SYMPLECTIC-MOMENTUM CONSERVING TIME STEPPING ALGORITHM FOR THE REISSNER-SIMO THEORY OF RODS

P. MATA; S. OLLER; A.H. BARBAT

Conferencia; COMPDYN 2009 ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering; 2009

A new explicit symplectic-momentum conserving algorithm for simulating the nonlineardynamics of conservative problems of geometrically exact rods with large rotations isdeveloped. The integration procedure is based on the simultaneous space and time discretization of the Lagrangian funtional of the system. The resulting variational integrator corresponds to the discrete EulerLagrange equations, which are explicit, second order accurate and can be identified with the generalized trapezoidal rule with constant time step. The spatially discrete form of the problem is obtained using the FEM for both the rotational and the translational parts of the motion and the time discretization is performed on the resulting nodal variables. The discrete Lagrange transform is used for deducing the position-momentum form of the algorithm. The proposed method avoids the numerical difficulties associated to the indefiniteness of the stiffness matrix near unstable configurations frequently appearing in iterative schemes of the Newton type. Most of the advantages of the variational integrators are clearly evidenced in numerical experiments for typical problems of technological interest.