Analysis of composite beams using reduced order modeling

Abstract

Beam-like components help to provide structural integrity in a wide range of applications. Initially made of alloys or natural materials such as wood, today’s technologies like pultrusion make possible the manufacturing of such components with composite materials providing good quality products with high performance to weight ratio. The anisotropic nature of composite materials, though, poses a challenging framework when numerically simulating them. This work presents the integration in standard Finite Element (FE) packages of a machine learning methodology that naturally captures the behaviour of composite materials: the multiscale method for periodic structures using domain decomposition and ECM-hyper reduction. The method provides a special type of finite element that can be assembled using FE libraries. However, the kinematics of this element may be described by more Degrees of Freedom (DoF) per node than most standard FE packages consider, hence implementing it is a non-trivial task. The strategy presented here tries to tackle the limitation by means of static condensation followed by a regression procedure. Periodic boundary conditions are employed for the extra DoFs while the regression consists in a polynomial on the logarithmic space. This paper focuses on the performance of the integrated beam element through the analysis of a pultruded omega profile whose anisotropy requires the use of complex models to accurately capture its mechanical behaviour. The agreement between the results obtained with the proposed model and those given by more complex formulations validates the methodology and enables its use in regular FE codes to characterize complex composite beam structures