Keywords: self-design, optimisation, minimum mass, finite element method.

Together with the growing demand for composites is the requirement for optimally designed structures with minimum mass. A number of studies concerning the minimum weight design of composite structures appear in the literature. The majority select some of the design variables as optimisation variables and attempt to determine their optimal values. For example, Walker et al [1] carried out an optimisation design study of laminated plates with the objective of minimising the deflection and weight, using finite element analysis and the Golden Section method, and this was limited to two design variables, viz. fibre orientation and layer thickness, while Adali et al [2] investigated the minimum weight and deflection design of thick sandwich laminates via symbolic computation. In contrast to these studies, some describe methodologies to minimise the mass of composite structures, like the papers by Walker and Smith [3,4]. In the first instance, a process is described which results in the optimal selection of material combinations, layer thicknesses and fibre orientations, and in the second, a technique for using genetic algorithms together with the finite element method is presented. The set of optimising variables in this case is discrete, and the objective was to minimise the mass of the composite structure.

So-called self-design research programmes generally deal with two and three- dimensional topological optimisation issues [5]. Most combine a procedure with finite element analysis, with the aim usually of adding material where stresses are high, and removing material where they are low, and work in an iterative manner. After each iteration, remeshing of the remaining geometry occurs, in order to ensure the accuracy of the finite element model and so that the shape becomes clear. All of the studies discussed in the literature deal with the optimisation of structures composed of isotropic materials, and trials have shown that large amounts of material can be removed without the structure failing.

The application of similar self-design methodologies to laminated composite structures is problematic, due to the orthotropic nature of these materials. The best approach would be to determine the optimal fibre orientations and laminae thicknesses at each iteration, so that the directional properties of these materials are optimally utilized, particularly as the shape (and thus load path) changes. This is difficult when there are several layers and thus many extra design variables. This paper presents a very simple self-design procedure for laminated composite structures, which works in conjunction with the finite element method. Remeshing during each iteration is not carried out, and the original laminae fibre orientations and thicknesses remain constant (for simplicity). Two test cases are used to illustrate the procedure, and it is shown that large mass savings are possible without affecting the integrity of the structure. In addition, it is also shown that remeshing is unnecessary.

1

M. Walker, T. Reiss, S. Adali, "Optimal design of symmetrically laminated plates for minimum deflection and weight", Composite Structures, 39(3 - 4), pp. 337-346, 1997. doi:10.1016/S0263-8223(97)00109-8

2

S. Adali, E.B. Summers, VE Verijenko, "Minimum weight and deflection design of thick sandwich laminates via symbolic computation", Composite Structures, 29, pp.145-160, 1994. doi:10.1016/0263-8223(94)90096-5

3

M. Walker, R.E. Smith, "A procedure to select the best material combination and optimally design composite sandwich cylindrical shells for minimum mass". Submitted to Structural Engineering and Mechanics.

4

M. Walker, R.E. Smith, "A technique for using genetic algorithms and finite element analysis to minimise the mass of laminated composite structures", Submitted to Finite Elements in Analysis and Design.

5

J.W. Bull, Z. Pitouras, "A review of the self-designing approach on the optimisation of engineering structures". Proc. Eighth Int. Conf. Civil and Structural Computing, Civil-Comp Press, Stirling, UK, 2001, Paper 96. doi:10.4203/ccp.73.96

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