A parallel aerostructural optimization framework for aircraft design studies

Preliminary aircraft design studies use structural weight models that are calibrated with data from existing aircraft. Computing weights with these models is a fast procedure that provides reliable weight estimates when the candidate designs lie within the domain of the data used for calibration. However, this limitation is too restrictive when we wish to assess the relative benefits of new structural technologies and new aircraft configurations early in the design process. To address this limitation, we present a computationally efficient aerostructural design framework for initial aircraft design studies that uses a full finite-element model of key structural components to better assess the potential benefits of new technologies. We use a three-dimensional panel method to predict the aerodynamic forces and couple the lifting surface deflections to compute the deformed aerodynamic flying shape. To be used early in the design cycle, the aerostructural computations must be fast, robust, and allow for significant design flexibility. To address these requirements, we develop a geometry parametrization technique that enables large geometric modifications, we implement a parallel Newton–Krylov approach that is robust and computationally efficient to solve the aeroelastic system, and we develop an adjoint-based derivative evaluation method to compute the derivatives of functions of interest for design optimization. To demonstrate the capabilities of the framework, we present a design optimization of a large transport aircraft wing that includes a detailed structural design parametrization. The results demonstrate that the proposed framework can be used to make detailed structural design decisions to meet overall aircraft mission requirements.     

Interval-based optimization of aircraft wings under landing loads

An interval-based automated optimization of aircraft wing structures subjected to landing loads is discussed in this paper. The interaction between landing gear and flexible airplane structure is considered as a coupled system. The uncertain system parameters are described as interval numbers. The computational aspects of the optimization procedure are illustrated with two examples – symmetric double-wedge airfoil, and supersonic airplane wing. Since, in most cases only the ranges of uncertain parameters are known with their probability distribution functions unknown, the present methodology is expected to be more realistic for the optimum design of aircraft structures under landing loads.     

Concurrent wing and high-lift system aerostructural optimization

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.     

Matrix-free algorithm for the optimization of multidisciplinary systems

Multidisciplinary engineering systems are usually modeled by coupling software components that were developed for each discipline independently. The use of disparate solvers complicates the optimization of multidisciplinary systems and has been a long-standing motivation for optimization architectures that support modularity. The individual discipline feasible (IDF) formulation is particularly attractive in this respect. IDF achieves modularity by introducing optimization variables and constraints that effectively decouple the disciplinary solvers during each optimization iteration. Unfortunately, the number of variables and constraints can be significant, and the IDF constraint Jacobian required by most conventional optimization algorithms is prohibitively expensive to compute. Furthermore, limited-memory quasi-Newton approximations, commonly used for large-scale problems, exhibit linear convergence rates that can struggle with the large number of design variables introduced by the IDF formulation. In this work, we show that these challenges can be overcome using a reduced-space inexact-Newton-Krylov algorithm. The proposed algorithm avoids the need for the explicit constraint Jacobian and Hessian by using a Krylov iterative method to solve the Newton steps. The Krylov method requires matrix-vector products, which can be evaluated in a matrix-free manner using second-order adjoints. The Krylov method also needs to be preconditioned, and a key contribution of this work is a novel and effective preconditioner that is based on approximating a monolithic solution of the (linearized) multidisciplinary system. We demonstrate the efficacy of the algorithm by comparing it with the popular multidisciplinary feasible formulation on two test problems.     

Coupled adjoint aerostructural wing optimization using quasi-three-dimensional aerodynamic analysis

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-three-dimensional 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 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 and airfoils shape as well as the wing internal structure.     

High-fidelity aerostructural optimization with integrated geometry parameterization and mesh movement

This paper extends an integrated geometry parameterization and mesh movement strategy for aerodynamic shape optimization to high-fidelity aerostructural optimization based on steady analysis. This approach provides an analytical geometry representation while enabling efficient mesh movement even for very large shape changes, thus facilitating efficient and robust aerostructural optimization. The geometry parameterization methodology uses B-spline surface patches to describe the undeflected design and flying shapes with a compact yet flexible set of parameters. The geometries represented are therefore independent of the mesh used for the flow analysis, which is an important advantage to this approach. The geometry parameterization is integrated with an efficient and robust grid movement algorithm which operates on a set of B-spline volumes that parameterize and control the flow grid. A simple technique is introduced to translate the shape changes described by the geometry parameterization to the internal structure. A three-field formulation of the discrete aerostructural residual is adopted, coupling the mesh movement equations with the discretized three-dimensional inviscid flow equations, as well as a linear structural analysis. Gradients needed for optimization are computed with a three-field coupled adjoint approach. Capabilities of the framework are demonstrated via a number of applications involving substantial geometric changes.     

Multi-fidelity wing aerostructural optimization using a trust region filter-SQP algorithm

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.     

Boundary control of flexible aircraft wings for vibration suppression

In this paper, we propose a boundary control strategy for vibration suppression of two flexible wings. As a basic approach, Hamilton's principle is used to ascertain the system dynamic model, which includes governing equations – four partial differential equations and boundary conditions – several ordinary differential equations. Considering the coupled bending and torsional deformations of flexible wings, boundary control force and torque act on the fuselage to regulate unexpected deformations of flexible wings. Then, we present the stability analysis of the closed-loop system through Lyapunov's direct method. Simulations are carried out by using finite difference method. The simulation experimental results illustrate the significant effect of the developed control strategies.     

高超音速二元机翼的颤振响应研究

在飞机结构设计中,非线性因素不可避免.本文以高超音速流下的,在俯仰自由度上含有立方非线性刚度的二元机翼为研究对象,采用平均法及颤振理论研究了超高速飞机机翼的非线性动力学行为,并通过数值计算验证了理论计算的正确性,给出了对比分析结果.     

