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FEA Complete Spar and Boom Model

Having assessed the main spar, we move on to a more complete model using all the main CFRP elements and nylon linking parts shown in Figure 14.5. When building models with multiple spars plus link parts and using contact analysis, care has to be taken to understand possible rigid-body modes in the assembled structure. These can occur because spars are free to rotate inside the nylon sockets created for them, or because a spar may be able to slide out of the joint it has been placed in. Clearly, in reality these behaviors are prevented by the action of clamping forces that will be generated by details that are not yet present during preliminary design. Therefore, additional constraints have to be imposed in the FEA, but care then has to be taken to ensure that such constraints do not provide excessive support or overly restrict the likely deflections; otherwise unrealistic deflections and stresses will result. To do this, we find it is useful to add tie constraints between the nodes on the end faces of spars to the nearest transverse spar in addition to the surface contacts between the spars and the nylon junction parts. Because the spars are all orthogonal to each other, this prevents them from sliding or rotating during analysis (notice that this will locally increase stresses in the spars but that any form of real clamp would also do this; also some spar-to-spar areas may appear not to need tying together to ensure that rotation and sliding of all parts is prevented, but we find convergence is helped by tying all spar ends where possible). We might also revisit how the whole model is being restrained; instead of symmetry and encastre constraints, the center plane of the main spar could simply be restrained in the transverse direction alone and the inner faces of the main forward nylon parts just in the vertical and fore and aft planes - an approach that will be examined later on. Reducing the supports in this way allows the main spar to flex between the nylon parts. Whether this is more realistic would depend heavily on the stiffness of the main fuselage element and the degree to which it might support the spar internally.

In this case, we take the previous 4g loading on the main spar and add pressure loads for the elevators and fins assuming that all the tail sections are operating at a local lift coefficient of unity, clearly an extreme case. Following the previous logic, the resulting mesh has 270 000 elements and 970 000 variables (Figure 14.8). The resulting deformed shape is shown

Abaqus loading for full Decode-1 spar model under wing flight loads taken from XFLR5 together with a load factor of 4 plus elevator and fin loading based on Cl values of unity

Figure 14.8 Abaqus loading for full Decode-1 spar model under wing flight loads taken from XFLR5 together with a load factor of 4 plus elevator and fin loading based on Cl values of unity.

in Figures 14.9 and 14.10. The various peak stresses and spar deflections are detailed in the first results column of Table 14.2. Note that the peak stress in the nylon is massively higher than the material yield stress: this occurs in the region where the starboard boom emerges from the forward supporting nylon structure. If a refined mesh is used, by reducing the seeds by 10% the whole model then contains some 509 000 elements and has 1.8 million variables in it. Now, Table 14.2 shows that while the various deflections have not changed significantly, the peak nylon stress has increased and the starboard boom stress is now 50% higher, see Figure 14.11. Although this model is almost twice as large, solution times are still much less than those for the RANS-based CFD models of the airframe considered in Chapter 13. Using a desk-side-based machine with 12 cores, the results take around 33 min to compute.

To proceed further, a number of subtleties need to be considered: first, the actual nylon part will not be fully solid; second, as the yield stress of nylon is massively below the peak stresses being indicated, this simple elastic model is no longer valid; and third, the element density in the nylon parts of the model is still rather low. The first thing to review is the mesh density in the region giving concern. In Abaqus this can be controlled locally by using edge seeding: so next a finer set of seeds is placed at the very rear of the nylon part and also along the spar, biased away from a collar placed in this location, see Figure 14.12, although this model requires adaptive stabilization to converge.[1]

When this is done, much more realistic stress results are obtained, although the nylon part still exceeds its yield stress at the very edge of the structure, see column 3 of Table 14.2. Notice that it is the transverse fin loading that is causing these stresses and not the vertical elevator loads, and also that these refinements barely affect the remaining results in the table. If this kind

Figure 14.9 Deformed shape and von Mises stress plot for full Decode-1 spar model under wing flight loads taken from XFLR5 together with a load factor of 4 plus elevator and fin loading based on Cl values of unity. The main spar tip deflections are 143.9 mm, the elevator spar tip deflections are 10.8 mm, and the fin spar tip deflections are 11.1 mm.

of refinement is applied throughout, even better results are obtained, although by this stage the solution takes some 32 h to complete, see column 4 of Table 14.2. For this model, the encastre restraints on the forward nylon parts have been replaced by simple displacement constraints in the vertical and fore and aft planes, while the center of the main spar is just restrained in the transverse direction. This change to boundary conditions significantly reduces the clamping of the model so that the main spar can then flex between the nylon supports, leading to much greater tip deflections, see Figure 14.13. This in turn places higher stresses on the elevator

