This paper describes an approach based on Genetic Programming to perform the metamodelling of cellular structure properties with in-plane auxetic behaviour. Common procedures to design microstructure topologies with complex shape is to use analytical and/or Finite Element (FE) models and quantify the variability of their homogenised mechanical properties versus internal cell parameters. For the FE case, the large number of computations involved can rule out many approaches due to the expense of carrying out many runs. One way of circumnavigating this problem is to replace the true system by an approximate surrogate/replacement model, which is fast-running compared to the original. In traditional approaches using response surfaces a simple least-squares multinomial model is often adopted. The object of this paper is to extend the class of possible models considerably by carrying out a general symbolic regression using a Genetic Programming approach. The approach is demonstrated on the optimisation of the unit cell of centresymmetric auxetic cellular solids composing a simply supported plate for maximum central deflection under transverse uniform pressure.
|Surface Response Optimisation of Auxetic Homogenised Cellular Plates using Genetic Programming