Finite Element Modeling and Multivariate Optimization Over Fibre Orientation and Volume Fraction of Fibre Composite Parts Aimed at Minimizing Targeted Displacements

Abstract

A software program was written that implements a finite element analysis (FEA) solution as the basis of an optimization function used for guiding the inverse design problem of aligning fibres, minimizing displacements in a fibre-reinforced polymer composite part in response to a given loading condition, for various part geometries. The FEA solution makes use of the superlinear RGNTet4 element, which includes 3 displacement and 3 rotational degrees of freedom at 4 nodes. Convergence testing verified the accuracy of the solver versus symbolic results for simple cases. Multivariate optimization over fibre orientations and volume fractions was carried out for a simple test case using the NLOpt nonlinear optimization library. Both derivative-free and gradient-based algorithms were tested. Low-Storage Broyden-Fletcher-Goldfarb-Shannon was the most effective algorithm. Four more complex cases were examined, and by varying fibre orientations, reductions of 48%, 66%, 58% and 32% were achieved in displacements at the loaded nodes.