Mixed continuous-discrete variable optimization of composite panels using surrogate models

One of the major challenges in successful design of modern aeronautical structure is to reduce the total weight of the system. In the recent decades, applications with unidirectional thermoplastic composite parts are considerably increased.Thermoplastic composites show performance benefits compared to previous used material. Moreover, unlike conventional materials, composites can be tailored with specific lay-out to satisfy certain requirements. However, the high number of variables involved and the complex mechanics associated to composites, makes the optimum design difficult to achieve. Structural optimization, due to its systematic nature and to the possibility of setting defined objectives, becomes the most suitable approach to support the designer, obtaining the expected properties. Nowadays, most of the optimization codes deal with continuous variables. On the other hand, new production technologies of unidirectional composite panels require handling some discrete parameters (e.g. thickness), giving more freedom for others (e.g. fiber orientation). Tape placement is considered the most promising. It consists in placing continuous strips of unidirectional thermoplastic composite and consolidating them in-situ. Therefore, a continuous-discrete variable optimization approach becomes essential to obtain a feasible optimum design from the engineering point of view. In this work, the authors show a weight optimization procedure developed for the design of composite panels under axial-compression. Minimum weight is the objective. Fiber angles are assumed to be continuous variables; thicknesses of single layers have discrete values. Moreover, the problem is subject to first-buckling constraints. This is a crucial point for the accomplishment of a successful optimization. The constraint behavior is not known a priori. A high number of FEM analyses have to be run. The data interpolated and the first-buckling function approximated. Otherwise, to reduce computational and experimental costs, a surrogate model, that provides a fast approximation of the considered function, can be used. It is generated from a limited number of information given from FEM calculations and/or from tests. To create the surrogate, several designs are generated (PRE-OPTIMIZATION, figure 1). Every design space is filled with N sampling points, which represent N combination of