This article presents a method for minimizing structural mass by optimizing the geometry and core density of sandwich beams comprising composite face sheets and polymer foam cores, loaded in three-point bending. The optimization is constrained by both strength and stiffness requirements. All possible locations in design space which might be global minima of mass are identified, and it is shown that, for a global minimum mass, at least two constraints must be simultaneously active. Calculations for a typical set of material properties are performed with the result that, for a wide range of standard materials, a minimum-mass sandwich beam satisfying both strength and stiffness requirements utilizes low-density foam and is constrained by stiffness and indentation strength.
AllenHG. Analysis and design of structural sandwich panels. Oxford: Pergamon Press, 1969.
2.
ZenkertD. An introduction to sandwich construction. Sheffield, UK: Engineering Materials Advisory Service, 1995.
3.
DanielIMAbotJLWangK-A. Failure modes of composite sandwich beams. Int J Damage Mech2002; 11(4): 309–334.
4.
EvansAG. Lightweight materials and structures. Mater Res Soc Bull2001; 26(10): 790–797.
5.
McCormackTMMillerRKeslerO. Failure of sandwich beams with metallic foam cores. Int J Solids Struct2001; 38(28–29): 4901–4920.
6.
ChirasSMummDREvansAG. The structural performance of near-optimized truss core panels. Int J Solids Struct2002; 39(15): 4093–4115.
7.
ZupanMDeshpandeVSFleckNA. The out-of-plane compressive behaviour of woven-core sandwich plates. Eur J Mech A Solids2004; 23(3): 411–421.
8.
ThomsenOT. Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localized loading. Compos Struct1993; 25(1–4): 511–520.
9.
FrostigYBaruchMVilnayO. High-order theory for sandwich-beam behavior with transversely flexible core. J Eng Mech1992; 118(5): 1026–1043.
10.
TriantafillouTCGibsonLJ. Minimum weight design of foam core sandwich panels for a given strength. Mater Sci Eng1987; 95: 55–62.
11.
WeaverPMAshbyMF. Material limits for shape efficiency. Prog Mater Sci1997; 41(1–2): 61–128.
12.
BudianskyB. On the minimum weights of compression structures. Int J Solids Struct1999; 36(24): 3677–3708.
13.
ChenCHarteA-MFleckNA. The plastic collapse of sandwich beams with a metallic foam core. Int J Mech Sci2001; 43(6): 1483–1506.
14.
ValdevitLHutchinsonJWEvansAG. Structurally optimized sandwich panels with prismatic cores. Int J Solids Struct2004; 41(18–19): 5105–5124.
15.
SteevesCAFleckNA. Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part I: analytical models and minimum weight design. Int J Mech Sci2004; 46(4): 561–583.
16.
SteevesCAFleckNA. Material selection in sandwich beam construction. Scripta Mater2004; 50(10): 1335–1339.
17.
SwansonSRKimJ. Optimization of sandwich beams for concentrated loads. J Sandwich Struct Mater2002; 4(3): 273–293.
18.
SharmaRSRaghupathyVP. A holistic approach to static design of sandwich beams with foam cores. J Sandwich Struct Mater2008; 10(5): 429–441.
19.
GibsonLJAshbyMF. Cellular Solids, 2nd edn. Cambridge: Cambridge University Press, 1997.
SteevesCAFleckNA. Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part II: experimental investigation and numerical modelling. Int J Mech Sci2004; 46(4): 585–608.
22.
AshbyMFEvansAGFleckNA. Metal foams: a design guide. Boston, MA: Butterworth–Heinemann, 2000.
23.
ValenzaAFioreVCalabreseL. Three-point flexural behaviour of GFRP sandwich composites: a failure map. Adv Compos Mater2010; 19(1): 79–90.
ChenCFleckNA. A creep model for polymeric foams. Technical Report CUED/C-MICROMECH/TR.32, Cambridge Centre for Micromechanics, University of Cambridge, July 2000.
