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EN
This paper describes an approach based on Genetic Programming to perform the meta-modelling 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 pararneters. 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.
EN
In this paper the static and dynamic performances of sandwich structures with in-plane negative Poisson's ratio core are investigated from an analytical point of view. The cellular material theory is applied to calculate the orthotropic mechanical properties of re-entrant cell honeycomb cores, which shows negative Poisson's ratio values. This special geometrical layout of the cells allows higher out-of-plane shear modulus, compared to the one of regular honeycombs. The laminate orthotropic plate theory with shear correction factors is applied in order to describe the static and dynamic behaviour of symmetric sandwich plates with different core to sheet thickness ratios. Comparisons are made with analogous structures with regular honeycomb. The maximum deflections due to uniform pressure and buckling loads are enhanced, while the natural frequencies show a slight enhancing for some parameters of the cells.
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