机翼气动结构耦合数值分析方法

针对机翼的静气动弹性问题,为准确预测其气动特性,研究一种实用有效的气动结构耦合仿真方法.以客机机翼设计为例,通过机翼的静气动弹性问题分析和机翼的气动结构耦合分析流程的分解,建立参数化、自动化、模块化的气动结构耦合仿真分析平台.该平台的流程包括基于全速势方程的气动分析、基于MSC Nastran的结构仿真、应用MATLAB的载荷到结构模型的传递、结构变形向气动外形的映射等环节.算例表明该方法能较好地解决机翼的静气动弹性分析问题.     

Design of aircraft wings subjected to gust loads: A system reliability approach

A method for system reliability-based design of aircraft wing structures is presented. A wing of a light commuter aircraft designed for gust loads according to the FAA regulations is compared with one designed by system reliability optimization. It is shown that system reliability optimization has the potential of improving dramatically the safety and efficiency of new designs. The reasons for the differences between the deterministic and reliability-based designs are explained.     

Composite stacking sequence optimization for aeroelastically tailored forward-swept wings

A method for stacking sequence optimization and aeroelastic tailoring of forward-swept composite wings is presented. It exploits bend-twist coupling to mitigate aeroelastic divergence. The method proposed here is intended for estimating potential weight savings during the preliminary aircraft design stages. A structural beam model of the composite wingbox is derived from anisotropic shell theory and the governing aeroelastic equations are presented for a spanwise discretized forward swept wing. Optimization of the system to reduce wing mass is undertaken for sweep angles of ?35° to 0° and Mach numbers from 0.7 to 0.9. A subset of lamination parameters (LPs) and the number of laminate plies in each pre-defined direction (restricted to {0°,±45°, 90°}) serve as design variables. A bi-level hybrid optimization approach is employed, making use of a genetic algorithm (GA) and a subsequent gradient-based optimizer. Constraints are implemented to match lift requirements and prevent aeroelastic divergence, excessive deformations, airfoil stalling and structural failure. A permutation GA is then used to match specific composite ply stacking sequences to the optimum design variables with a limited number of manufacturing constraints considered for demonstration purposes. The optimization results in positive bend-twist coupling and a reduced structural mass. Results are compared to an uncoupled reference wing with quasi-isotropic layups and with panel thickness alone the design variables. For a typical geometry and a forward sweep of ?25° at Mach 0.7, a wingbox mass reduction of 13 % was achieved.     

Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization

The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The papers new contributions to multidisciplinary optimization are the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations for the utilization of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization, as well as the numerical noise and discrete variables present in the current example problem.     

Shape optimization of underwater wings with a new multi-fidelity bi-level strategy

Structural and Multidisciplinary Optimization - This paper proposes a new multi-fidelity bi-level optimization (MFBLO) strategy for shape designs of underwater wings. Firstly, hydrodynamic analyses...     

新涡桨飞机机头结构优化设计

在新涡桨支线飞机机头结构初始方案设计阶段,采用MSC Nastran对机头初始设计方案进行总体结构分析和尺寸优化,为机头结构选型和详细设计提供参考.     

Multi-criteria optimization of an aircraft propeller considering manufacturing

Carbon-fiber-reinforced polymers are gaining ground; high mass-specific stiffness and strength properties in fiber direction are commonly identified as reasons. Nonetheless, there are great challenges unleashing the entire light-weight potential. For instance, the multitude of parameters (e.g. fiber orientations), also being linked with each other and having huge influence on, not only structural mechanics, but also onto effort in terms of manufacturing. Moreover, these parameters ideally need to be determined, such that mass and costs are minimal, while all structural and technical requirements are fulfilled. The challenge of considering manufacturing aspects along with structural mechanics are mainly addressed in this paper. It is outlining an approach for modeling manufacturing effort via expert knowledge and how to actually consider this model in a multi-criteria optimization framework. In addition, it will be shown how to incorporate these knowledge-based models into an efficient structural design optimization. For this sake, a braided propeller structure is optimized.     

Integrated cost/weight optimization of aircraft structures

A methodology for a combined cost/weight optimization of aircraft components is proposed. The objective function is formed by a simplified form of direct operating cost, i.e. by a weighted sum of the manufacturing cost and the component weight. Hence, the structural engineer can perform the evaluation of a design solution based on economical values rather than pure cost or weight targets. The parameter that governs the balance between manufacturing cost and weight is called weight penalty and incorporates the effect of fuel burn, environmental impact or contractual penalties due to overweight. Unlike previous work, the analytical cost model and structural models are replaced by commercially available software packages that allow a more realistic model of the manufacturing costs; further, arbitrary constraints for the structural analysis can be implemented. By means of parametric studies it is shown that the design solution strongly depends on the magnitude of the weight penalty.     

飞机结构总体优化设计方法

优化设计可以改善结构的应力分布,合理布置材料,从而提高材料的利用率.通过对全机结构逐层分解,确定优化设计变量、优化区域以及响应约束,并应用MSC Nastran中的可行方向法和敏度分析方法,对MA700飞机的机翼进行优化设计方法研究,考虑稳定性因素,初步解决长桁尺寸确定的问题,为后续优化设计工作积累经验.     

飞机结构整体优化和细节分析

飞机结构复杂,部件众多,连接形式复杂,传统的单一计算方法已很难满足计算要求,为更好地挖掘飞机的承载能力,还要考虑结构局部进入塑性区应力分布.对飞机结构进行有限元分析,有时需同时考虑整体和局部,大型结构采用较密的网格会耗费大量时间、资源等,甚至会导致计算不收敛;局部结构须划分较细的网格才能得到局部构件的细节应力.以某型飞机机翼为例,简单介绍开展飞机结构整体优化和细节分析的方法与流程.