Fluid-Structure Optimization of a Rectangular Wing
In an advanced society like ours we all depend on composite materials in some aspect of our lives. Most composites are made up of just two materials. One material (the matrix or binder) surrounds and binds together a cluster of fibres or fragments of a much stronger material (the reinforcement). Over recent decades many new composites have been developed, some with very valuable properties. By carefully choosing the reinforcement, the matrix, and the manufacturing process that brings them together, engineers can tailor the properties to meet specific requirements. They can, for example, make the composite sheet very strong in one direction by aligning the fibres that way, but weaker in another direction where strength is not so important. It can easily be seen that the long fiber composite will have directionality depending on the direction in which the fibers are laid out in the composite. Furthermore composite materials can be used to create a layered sandwich having orthotropic characteristics. The greatest advantage of composite materials is strength and stiffness combined with lightness. By choosing an appropriate combination of reinforcement and matrix material, manufacturers can produce properties that exactly fit the requirements for a particular structure for a particular purpose. The efficiency of an airplane wing, in flying condition (deformed wing), is different from the efficiency of the undeformed shape. The deformation of the wing, in fling condition, is univocally determined for a isotropic material wing while it depends on sandwich composition and the fiber orientation for a multi-layered composite wing. The performance of the wing, in flying can be optimized modifying parameters defining the properties of the multi-layered materials.
Since the huge number of parameters defining the mechanical properties of the layered sandwich (orthotropic mechanical properties and orientation angle of each composite forming the sandwich) and the nonlinearity of the problem optimization algorithms can help the designer to save time in configuring the material taking in account different and conflicting targets (e.g.: efficiency, lift, drag, mass of the wing).
A weak formulation was used to solve the aero-elastic model: the structural model is initially loaded with the pressure field created by the undeformed shape than the deformation of the structural model is used to modify the aerodynamic model, the new pressure field is then applied to the structural model and the difference between the current displacements and the displacements of the previous iteration is computed. The loop is stopped when there is a convergence in the deformed wing shape. The aero-elastic loop is implemented using the modeFRONTIER workflow (fig. 1) A structured 3D mesh represents aerodynamic model (fig. 2), while a shell element model represents the structural model (fig. 3). The two meshes are independent and a interpolation procedure is used to load the structural model and deform the aerodynamic model (fig. 4).
The mechanical properties of the composites forming structural model are fixed: there are two layers of VICOTEX 1454/48%/G1051 and one layer of NCHM 1748/38%/M46J. The optimization parameters are: three parameters defining the thickness of the layered material (a second order function gives the thickness from the root to the tip of the wing), three parameters defining the fiber orientation angle of the two materials and two parameters defining the relative thickness of the two composite in the layered material (fig. 5). Objectives of the optimization are the maximization of the wing efficiency in flying condition, the minimization of the wing weight. A constraint is also defined to warrant a certain lift. The Multi-objective Genetic Algorithm (MOGA) explored the possible composite wing configurations in a efficient way automatically improving the performance of the undeformed wing shape in spite of the nonlinearity of the problem and the conflicting objectives.