Keywords: sandwich, optimal design methodology.

Fibre reinforced composites (FRCs) are increasingly used as structural materials, due primarily to their excellent stiffness and weight characteristics. Additionally, the effectiveness can be increased in many applications by using these materials as facings in conjunction with low density core materials to form so-called sandwich laminates. For example, the in-plane load carrying capacity of laminates can be enhanced via sandwich construction[1,2]..

Anisotropic facesheets effect the buckling properties of sandwiches[3]. Thus, an advantage of FRC materials over conventional ones is the possibility of tailoring their properties to the specific requirements of a given application. The tailoring is mostly achieved by maximising the mechanical properties as a result of selecting the fibre angles of the skins optimally, and thus realising the full potential of fiber-reinforced sandwiches. It appears that only a few researchers have studied the optimisation of composite sandwich panels under buckling loads. Moh, for example, examined the benefits of selecting the fibre angles of the skins optimally[4], as did Rikards[5].

The high cost of FRCs may inhibit their use and it is thus essential to improve their cost effectiveness. One way that this may be done is to carefully select the skin/core material combination. In this study, a procedure to select the best material combination and optimally design sandwich laminates with fibre reinforced skins and low density cores for minimum cost is described. The optimal combination with least cost is determined by admitting different candidates into the design space. This space consists of three continuous variables, viz. the skin fibre angle, and the layer thickness of the skins and core. There is also one discrete variable in the design space; the material combination. The plates are optimised for minimum cost subject to a minimum buckling load and maximum mass constraint. The optimisation procedure has two stages and leads to an optimal design that is chosen from amongst the candidate designs.

For a particular buckling load capacity and mass requirement, together with a choice of skin and core material combinations that results in candidates, the design optimisation procedure consists of two steps:

Step 1.For each candidate, determine the skin fibre angle optimally by determining the value of for which the resulting skin and core thicknesses lead to a minimum candidate cost, viz.

subject to

and ,

where is the buckling load capacity required, and the maximum mass allowable.

Step 2. Select the cheapest candidate.

Given that the buckling load is dependant on , and , and the sandwich mass on and , for a particular design buckling load capacity and mass requirement, and can be determined (generally) for any value of . Thus, a suitable optimisation routine can be used to determine . Once and the resultant cost have been determined for each candidate, the cheapest is selected. For the optimisation, the Golden Section method is employed, and is determined within a prescribed accuracy of 1.

By way of conclusion, optimal designs of sandwich panels with FRC skins and low-density cores for minimum cost are obtained by the use of a procedure described in the paper. Candidates with different skin and core material combinations are each optimally designed for least cost subject to in-plane load and mass constraints, and then the cheapest candidate is selected. The examples used to demonstrate the procedure show that the best design candidate can be several magnitudes cheaper than the most expensive rival.

1

Muc, A., (2000), Buckling and failure analysis of FRP faced sandwich plates, Composite Structures, Vol. 48, No. 1, pp. 145. doi:10.1016/S0263-8223(99)00087-2

2

Hao, B., (2000), Buckling and Postbuckling of soft-core sandwich plates with composite facesheets, Computational Mechanics, Vol. 25, No. 5, pp. 421. doi:10.1007/s004660050489

3

Hause, T., (2000), Effect of face-sheet anisotrophy on buckling and postbuckling of sandwich plates, Journal of spacecraft and rockets, Vol. 37, No. 3, pp. 421. doi:10.2514/2.3583

4

Moh, J. S., (1997), Optimisation for buckling of composite sandwich plates, AIAA, Vol. 35, No. 5, pp. 863. doi:10.2514/2.7459

5

Rikards, R., (1997), Modelling, damping analysis and optimisation of sandwich and laminated composite structures, Pitman Research Notes in Mathematics Series, Wiley, New York, No. 374, pp. 149.

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