Abstract
We present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.
Highlights
The finite element (FE) method has long been a fundamental analysis and design tool in many areas of science and engineering
We presented a reducedorder model (ROM) for geometric nonlinearities that can parametrically describe a shape imperfection with respect to the nominal design, named for brevity DpROM
This result has been made possible thanks to a polynomial representation of the internal forces resulting from a two-step deformation process and from the approximation of the strains obtained by a Neumann expansion
Summary
The finite element (FE) method has long been a fundamental analysis and design tool in many areas of science and engineering. This need for fast and affordable FE simulations has given rise to numerical techniques to improve computational efficiency: Domain decomposition and substructuring [2,3] and FE Tearing and Interconnecting (FETI, [4]) are just a few examples. Guyan reduction [5] and modal analysis [6] are two well-known examples in mechanical statics and dynamics, respectively, where FOM’s static deformations and vibration modes (VMs, known as eigenmodes or natural modes of the linear system) are used to construct a reduced basis (RB) that projects the governing equations onto a lowerdimensional subspace. Linear ROMs were successfully coupled with substructuring techniques in the Craig–Bampton and Rubin methods [7,8], which are available in many commercial software
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