Application of Tsai’s Theory for the Laminate Optimization of an Aerospace Wing Box

This work includes the application and evaluation of new methods to describe laminate stiffness and strength. Tsai et al. have shown that the trace of laminate stiffness is a rotationally invariant quantity and accurately describes the stiffness potential of a material [1]. In combination with a rotationally invariant strength criterion, the Unit Circle criterion, this allows a simple approach for the dimensioning of fiber composite structures [2]. The use of two biaxial, so called “double-double” [±ϕ/±ψ] sublaminates with the possibility of asymmetrical stacking sequences but homogenization of laminates further simplifies the design and manufacturing process of such structures [3].The principles mentioned above are applied as an example for the optimization of an aerospace wing box. They are compared with classical optimization algorithms, an Evolutionary Algorithm (EA) and the Adaptive Response Surface Method (ARSM) [4]. The wing box is optimized with respect to stiffness while simultaneously minimizing weight. It is shown that the use of [±ϕ/±ψ] sublaminates instead of the traditional [0/±45/90] sublaminates can lead to a weight reduction of the composite skins of more than 10%. The simplified search algorithm based on the principles of Tsai et al. yields a different sublaminate than the classical optimization methods EA and ARSM. The computational effort though can be significantly reduced with the former.