Three-dimensional structural topology optimization of aerial vehicles under aerodynamic loads Erdal Oktay a,1 , Hasan U. Akay b,⇑ , Onur T. Sehitoglu c a EDA – Engineering Design and Analysis, Ltd., Ankara, Turkey b Department of Mechanical Engineering, Atilim University, Ankara, Turkey c Department of Computer Engineering, Middle East Technical University, Ankara, Turkey article info Article history: Received 12 March 2013 Received in revised form 12 September 2013 Accepted 12 November 2013 Available online 28 November 2013 Keywords: Structural topology optimization Aerial vehicle structural design Parallel CFD Mesh coupling Code coupling Parallelized solvers abstract A previously developed density distribution-based structural topology optimization algorithm coupled with a Computational Fluid Dynamics (CFD) solver for aerodynamic force predictions is extended to solve large-scale problems to reveal inner structural details of a wing wholly rather than some specific regions. Resorting to an iterative conjugate gradient algorithm for the solution of the structural equilibrium equations needed at each step of the topology optimizations allowed the solution of larger size problems, which could not be handled previously with a direct equation solver. Both the topology optimization and CFD codes are parallelized to obtain faster solutions. Because of the complexity of the computed aerody- namic loads, a case study involving optimization of the inner structure of the wing of an unmanned aerial vehicle (UAV) led to topologies, which could not be obtained by intuition alone. Post-processing features specifically tailored for visualizing computed topologies proved to be good design tools in the hands of designers for identifying complex structural components. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Determining the right topology for a load bearing structure, i.e., finding an optimum distribution of materials and placement of structural components over a structure are very important in terms of efficiency and cost. The traditional approaches of structural topology design were based on the experience, intuition and crea- tivity of designers. In most cases, topology of existing structures were emulated or improvised. However, for complex structures, there is a need for more systematic approaches. When, a system- atic optimization method is used during the conceptual design of a structure, major savings may be achieved from the amount of material and weight. Especially in automotive and aerospace industries, since there is always a need for reduced weight and sav- ings in materials for efficiency and cost, the optimization is even more important. Because of that, the use of topology optimization methods has increased during the recent years. Since they offer many more useful alternatives in the hands of designers, intense research is continuing in this area. With the tools developed, the designers can use their experience and creativity for testing their new ideas. Today, structural topology optimizations are mostly done using the finite element method because of its generality. For optimiza- tion process, there are two broad approaches: (1) Microstructural approach and (2) Macrostructural approach. A good review of these two approaches is given by Eschenauer ve Olhoff [1]. In this paper, we use the microstructural approach because of its versatility. This approach is also known as materials or density dis- tribution method in the literature. In this method, the geometry of the optimum topology evolves by systematically computing a non-dimensional material density q e in each finite element, which varies from zero to one to match a given volume reduction (volume fraction) of an initially defined design space. The element struc- tural stiffness matrix denoted as k e ij is assumed to be linearly pro- portional to density. The density represents the volume fraction of the element. Thus, as density approaches to zero, so does the element stiffness, as a result an empty region is formed. Con- versely, in regions where the density becomes one, the full stiffness of the material is fully reached, thus a fully solid region is formed. In regions where density varies between zero and one, a non- homogeneous region is formed. To enforce formation of distinct empty and solid regions, a penalty constant n greater than one is introduced to the optimization scheme as a power of density as in q n e for magnification of differences between low and high values of density. The density distribution method was proposed for the first time by Bendsoe and Kikuchi [2] as a topology optimization method. A 0045-7930/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compfluid.2013.11.018 ⇑ Corresponding author. E-mail addresses: eoktay@eda-ltd.com.tr (E. Oktay), hakay@atilim.edu.tr (H.U. Akay), onur@ceng.metu.edu.tr (O.T. Sehitoglu). 1 Tel.: +90 312 210 1991. Computers & Fluids 92 (2014) 225–232 Contents lists available at ScienceDirect Computers & Fluids journal homepage: www.elsevier.com/locate/compfluid