A C++ pseudo-arclength pathfollowing scheme for generally nondifferentiable multi-dof dynamic systems

The  computational efficiency of an enhanced version of a pseudo-arclength pathfollowing scheme tailored for general multi-degree-of-freedom (multi-dof) nonlinear dynamical systems is discussed. The pathfollowing approach is based on the numerical computation of the Poincaré map  and its Jacobian in order to tackle nonautonomous systems  with discontinuous vector fields.

The scheme is applied to obtain  frequency response curves of multi-dof hysteretic systems with a state vector size up to 120, as well as various reduced-order  models of single and multiple cantilever beams on a shuttle mass.  The proposed approach is shown to drastically increase the speed of convergence in the modified Newton-Raphson scheme thanks to a Krylov sub-space iteration which makes use of the LU decomposition of a frozen Jacobian matrix, which, upon convergence, becomes the monodromy matrix.

If you use this software, please cite this work as: G. Formica, F. Milicchio, W. Lacarbonara, "A Krylov accelerated Newton–Raphson scheme for efficient pseudo-arclength pathfollowing", International Journal of Non-Linear Mechanics, Vol. 145.