Variable-stiffness composites optimisation under multiple design requirements and loads

Abstract

The aim of this paper is twofold. On the one hand, it presents a methodology for the deterministic optimisation of a general class of variable-stiffness composite (VSC) structures, including a solution obtained by using laminæ with a curvilinear fibres-path and variable-thickness, by considering different design requirements under multiple load cases. The considered framework is the multi-level design methodology based on the polar parameters (PPs) to describe the macroscopic behaviour of the VSC structure. Particularly, only the first-level problem is addressed in this work: the design variables are, thus, the PPs and the thickness of the VSC laminate, whose spatial distribution is described via basis spline (B-spline) surfaces. The goal is to minimise the mass of the VSC structure subject to design requirements on feasibility, strength, first buckling load and maximum curvature of the fibres-path. This latter is formulated as an equivalent (conservative) constraint in the PPs space, regardless of the fibres-path within each lamina. Moreover, a general formulation of the gradient of the requirements related to buckling load and strength is proposed, which takes advantage from the main properties of B-spline entities and PPs. On the other hand, this paper aims to propose a new benchmark problem that is representative of a panel belonging to the fuselage of a standard civil aircraft subjected to multiple loading conditions. To this end, a wide campaign of numerical tests has been performed by considering a sensitivity analysis of the optimised solution to: (a) the integer parameters involved in the definition of the B-spline entities describing the distribution of the PPs and, possibly, of the thickness, (b) the type of VSC structure, (c) the type of deterministic optimisation algorithm. The results can be used as a database to assess the effectiveness of different design strategies against the optimised solutions presented in this paper.