper ICAS 2000-4.6.R1

NONLINEAR ELASTIC CONSTRAINED MULTIBODY SYSTEMS - AN ADAPTIVE TIME-STEPPING ALGORITHM BASED ON THE TIME-DISCONTINUOUS GALERKIN SCHEME

J. G. Damilano
Instituto de Aeronáutica e Espaço, Centro Técnico Aeroespacial, CTA/IAE/ASE, BRAZIL

Keywords: multibody systems, structural dynamics, nonlinear dynamics, time-discontinuous galerkin

This work is related to the time integration of the equations of motion of nonlinear constrained multibody systems discretized using the finite element method. The resulting system of nonlinear differential-algebraic equations is prone to high frequency oscillations and instabilities of a purely numerical origin. A time-discontinuous Galerkin scheme is used to obtain the transient responses of the system. The scheme is cast in a predictor-multicorrector form, which provides unconditional stability, third order accuracy and high frequency numerical dissipation. The total energy of the system, which monitors the stability characteristics of the response, is used as error measure and a time step adaptation algorithm is employed. The scheme is not sensitive to configuration singularities that may occur during the motion of the structural system. Some of the results presented, compared to their analytical counterparts, showed excellent agreement. Kinematic constraints are satisfied at the order of machine accuracy. The algorithm may be fully implemented on existing structural dynamic computer codes requiring minor modifications on the routines. Already implemented nonlinear structural finite element libraries do not need to be rewritten. However, the finite element formulation of the mechanical joints has to be done accordingly and then included into the code’s library of elements.

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