The Poly-SAFE method: A semi-analytical representation of finite element models via nested polynomial reduction of modal data

Abstract

This paper introduces a novel semi-analytical representation of a displacement-based finite element model reduced via nested polynomials obtained through fitting of modal data. This method, termed Poly-SAFE (Polynomial Semi-Analytical Finite Element), is particularly suitable for modelling thin-walled composite structures subject to recursive analyses under varying loads, a common scenario in fluid–structure interaction (FSI) and Progressive Failure Assessment (PFA). The resulting functionals, i.e. polynomials inside polynomials, can be evaluated in an analytical fashion to yield displacements at arbitrary positions not limited to typical finite element grid nodes. These functionals remain virtually load-independent, allowing a Poly-SAFE model to be constructed without previous knowledge of magnitude, direction and location of applied loads, either static or dynamic. In this paper the theoretical framework of the Poly-SAFE method is presented in some detail, followed by an application of the theory to an extruded airfoil-shaped, laminated thin-walled beam subject to static loads. The displacement field captured by the new method is compared to the predictions of its associated finite element model, showing an excellent overall agreement. Finally, the advantages of Poly-SAFE against FE models in specific analyses and contexts are emphasised.