An Impulse Based Substructuring method for coupling impulse response functions and finite element models

• Published in: Computer methods in applied mechanics and engineering 2014-06, Vol.275, p.113-137
• Main Authors: van der Valk, Paul L.C., Rixen, Daniel J.
• Format: Article
• Language: English
• Subjects: Dynamic Substructuring; Dynamics; Finite element method; Finite elements; Impulse Based Substructuring; Impulse response; Impulse response functions; Joining; Mathematical analysis; Mathematical models; Substructures; Substructuring; Time integration
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2014.03.003

In the field of Dynamic Substructuring (DS), large and complex structures are divided into several smaller and simpler components. The linear substructures are subsequently described in their dominant dynamics and reassembled, allowing one to compute the coupled dynamic behavior. DS methods are often classified into two distinct families, the Frequency Based Substructuring (FBS) methods and Component Mode Synthesis (CMS) techniques. In the former substructures are assembled whose dynamics are described in terms of frequency response functions (FRFs) and the latter are used to reduce and assemble the substructure finite element (FE) models. Lately a new substructuring method has been proposed, one that does not fit the framework of the FBS and CMS methods. The method, named Impulse Based Substructuring (IBS), was first used to obtain the coupled response of a system by assembling its component impulse response functions (IRFs). In this paper the IBS method is extended, thereby allowing one to determine the coupled behavior of structures that are composed of both substructure FE models and substructure IRFs. The method can be regarded as an extension to the normal time integration methods used for obtaining the time responses of FE models. As the linear substructures (described in their IRFs) are fully condensed on the interface of the FE model, one can significantly reduce the computational cost required for time integrating otherwise large FE models. However, as the linear (IRF) domains are exactly accounted for, the IBS method can be seen as a dynamic condensation on the interface, but not as a reduction method in the classical sense. Nonetheless, one can regard IRFs as a sort of “superelements in time” and the IBS method can therefore serve as an attractive alternative to CMS methods in case these are not available in the applied FE modeling programs, or if a high spectral bandwidth of the substructure is required. The method proposed in this work is based on the generalized-α time integration scheme and it is analytically proven that it can be applied in such a way that the simulation results are identical to the responses obtained from a monolithic integration of the full system, thereby guaranteeing its stability and accuracy. The method is demonstrated using a numerical test case, where a wind turbine FE model is coupled with a the IRFs of a marine foundation.