Constrained generic substructure transformations in finite element model updating

Model updating is a powerful technique to improve finite element models of structures using measured data. One of the key requirements of updating is a set of candidate parameters that is able to correct the underlying error in the model. Often regions such as joints are very difficult to parameterise satisfactorily using physical design variables such as stiffnesses or dimensions. Parameters arising from generic element and substructure transformations are able to increase the range of candidate parameters, and furthermore are able to correct structural errors. However, unconstrained generic substructure transformations change the connectivity of the model matrices. In many instances retaining the connectivity is desirable and this paper derives constraint equations to do so. The method assumes that substructure eigenvalues are the parameters used in the global updating procedure and that the substructure eigenvector matrix is optimised to enforce the connectivity constraints. The method is demonstrated on a simple L shape test structure, where the substructure is the corner.