Modeling composite wing aeroelastic behavior with uncertain damage severity and material properties G. Georgiou a , A. Manan a , J.E. Cooper b,n a School of Engineering, University of Liverpool, Liverpool, L69 3GH, UK b Department of Aerospace Engineering, University of Bristol, Bristol, BS8 1TH, UK article info Article history: Received 20 June 2011 Received in revised form 1 May 2012 Accepted 7 May 2012 Available online 16 June 2012 Keywords: Composite wing Damage severity Uncertainty propagation Aeroelastic behavior abstract The effect of uncertain material properties and severity of damage on the aeroelastic behavior of a finite element composite wing model are predicted by applying the Polynomial Chaos Expansion method (PCE). Different damage modes, including the transverse matrix cracking and broken fibers, are induced into pre-defined locations in the laminates and the aeroelastic stability and dynamic response of the wing due to ‘‘1-cosine’’ vertical gusts are evaluated. For this purpose, PCE models that predict the variation due to uncertainty of the flutter speed and an ‘‘Interesting Quantity’’ (root shear force) of the wing box are developed based upon a small sample of observations, exploiting the efficient Latin Hypercube sampling technique. The uncer- tainty propagation on the output responses, in the form of probability density functions, is evaluated at low computational cost, implementing the PCE models and verified successfully against the actual results. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Composite materials are being used increasingly in aerospace structures, primarily due to their attractive strength– weight ratios. A further advantage is the inherent anisotropic behavior which can be exploited to induce beneficial bending–torsion couplings in aircraft wings during flight, thus providing a greater design flexibility compared with metallic structures. A number of aeroelastic tailoring applications have sought to use composite materials for a range of applications, including the increase of divergence speed, the minimization of drag, the reduction of gust loads, etc.[1–8]. However, the complex manufacturing process of fibrous laminates induces an increased number of possible uncertain geometrical (thickness) and material (in-plane moduli, fiber orientation, etc.) parameters, which affect in a considerable degree the strength and the overall performance of composite structures. Additionally, under monotonic or cyclic loading the strength difference between the fibers and the matrix is usually related to damage mechanisms. The damage process is initiated from defects randomly distributed in a ply, leading to the development of transverse and longitudinal matrix cracks, inter-laminar delamination and fiber fracture [9]. The transverse matrix cracking, which starts at low loads and propagates in the fiber direction, is the predominant damage mode related to a significant reduction of the effective stiffness and strength for composite laminates [10]. Taking into account that the initiation and propagation of transverse matrix cracks is a stochastic procedure, the severity of damage in composite materials represents a considerable source of uncertainty. Moreover, at high loads, the matrix cracking triggers also the growth of resin-dominated damage modes, such as delamination and fiber breakage, which is Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2012.05.003 n Corresponding author. Tel.: þ44 117 954 5388; fax: þ44 117 927 2771. E-mail addresses: g.georgiou@liverpool.ac.uk (G. Georgiou), j.e.cooper@bristol.ac.uk (J.E. Cooper). Mechanical Systems and Signal Processing 32 (2012) 32–43