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We present an enhanced version of the parametric nonlinear reduced ordermodel for shape imperfections in structural dynamics we studied in a previouswork [1]. The model is computed intrusively and with no training usinginformation about the nominal geometry of the structure and some user-defineddisplacement fields representing shape defects, i.e. small deviations from thenominal geometry parametrized by their respective amplitudes. The linearsuperposition of these artificial displacements describe the defected geometryand can be embedded in the strain formulation in such a way that, in the end,nonlinear internal elastic forces can be expressed as a polynomial function ofboth these defect fields and the actual displacement field. This way, atensorial representation of the internal forces can be obtained and, owning thereduction in size of the model given by a Galerkin projection, high simulationspeed-ups can be achieved. We show that by adopting a rigorous deformationframework we are able to achieve better accuracy as compared to the previouswork. In particular, exploiting Neumann expansion in the definition of theGreen-Lagrange strain tensor, we show that our previous model is a lower orderapproximation with respect to the one we present now. Two numerical examples ofa clamped beam and a MEMS gyroscope finally demonstrate the benefits of themethod in terms of speed and increased accuracy.

An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion