A method is presented for concurrent aerostructural optimization of wing planform, airfoil and high lift devices. The optimization is defined to minimize the aircraft fuel consumption for cruise, while satisfying the field performance requirements. A coupled adjoint aerostructural tool, that couples a quasi-three-dimensional aerodynamic analysis method with a finite beam element structural analysis is used for this optimization. The Pressure Difference Rule is implemented in the quasi-three-dimensional analysis and is coupled to the aerostructural analysis tool in order to compute the maximum lift coefficient of an elastic wing. The proposed method is able to compute the maximum wing lift coefficient with reasonable accuracy compared to high-fidelity CFD tools that require much higher computational cost. The coupled aerostructural system is solved using the Newton method. The sensitivities of the outputs of the developed tool with respect to the input variables are computed through combined use of the chain rule of differentiation, automatic differentiation and coupled-adjoint method. The results of a sequential optimization, where the wing shape and high lift device shape are optimized sequentially, is compared to the results of simultaneous wing and high lift device optimization.

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An alternative to the lamination parameters framework is proposed that uses the fiber angles as design variables: the manufacturing finite element mesh (MFEM) framework. The structure and implementation of the MFEM framework allows for both stiffness and strength constraints. In this manuscript the maximum failure index is minimized the case of a static analysis, while for buckling analysis the first buckling mode is maximized. For each case example are presented and discussed. To complete the manuscript the post- processing tool used to obtain feasible automated fiber placement machine tow paths is briey discussed. @en

The least-squares finite element method is used to solve the compressible Euler equations around airfoils in transonic regime. The symbolic analysis method is used to generate the element stiffness and force matrices. The equations of the element matrices are derived symbolically based on the flow primitive variables and the position of the element nodes. The symbolic analysis is also used to compute the exact derivatives of the residuals with respect to both design variables (e.g. the airfoil geometry) and the state variables (e.g. the flow velocity). The symbolic analysis allows to compute the exact Jacobian of the governing equations in a computationally efficient way, which is used for Newton iteration. Besides, using the symbolic analysis the sensitivities of the outputs, such as the airfoil drag, with respect to the design variables, such as the airfoil geometry, are computed using the discrete adjoint method without the need for automatic differentiation. This makes the analysis and optimization computationally more efficient. @en

An uncertainty-based approach is undertaken to deal with multipoint wing aerostructural optimization. The flight points are determined by the quadruple set of parameters: Mach number, cruise altitude, carried payload, and flight range. From this set, the payload and range are modeled as probabilistically uncertain based on U.S. flight data for the operations of an A320 aircraft. The fuel burn is selected as the performance metric to optimize. Structural failure criteria, aileron efficiency, and field performance considerations are formulated as constraints. The wing is parametrized by its planform, airfoil sections, and structural thickness. The analyses disciplines consist of an aerostructural solver and a surrogate-based mission analysis. For the optimization task, a gradient-based algorithm is used in conjunction with coupled adjoint methods and a fuel burn sensitivity analytical formula. Another key enabler is a cost-effective nonintrusive uncertainty propagator that allows optimization of an aircraft with legacy analysis codes, within a computational budget. @en

In this paper, a method is introduced that predicts the influence of gaps and overlaps introduced by fiber steering on the stiffness and strength of composite laminates. This method is based on the incorporation of a “density functional” which translates the effect of discrete gaps and laps into a continuous correction of the reduced stiffness matrix. It also includes a function to incorporate a fiber placement manufacturing strategy. Test configurations used to test the validity of the density functional approach show results consistent with the expected gap/overlap distributions, and also demonstrate the robustness of the manufacturing strategy function. The method is to be included in the TopSteer optimization code1 to study the influence of gaps and overlaps on optimization results. @en

The application and computational efficiency of wing aerostructural optimization us- ing simultaneous analysis and design (SAND) strategy is investigated. A coupled adjoint aerostructural analysis method based on quasi-three-dimensional aerodynamic analysis is used for this research. Two different optimization problems are tested. In the first case a wing aeroelastic optimization is performed using both nested analysis and design (NAND) and SAND strategies. In this optimization the wing box structure is optimized to achieve minimum wing weight. In the second optimization the wing structure as well as the outer aerodynamic shape are optimized to achieve minimum aircraft fuel weight. The results of both SAND and NAND optimizations have been compared based on accuracy and compu- tational cost @en

This paper discusses the development of a multidisciplinary design optimization tool intended for electronically power aircraft. The test subject of the optimizations is a hybrid blended wing body, delta wing UAV. First, the optimization problem is presented with the objective function, constraints, and design vector. Next, we describe the tool’s architecture and the analysis tools that are utilized. Finally, preliminary results for the test subject UAV are discussed for both the previous and current formulation of the MDO tool.@en

A trust region filter-SQP method is used for wing multi-fidelity aerostructural optimization. Filter method eliminates the need for a penalty function, and subsequently a penalty parameter. Besides, it can easily be modified to be used for multi-fidelity optimization. A low fidelity aerostructural analysis tool is presented, that computes the drag, weight and structural deformation of lifting surfaces as well as their sensitivities with respect to the design variables using analytical methods. That tool is used for a mono-fidelity wing aerostructral optimization using a trust region filter-SQP method. In addition to that, a multi-fidelity aerostructural optimization has been performed, using a higher fidelity CFD code to calibrate the results of the lower fidelity model. In that case, the lower fidelity tool is used to compute the objective function, constraints and their derivatives to construct the quadratic programming subproblem. The high fidelity model is used to compute the objective function and the constraints used to generate the filter. The results of the high fidelity analysis are also used to calibrate the results of the lower fidelity tool during the optimization. This method is applied to optimize the wing of an A320 like aircraft for minimum fuel burn. The results showed about 9 % reduction in the aircraft mission fuel burn.@en

This paper presents a wing aerostructural optimization framework based on the Indi- vidual Discipline Feasible (IDF) architecture. Using the IDF architecture the aerodynamic and the structure disciplines are decoupled in the analysis level and the optimizer is re- sponsible for the consistency of the design. The SU2 CFD code is used for the aerodynamic analysis and the FEMWET software is used for the structural analysis. The SU2 code is modi_ed in a way to receive the structural deformation as inputs and compute the sensi- tivity of the outputs, e.g. drag, with respect to the deformation. An Airbus A320 type aircraft is used as a test case for the optimization. A reduction of the aircraft fuel weight of 11% is achieved. This reduction was attained by increasing the wing span, reducing the wing sweep, improving the lift distribution and improving airfoil shapes. @en

A coupled-adjoint aerostructural wing optimization tool has been modi_ed to include the optimization of high-lift devices from the start of the optimization process. The aerostruc- tural tool couples a quasi-three-dimensional method with a _nite beam element model. In this paper, the quasi-three-dimensional method is modi_ed using the _ method of Van Dam to enable high-lift aerodynamic analysis. In order to estimate the maximum wing lift coe_cient of an elastic wing, the Pressure Di_erence Rule is coupled with the aerostruc- tural tool. The proposed method is able to compute wing drag and maximum wing lift coe_cient with reasonable accuracy compared to high-_delity CFD tools that require much higher computational cost. The coupled systems are solved using the Newton method for iteration. The sensitivities of the outputs of the tool with respect to the input variables are computed through combined use of the chain rule of di_erentiation, automatic di_eren- tiation and coupled-adjoint method. Using the presented tool, a sequential and combined gradient based optimization is performed in order to minimize the fuel weight of a Fokker 100 class aircraft. The combined optimization results in a fuel weight reduction of 4.1% while achieving a maximum wing lift coe_cient in both takeo_ and landing con_guration equal to that of the initial wing. @en

This paper presents a method for wing aerostructural analysis and optimization, which needs much lower computational costs, while computes the wing drag and structural deformation with a level of accuracy comparable to the higher fidelity CFD and FEM tools. A quasi-threedimensional aerodynamic solver is developed and connected to a finite beam element model for wing aerostructural optimization. In a quasi-three-dimensional approach an inviscid incompressible vortex lattice method is coupled with a viscous compressible airfoil analysis code for drag prediction of a three dimensional wing. The accuracy of the proposed method for wing drag prediction is validated by comparing its results with the results of a higher fidelity CFD analysis. The wing structural deformation as well as the stress distribution in the wingbox structure is computed using a finite beam element model. The Newton method is used to solve the coupled system. The sensitivities of the outputs, for example the wing drag, with respect to the inputs, for example the wing geometry, is computed by a Ali Elham a.elham@tudelft.nl Michel J. L. van Tooren vantooren@cec.sc.edu 1 Faculty of Aerospace Engineering, Delft University of Technology, Delft, Netherlands 2 McNair Center for Aerospace Research and Innovation, University of South Carolina, Columbia, South Carolina, USA combined use of the coupled adjoint method, automatic differentiation and the chain rule of differentiation. A gradient based optimization is performed using the proposed tool for minimizing the fuel weight of an A320 class aircraft. The optimization resulted in more than 10 % reduction in the aircraft fuel weight by optimizing the wing planform @en