Tool for preliminary structural sizing, weight estimation, and aeroelastic optimization of lifting surfaces*

Abstract

This paper presents the development and implementation of a tool for wing structural sizing and aeroelastic optimization in early design steps, where the amount of available data about the wing structure is not enough to allow high-fidelity finite element analysis and optimization. The proposed tool consists of two levels. The first level is a quasi-analytical method for wing structural weight estimation and initially sizing of the wing box structure. The second level is an aeroelastic tool that uses a vortex lattice method and a finite beam element to compute the stress distribution in the wing box structure. The Newton method is used to solve the coupled system. The coupled adjoint sensitivity analysis method is used to compute the sensitivity of any function of interest with respect to the design variables. The tool was used for a series of wing aeroelastic optimizations to minimize the wing weight with a series of constraints on the wing structural failure modes and aileron effectiveness. Another series of optimizations is also used to find the wing jig shape for a predefined cruise shape. The outputs of the optimizations showed that the wing box weight varies quadratically with the required value for the aileron effectiveness.

Combined Aerostructural Wing and High-Lift System Optimization

“…The core of the structural analysis is performed by the 'Finite element based Elham Modified Weight Estimation Technique' ( FEMWET) tool [36]. This tool is used for sizing of the wing structure and is capable of calculating the aeroelastic deformation and the resulting stresses, while providing an accurate wing weight estimation.…”

“…In order to compute this stress distribution, the wing box four equivalent panels are divided into small elements of which each position is measured from the shear center (see Figure 2.19). [36] Using the computed stress distribution, failure criteria are then set up based on material yield stress, Euler buckling and shear buckling using Equations 2.22 to 2.24.…”

“…[36] After determining the node positions, the element stiffness, mass and force matrices are constructed using the shape functions for a 3D 2-node Timoshenko beam element [38]. For a complete explanation of the method, the reader is referred to [36]. With the stiffness matrix K and force matrix F , the displacement vector U can be computed by solving:…”

“…A graphical representation of the node positioning is presented in Figure 2.18. [36] After determining the node positions, the element stiffness, mass and force matrices are constructed using the shape functions for a 3D 2-node Timoshenko beam element [38]. For a complete explanation of the method, the reader is referred to [36].…”

Concurrent wing and high-lift system aerostructural optimization

“…In this approach, the wing is divided into a number of spanwise sections (or strips), for which the aerodynamic forces and moments are computed using the effective flow properties, which are determined from the free stream flow properties taking into account the effects of sweep ( ) and downwash (α i ). The Q3D method is coupled to the structural analysis tool FEMWET (Elham and van Tooren 2016b), which simulates the wingbox structure using equivalent panels and computes the wing deformation using a FEM. The coupled aerostructural system is formulated using 4 governing equations R 1 to R 4 as follows:…”