Metamodels in optimisation of plywood sandwich panels

Abstract

In this paper, the strength and the weight effectiveness for the plywood I-core sandwich structure is elaborated. For the plywood sandwich concept the plywood sheets are used at the outer surfaces to maximize rigidity while introducing in between adhesively bonded plywood stiffeners to keep the whole sandwich structure together. The structural stiffness capacity and weight efficiency are elaborated for the pure plywood structure and the I-core sandwich panel with the corresponding height and width dimensions. A metamodelling procedure is applied by approximating the finite element stiffness response values with parametrical functions employing the Adaptive Basis Function Construction approach. The resulting design procedure provides an effective optimal design tool that enables to estimate the stiffness and the weight optimum solutions. ing practice, as they require low number of sample points and are computationally very efficient. On other hand they are loosing efficiency when highly nonlinear behaviour should be approximated. Instead, higher-degree polynomials can be employed. However, if no special care is taken, they tend to overfit the data and produce high errors especially in regions where the sample points are relatively sparse. One possible remedy for the overfitting problem is employment of the subset selection techniques. These are aimed to identify the best (or near best) subset of individual polynomial terms (basis functions) to include in the model while discarding the unnecessary ones, in this manner creating a sparse polynomial model of increased predictive performance. However the approach of subset selection assumes that the chosen fixed full set of userpredefined basis functions (usually predefined just by fixing the maximal degree of a polynomial) contains a subset that is sufficient to describe the target relation sufficiently well. Hence the effectiveness of subset selection largely depends on whether or not the predefined set of basis functions contains such a subset. In this study a different sparse polynomial model building approach is used – Adaptive Basis Function Construction, ABFC (Jekabsons 2008, Jekabsons & Lavendels 2008). The approach enables generating sparse polynomials of arbitrary complexity and degree without the requirement to predefine any basis functions or to set the degree – all the required basis functions are constructed adaptively specifically for the data at hand. Additionally, in contrast to a number of other state-of-the-art metamodelling techniques the models built by the ABFC can be expressed as explicit and simple-to-use regression equations. Assuming that x is an input to the actual computer analysis or natural test, generally a polynomial regression model can be defined as a basis function expansion: