A Metamodel Based on Non-Uniform Rational Basis Spline Hyper-Surfaces for Optimisation of Composite Structures

Abstract

This study presents a new strategy to generate a surrogate model used for design purposes. The metamodel is based on Non-Uniform Rational Basis Spline (NURBS) hyper-surfaces and is able to fit non-convex sets of target points (TPs). The proposed method aims at determining all the parameters involved in the definition of the NURBS hyper-surface, i.e. control points (CPs) coordinates, weights, degrees, CPs number and knot-vector components. To this purpose, the problem of finding a suitable metamodel is formulated as a constrained non-linear programming problem (CNLPP) wherein the above variables are optimised in order to fit a set of TPs. Nevertheless, when the number of CPs and the degrees of the basis functions are included among the design variables, the resulting problem is defined over a space having a variable dimension. This problem is solved by means of a special genetic algorithm able to determine simultaneously the optimum value of both the design space size (related to the integer variables of the NURBS hyper-surface) and the NURBS hyper-surface continuous parameters. The NURBS-based metamodel is then used to emulate the first buckling load of a composite stiffened panel and it is used in the framework of a meaningful design problem.