21st Congress of International Council of the Aeronautical Sciences, Melbourne, Australia, 13-18 September, 1998
Paper ICAS-98-4.9.4

STRUCTURAL DYNAMIC ANALYSIS OF NON-LINEAR MULTIBODY SYSTEMS BY A TIME-DISCONTINUOUS GALERKIN FINITE ELEMENT FORMULATION

Damilano J. G., Duarte J. A. A.
CTA/IAE/ASE-E, Brazil

Keywords: structural dynamic analysis, non-linear multibody systems, time-discontinuous galerkin, finite element formulation

This paper is concerned with an adaptive time-stepping algorithm to solve the equations of motion , of nonlinear constrained multi body systems discretized using the finite element method. A time-discontinuous Galerkin scheme is used as the basis for the formulation. The resulting scheme presents unconditional stability, third order accuracy and high frequency numerical damping. The Lagrange multiplier technique is used to enforce the kinematic constraints among the bodies. The formulation uses Cartesian coordinates to represent the position of each body with respect to an inertial system. The adaptive time-stepping algorithm selects time step sizes that reduce computational cost and maintain the accuracy of the solution. The results presented confirm the high order accuracy of the scheme and the significant reduction in computational cost of the solutions. Two examples are successfully analyzed with the algorithm: a nonlinear oscillator and a simple nonlinear constrained multi body system. In light of the results the algorithm seems to be very promising to treat complex nonlinear elastic multibody systems.

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