Technical Report A materials selection procedure for sandwiched beams via parametric optimization with applications in automotive industry Mohamed F. Aly a,⇑ , Karim T. Hamza b , Mahmoud M. Farag a a Dept. Mech. Eng., The American University in Cairo, Egypt b Dept. Mech. Eng., University of Michigan, Ann Arbor, MI 48109, United States article info Article history: Received 17 June 2013 Accepted 27 October 2013 Available online 16 November 2013 abstract The future of automotive industry faces many challenges in meeting increasingly strict restrictions on emissions, energy usage and recyclability of components alongside the need to maintain cost competive- ness. Weight reduction through innovative design of components and proper material selection can have profound impact towards attaining such goals since most of the lifecycle energy usage occurs during the operation phase of a vehicle. In electric and hybrid vehicles, weight reduction has another important effect of extending the electric mode driving range between stops or gasoline mode. This paper adopts parametric models for design optimization and material selection of sandwich panels with the objective of weight and cost minimization subject to structural integrity constraints such as strength, stiffness and buckling resistance. The proposed design procedure employs a pre-compiled library of candidate sand- wich panel material combinations, for which optimization of the layered thicknesses is conducted and the best one is reported. Example demonstration studies from the automotive industry are presented for the replacement of Aluminum and Steel panels with polypropylene-filled sandwich panel alternatives. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Newer generations of vehicles are expected to comply with strict regulations in eco-friendliness such as reduced emissions, in- creased component recyclability and most importantly, reduced energy usage throughout the vehicle lifecycle. In addition, vehicles also need to comply with safety regulations with regards to struc- tural integrity and crashworthiness, as well as meet customers’ expectation in terms of price affordability and comfort (aesthetics, ergonomics, noise and vibrations). Rising up to the challenge of meeting all goals is a difficult task and not one without compro- mises. Weight reduction is one area of profound impact in the de- sign of vehicles. This is mainly because weight reduction reduces energy consumption during the use phase of a vehicle, and the fact that the use phase typically comprises about 85% of the lifecycle energy consumption. Approaches in weight reduction may be di- vided into: (i) innovative and optimized structural layout and topology of vehicle components and (ii) incorporation of advanced lightweight and composite materials. One category of composite materials that has high potential gain and is relatively easy to implement is that of sandwich panels. Sandwich panels [1] differ from normal panels in that they are comprised of multiple layers of different (at least two) materials (Fig. 1). The main principle is that soft/light materials can be used for the panel core while relatively stronger materials are used in the facing layers. This allows for increasing the thickness of the pa- nel, which often improves the structural attributes, while maintain- ing and/or reducing the weight. Several studies in the literature were dedicated to theoretical modeling and experimental verifica- tion of failure behaviors of sandwich panels [2–12]; Marissen [2] and Yeh [3] studied fatigue crack growth in Aramid-reinforced Aluminum laminates. Schoutens [4] proposed methodologies for direct measurement of stress–strain curves for metal-matrix com- posites. Bakos and Papanicolaou [5] examined the effects of surface finish on Aluminum face sandwich composites with fiber glass core. Steeves and Fleck [6,7] studied the collapse mechanisms under three-point loading of foam-core composite beams. He and Hu [8] compared simplified analysis models with experimental results for aluminum honeycomb sandwich composites. Barbieri et al. [9] applied a frequency response measurement technique to estimate the parameters of polyurethane core composites. Manalo et al. [10,11] compared a simplified fiber analysis model to experimental tests of laminated fiber glass glued to phenolic core beams, while Mostafa et al. [12] compared static shear tests with finite element analysis for PVC foam core composites. With several failure modes well understood and modeled, pos- ing the design of sandwich panels as an optimization problem has been an ongoing research activity [13–19]. Earlier attempts by Gibson [13] sought the minimization of weight for preset desirable 0261-3069/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.matdes.2013.10.075 ⇑ Corresponding author. Tel.: +20 26153088, mobile: +20 1001471011. E-mail address: mfawzyaly@aucegypt.edu (M.F. Aly). Materials and Design 56 (2014) 219–226 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes