Aircraft Structural Mechanics 3 Design & Optimisation Project UK

This project aims to design the structural wing box for a regional aircraft flying from Glasgow to one of the nearby Scottish islands for medical evacuation and other emergency evacuation purposes. 

The wing has a structural wing box (shown in thick blue lines in Fig 1), which is expected to carry all structural loads. The wing section has a chord of 2 m, with the dimensions of the structural wing box as shown in Fig. 1. Let us consider the aircraft is in trim condition, i.e., steady and level flight. 

We want to design the wing box section thickness such that its weight can be minimised for all the loads acting on the aircraft during the flight conditions, while satisfying the constraints on the material’s yield stresses. The contribution of the other part of the wing section for structural stress analysis can be neglected. Similarly, you do not need to calculate the weight of those part of the wing. You can use thin-wall sections assumptions for all section property calculations and structural analysis.

The wing can be easily represented by a cantilevered beam with one end fixed at the wing root, as shown in Figs. 2 and 3. The aircraft wing has a semi-span of 10 m. The elliptical lift distribution on one half of the wing is as shown below in Fig. 3. Let us assume for simplifying the calculations that the lift acts through the centre of pressure line of the wing, which is at a constant 27.5% of the chord or 550 mm from the leading edge of the wing section. 

Please use the material properties as provided below:

• Maximum allowable tensile (or compressive) yield stress: 250 MPa
• Maximum allowable shear yield stress: 150 MPa
• Material density: 2700 Kg/m3
• Shear modulus G: 25 GPa

Instructions on solving the design problem Design variables

as per the figure provided below, the design variables are the wall thickness 𝑡1, 𝑡2, 𝑡3 and 𝑡4, leading to a structural section fully symmetric about the x-axis. Loads acting on the structural wing box: aerodynamic lift and self-weight of the wing box. Note: a real aircraft wing would include engine nacelle weight, actuator and cables weight and fuel weight (if fuel placed in wings). Here we have neglected these for simplicity. 

Design and optimisation strategy:

• The design strategy would be to start with some relatively high wall thickness variablesthat ensures all bending and shear stresses (including shear loads and torsion) are within allowable limits.
• Then, iteratively reduce the wall thickness design variables and ensure that the wing box weight (which would depend on the wall thickness) goes down while the maximum bending and shear stresses in the section remain below the allowable yield stresses forbending and shear, respectively.
• You are not expected to set up this problem as a constrained optimisation problem in MATLAB. Iterative calculations via programming in MATLAB/Python or even Excel spreadsheet is sufficient. However, you must clearly demonstrate that your design strategy is working, and you are able to reduce wall thickness from your initial value.
• Can you see any improvement after a few iterations? 

Marking guidance

The project has 30 marks in total and counts for 15% of the course marks.Please submit a single file for your design project report. You are free to use hand calculations and hand-drawn figures. However, your workings and labels must be legible. 3 It would be best if you could provide some tables or some plots to show how your wall thickness variables change over the design iterations.

Mark distribution:

• Calculation of maximum bending, shear and torsion loads [10]
• Setting up bending and shear stress calculations for iterative design and optimisation application [10]
• Demonstration of successful weight optimisation strategy by iteratively reducing thickness [5]
• Clarity of reported working, tables and figures [5]

Answer

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