Figure 14.10 Further details of the deformed shape and von Mises stress plot for full Decode-1 spar model under wing flight loads taken from XFLR5 together with a load factor of 4 plus elevator and fin loading based on Cl values of unity.

spar, although the other spar stresses are not changed significantly. Whether this more loosely supported model is more realistic is a matter of conjecture. Clearly, the main fuselage would support the wing spar to some extent; the actual tip flexure would thus probably lie somewhere between the results reported here in columns 3 and 4 of the table. At the same time, the greater mesh refinement reduces the peak stresses in the SLS parts to just 37% over yield, and this again occurs only in the very thin areas of the nylon where local yield would be inevitable in this design.

Table 14.2 A selection of results from various Abaqus models of the Decode-1 airframe.

Model

Units

Basic mesh,

encastre/

symmetry

Refined mesh,

encastre/

symmetry

Refined boom-biased mesh, encastre/ symmetry

Refined all biased mesh, XYZ pinned

Cell count

271 123

508 723

487 627

623 040

Number of variables

967 719

1 825 611

1 781 196

2 315 880

Main spar tip defln.

m

0.1490

0.1439

0.1427

0.2540

Main spar max. stress

MPa

262.5

238.0

235.7

235.3

Stbd. boom max. stress

MPa

472.7

676.0

55.5

59.8

Port boom max. stress

MPa

255.4

254.4

48.2

49.5

Elevator spar tip defln.

m

-0.0113

-0.0128

-0.0135

0.0063

Elevator spar max. stress

MPa

15.4

19.2

23.0

66.9

Fin spar tip defln.

m

0.0111

0.0129

0.0134

0.0100

Fin spar max. stress

MPa

115.4

167.4

163.9

180.0

Peak nylon stress

MPa

796.5

937.9

85.9

61.5

Further increasing the mesh refinement and moving to a thick-walled structure will make the Abaqus predictions even more realistic. However, in such analyses it is important to understand the elastoplastic nature of the nylon junction parts. If rather fine areas are adopted in the geometric design of the nylon, as here where the tail booms emerge from the forward nylon supports, it is almost certain that the yield stress of the nylon really will be reached locally. This is generally not a problem since some permanent stretching of these areas of nylon is probably acceptable, although detail design improvements might sensibly be made later on.[2]

Overall, the results in Table 14.2 suggest that the main spar is moderately loaded (to about half yield) while the elevator spar is rather too strong for its role, with the fin spars being somewhere in between. Clearly, it might make sense to reduce the diameter of the elevator spar at this stage, saving mass in a very weight-sensitive area of the aircraft. Reducing the fin spars would be possible from a structural point of view, but they are already of quite small diameter and making them smaller might lead to assembly and maintenance issues. The very high stresses initially found in the booms would have been a cause for concern, but by revising the element density in the contact region, their loading is revealed to be, in fact, quite modest, although reducing their diameters might make the aircraft too flexible from a controllability

Figure 14.11 Deformed shape and von Mises stress plot for nylon support part in full Decode-1 spar model under wing flight loads taken from XFLR5 together with a load factor of 4 plus elevator and fin loading based on Cl values of unity.

perspective. Accurate stressing of the nylon parts clearly needs more sophisticated models, and as yet no attention has been focused on the main lifting surfaces that are made from foam with a surface cladding.

  • [1] When convergence difficulties are experienced during solution, the user can turn on the Abaqus automatic stabilization mechanisms for the loading step using the “Specify dissipated energy fraction” and “Use adaptive stabilization”boxes when defining the loading step. This does, however, slow down the convergence process considerably andincreases significantly the size of output databases, so it is best avoided if at all possible. Convergence problems commonly arise when either the problem is over- or under-constrained, or contact elements have been included whereno or very large deformation occurs during the analysis or finite friction has been included. Generally, to avoid suchissues it is best to build up the structural model, piece at a time, solving at each stage rather than directly building afully featured model and attempting to solve it all in one go. During the development of such a model, the use of tieconstraints rather than contact pairs simplifies the analysis and speeds up solutions considerably. These can also beused in areas of the model where detailed contact stress results are not required.
  • [2] To model yielding, the material could be treated as an elastoplastic one. This would get around the issue but wouldalso make the solution convergence rather more temperamental and probably to little benefit.
 
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