An effective method for assembling impulse response functions to linear and non-linear finite element models

The Impulse Based Substructuring (IBS) method has been proposed lately as an effective approach to evaluate the dynamic response of a system, using either the numerically or experimentally obtained Impulse Response Functions (IRFs) of its components. In this paper, the method will be combined with the (non-linear) Newmark time integration scheme in order to couple IRFs with linear and non-linear finite element models. In the linear case this is done by performing, for each time step, the Newmark step for the FE substructures and solving the convolution integrals for the IRFs simultaneously. After this, the interface forces are computed that are required to enforce compatibility between all the substructures. For the non-linear case, all the neighboring linear subsystems are condensed in the non-linear subsystems, which is then solved using Newton-Raphson iterations on this condensed (non-linear) problem. A general multi-degree-of-freedom case will be shown to illustrate the accuracy and versatility of the method. From the numerical results it is shown that the method yields the same results as a Newmark time integration, thereby showing that the IBS method can be an efficient method to quickly compute the response of a system obtained by assembling precomputed numerical components or measured substructures.