Topology optimization, variable stiffness design and staggered optimization for laminated composite structures: a comparative study

Abstract

The demand for efficient lightweight structures grows rapidly in the aerospace sector. Topology optimization, introduced in the late 80s, is a method capable of producing such structures and has been mainly studied for isotropic materials. On the other hand, the performance of composite structures, which are already widely employed in the aerospace industry, can be now improved due to the latest advances in manufacturing. Automated Fiber Placement has paved the way for further exploiting the capabilities of composites and led to the introduction of an optimization method, namely three-step variable stiffness design, that alters the fiber orientation within each ply, leading to a variable stiffness laminate. In this thesis, a staggered optimization method that simultaneously improves the material and the structural performance of balanced and symmetric laminated composite structures under planar loading is developed by coupling the two aforementioned methods. A finite element code is developed based on the equations for a static and linearly elastic problem. For the topology optimization problem, the nodal density values are used as design parameters and the Solid Isotropic Material with Penalization approach is chosen, along with a density filtering. The first step of the variable stiffness design method is implemented, using the nodal lamination parameters as design variables. The coupling of the two optimization techniques is performed through a staggered optimization, where both techniques are implemented successively, at each iteration. A gradient-based scheme is used for both topology optimization and variable stiffness design and the steepest descent method is implemented for the design update. The sensitivity analysis is performed based on the continuous adjoint method. Three different examples are demonstrated in this thesis; the case of a flat composite plate, a lug and an aircraft chair bracket. The whole optimization procedure, including pre- and post-processing, is carried out using an algorithm developed in MATLAB. The meshes are externally created and imported in the code. Convergence studies and a comparison with indicative examples from the literature are performed in order to verify the obtained results. A parametric analysis of the plate studies the effects of the different topology optimization parameters. Finally, comparative analyses are executed for the three aforementioned designs investigating both the structural and the computational efficiency of the results obtained with each of the three optimization methods, i.e. topology optimization, variable stiffness design and staggered optimization.