Optimisation of composite materials using a multilevel decomposition approach

The design optimisation of thick composite components requires dealing with large number of design variables, highly non-linear equations and huge computational demand. A multi-level decomposition process has been developed to optimise these elements, investigating the potentialities of pre-existing approaches of the bioengineering field of hip and femoral implants. The strength of exploiting a multi-level decomposition process is related to the flexibility of choosing at each level specific optimisation methods which modulate according to the design variables appointed and to the difficulty level of the application. Specifically the proposed framework is developed through two main applications, Basic and Intermediate Example, with increasing difficulty. The Basic Example uses Graphical Optimisation tools selecting the typical design variables such as thicknesses and orientation angles. Then, the Intermediate Example considers numerical optimisation conditions with Kuhn- Tucker and Lagrange Multipliers and again Graphical Methods, but using lamination parameters. The optimisation analyses and classical lamination theory calculations are performed through a Matlab code linked with an external solver, Nastran, to perform the numerical structural analysis. These two applications, designed as 2-level decomposition approach, do not consider any inter-laminar effect and out-of-plane loading that it will be taken into account in the proposed final frame work application, Advanced Example. A single level optimisation analysis is performed by commercial software optimiser, Nastran Sol 200, as alternative mean to validate the two numerical applications. Results show the potentiality of this technique, mainly related to the capability to control each design cycle, though the full understanding will come after a numerical application of the advanced example. In fact, adding within the current Matlab code genetic algorithms, sequential linear programming, and gradient based methods capable to deal with out-of-plane loadings, quadratic failure criteria taking into account the through-thickness stress effects is still a complex direction of enhancement recommended to be explored.