Advanced Aircraft Structures Assignment 1 Questions 2025-26

Problem

The geometry of a simplified wing-box is shown in Figure 1. The wing-box is composed of upper and lower skins, five spars, twenty-one ribs, ten spar caps, and forty-two rib caps with nominal thicknesses and radius defined in Table 1. Assume that spar and rib caps have circular cross-sections with a radius of 25 mm, and the 105 posts have circular cross-sections with a radius of 10 mm. Also assume that all the materials are made of aluminum alloy with  0.1 % proof stress = 510 MPa, tensile strength =580 MPa, modulus of elasticity 70 GPa,  Poisson ratio = 0.33 and density 2700 kg/m3. Figure 2 shows an exploded view of the wingbox. The wing is clamped at the root (assume the fuselage is a rigid body)

Table 1: Nominal values of thicknesses and areas for the simplified wing finite element model.

Construct the FE model of the wing using 4 nodded quad (Quad 4 shell) elements for skins, spars and ribs and 2 nodded bar elements (bar 2) for spars and ribs caps and posts using dimensions given in Table 1 and Figure 1.

Questions

1. Calculate the aerodynamic loads using the modified strip theory (10 strips) and data given in Table 2 (assume symmetric aerofoil). Using the worst-case flight condition (the case which generates the highest lift), show that the mesh size you have chosen will not significantly affect the results of linear static analysis (maximum Von Misses stress and max displacement) and buckling analysis (load factor). This is known as a mesh convergence study, and suggestions for mesh size in this question are 0.5, 0.25, 0.1, 0.0625, 0.05. Plot the mesh convergence results. Describe/discuss the results.

Note: in calculation of aerodynamic loads, please assume 𝑎1 = 5.73 /radian and use

assumptions and how they impact the load distribution should be included in the discussion.

Table 2: Flight Conditions (FCs).

[12% of total marks]

2. Using the FE model with the right mesh size (obtained from Q1), determine approximate values of elastic twist angle for each strip and all 3FCs. Update the initial values of the lift and reapply them to the wing (all 3 FCs). Obtain new values of elastic twist angle for each strip and check if they have changed (converged). If they have NOT changed, you can conclude that the aerodynamic load has been converged (note we call them converged aerodynamic loads).

 If not, continue this iteration until convergence achieves. Using the converged aerodynamic loads, determine the maximum displacement and maximum Von misses stress for all 3 FCs. Show the aerodynamic load distribution for all iterations and for all 3 FCs (these graphs should show the initial distribution (Q1) and converged aerodynamic loads). Also show the variation of elastic twist angle along span for all 3 FCs. Determine whether the maximum Von mises stress has reached the 0.1 % proof stress. Describe/discuss the results. [16% of total marks]

3.  Using the FE model with the right mesh size and initial aerodynamic loads (they are obtained in Q1), perform buckling analysis and determine the buckling load factors for all 3 flight conditions and critical lift distribution (use table or graph to show the critical lift distribution). Then calculate the buckling stress. Substitute the value of buckling stress into the theoretical buckling stress equation in slide 52 of the notes for buckling in aircraft structures, determine the value of ‘k’, and discuss possible boundary conditions that might be assumed for the theoretical model. Finally, describe/discuss the results. [20% of total marks]

4.  For this question, please use the FE model of the wing with 0.05 mesh size and converged aerodynamics load for FC2, i.e. altitude 3000 m, velocity 250 m/s and AOA 1o (only one load case)). Consider a section of the wing located 0.6 m from the built-in end. Idealise this section (assume that the booms resist all normal stresses while the skins are effective only in shear). Calculate the normal stresses and forces in the booms and shear stresses in the wing skins. Compare the results with those achieved by FE analysis (please see the video for instructions on how to calculate the internal shear load for this section and also see how to determine normal/shear stresses at this section in PATRAN).

 Demonstrate the results in a table. Discuss the results and explain the reasons for differences between FE and idealised section results. Hand calculation AND/OR MATLAB scripts/Excel sheets MUST be provided in the appendix of the report, and there is no page limit for the appendix, and they will not be counted towards the 5-page limit of the report of assignment 1. [32% of total marks]