Curved cantilever type beam (Cessna 150 Landing gear) Finite Element Calculations 3

[kgjuggy]

The image shown as an attachment with this post is the actual front view of the landing gear of Cessna 150. I am working on a project to calculate the stress and strain acting on the cantilever type variable cross-section beam. After dividing into 8 sections/elements, the dimensions have been jotted down. during a drop test the landing gear will tend to bend and come under stress/moment. can anyone help me how to work out the FEA calculations using the matrices based method or any other follow up.

Many thanks in advance.

 

[rb1957]

i think you need to consider the landing impact as a dynamic event, rather than as a static one. eight elements isn't much for a model, eighty is more like it, maybe 800. you can still use your experimental data (8 points) to match the model results. i think you need something like MARC (or similar) to analyze the impact. i'm assuming that you were video-taping your test, so that you have displacement data at eight points at different times.

you could do a quasi-static analysis ... apply a load at the axel in the model to get the deflection measured, repeat for different times to see how the ground load builds up as the test progresses. maybe make a prediction about how another test will behave to see if you've done anything more than curve-fit !

FEA, make sure you're using large displacement elements.

 

[Screwman1]

Which class is this for? Sounds like a homework assignment.

 

[kgjuggy]

Actually, i do have everything to start off my dynamic testing, i have got NI Data acquisition hardware with labview software to calculate the stress staright. But to start with the practical approach, i wanted to learn about how the load or even stress distributes over such a type initially curved cantilever beam. 8 elements were chosen juat to make things simpler and to understand things to trigger the project with. I hope that makes much more sense than my first thread. The beam is not even curved, its area is also variable throughout.

Thanks rb1957.

 

[kgjuggy]

The main purpose of such study is to chose the type of strain gauge would be needed and where it should be bonded on the structure to be tested. There will be tension, compression taking place at different location and probably there might be some other forces, which will be acting in 2 or even 3 directions. Thats the sort of thing i would like to research before buying any strain gauge.

 

[GregLocock]

Strain gauges on leaf springs are always good fun. Make sure you fit about 4 times as many as you need, they'll debond at very inconvenient times.



Cheers

Greg Locock


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[rb1957]

look up curved beam theory in most any strength of materials text; a quick goggle "curved beam stress analysis" reports many hits.

if this is for a real live aircraft LG test there are Many more things to consider ...
how to apply the vertical ground load ?
how to apply the drag ground load ? remember spin-up (+ve drag) and spring back (-ve drag)
but then you say "during a drop test the landing gear will tend to bend ..." so maybe you have addressed these questions ?

i'd probably look into getting specialised LG references.

"can anyone help me how to work out the FEA calculations using the matrices based method or any other ..."
what really did you mean by this ? Surely you're using a standard FEA package (like NASTRAN/MARC or ANSYS or other) yes?
Surely you're not going to develop your own FEA ??

you'll be looking at a dynamic analysis, with large displacements. i'd model the gear with 3D elements (approximately 1 gila-zillion).

s/gauges ... use rosettes ... don't think you can get away with axial gauges.

trial load the test pices in controlled static manner, campare with FEA predictions.

 

[Aerodesign]

Hi Greg,
I have done a fair amount of stress work (inc FE) on light aircraft landing gear. The steel leaf of the C150 is a very straight forward design using conventional materials and attachments - hence it is possible to get very accurate correlation between a decent FE model and a full scale test.

As with all things in the stress world, especially FE, your assumptions and methods will dictate the outcome.

The FE methodology you adopt depends on a) what you have available to you, b) what you need, c) the purpose of the analysis, d) how much time/budget have you got, e) etc (plus others.

I attached some pictures of a similar project l completed about 12-13 years ago. In that instance an aircraft (CFM Shadow, ultralight) had a landing gear that was originally designed for an aircraft mass of 396kg, landing ground reaction load factor of around 2.5. The designer used innovative materials (for the time) but was unable to control the quality of supply of some materials. Consequently the performance reduced, the aircraft mass grew and damages and failures started to occur. My brief was to design, test and certify (against JAR-VLA and BCAR Section S) a new main landing gear.

The design was developed using stress analysis and predictive FE modelling/analysis. The prototypes were tested against the regulations and the design was certified to JAR-VLA.

The tools needed were more extensive than you need (as the landing gear l designed was composite and hence had infinite variations in potential material properties. In summary the following steps were performed:

1. A thin shell FE model was created of the design. The FE model used elements of nominal length 20mm. Today l would use variable size, down to 10mm. The maximum thickness of my layups was around 12mm, so 20mm seemed reasonable.
2. Material properties were obtained from MSC Laminate Modeler software (a composites draping and layup tool now embedded within Patran. You can use metallic values direct from MMPDS (Mil Handbook).
3. The constraints and attachment structure for the aircraft were simulated in stages: a) initially assumed as rigid with a clamp hold down (like a C150), b) later the fuselage was modelled to enable the local structural compliance to reduce the stresses adjacent to the attachments. c) fully detailed clamp modelled in FE - straps, clamp bolts (inc pre-tension).
4) The first runs were made using a linear static solution (SOL 101 Nastran). This was OK for small displacements. However, the design needed to deflect around 220mm to achieve the right balance between a reasonable ground reaction load factor (3.0) and retaining reasonable prop clearance (it was a high boom pusher config a/c).
5) A large displacement FE solution was obtained initially using Nastran SOL 106, however, l dislike this code as the convergence criteria is weak and limiting when attempting to simulate dynamic performance (drop tests). These runs allowed the design to be partially optimised.
6) Dynamic performance was evaluated using LS-Dyna3D, this is a wonderful FE package/solver that is fully explicit. Sliding contacts, non-linear material models and extensive data recovery enable a full understanding of the potential performance to be made.
7) Having established the design criteria (geometry, laminate materials, layup and a ply by ply definition) l ensured the design was feasable for production. Small changes were incorporated.
8) The final design's static and dynamic performance was predicted using another iteration of analyis and hand calcs (detail stressing of the attachments, local fuselage reinforcements, etc).
9) Prototypes were manufactured and tested in lab conditions.
10) Predicted results were compared to the tests, some adjustments made to the FE models (in this case to the non-linear stress-strain curves of the composite parts) and correlation achieved (stiffness based to within +/-5% across the test range). The critical design criteria was proven to be reserve energy drop tests.


Advice for you:

1. Initially use a beam model and then a thin shell element model. Model the attachment system - do not over-constrain. If you want good stress correlation you may need to adopt a 3D mesh. If so ensure you use at least 3 elements through the thickness. Personally l would probably use 3D elements from the outset, but l have been doign FE work since 1984.
2. Use an FE solver than can cope with both material and geometric non-linearity. The C150 legs deflect over 300mm at ultimate loads, this is way outside ETB. I recommend LS-Dyna for drop tests simulation, but for a metallic structure Nastran SOL 106 will work or ABAQUS.
3. If you are trying to correlate to tests on a statically loaded aircraft (on its wheels) you will need to model the ground and the tyre/wheel. A LOT of energy is absorbed by the tyre. The sliding contact with the ground (even in a static test) are critical. To simplify things you may want to dis-assemble the gear from the plane and test separately. However, this will not achieve your goal for a drop test analysis.
4) Read and understand Pazmany's excellent book on Landing Gear design.

http://www.amazon.co.uk/Landing-Gear-Design-Light-Aircraft/dp/0961677708

5) The C150 in the pictures looks like a typical high hours plane, be aware that the gear sags on high hours planes - so the measured performance will differ from a factory fresh version (if it still existed today).

I hope it all works out for you.
Regards
John W

 

[kgjuggy]

rb1957

Thanks for that knowledge.
With not having any FEA application experience, i am trying to look at theoretical approach of matrices rather than modelling and simulating it. I am sure you will be aware of this formula,

Force = [(Area * Modulus of elasticity)/Length]*nodal displacement.


This sort of approach i am looking for. but this formula is applicable on the structure will horizontal pulling forces rather than perpendicular one point load in my case. See the attachment to have a look on the forces acting perpendicularly and horizontally in two different pictures. The formula for horizontal force approach is known but how to work out it when the force is in perpendicular direction.

 

[kgjuggy]

here is another drawing as an attachment.

 

[rb1957]

sure you can develop FEA from first principles, but it will take you a ton of time, especially considering that you need a dynamic analysis.

you can easily build the stiffness matrix of a beam element (6dof at two nodes), 8 elements in the model ... you can solve a 54*54 matrix in excel ...
for static stress analysis. you might review "finite difference models".

in your case you'll need large displacements (a modified theory, usual assumption is "small" displacements) and a dynamic analysis.

and you've got highly non-linear components (the tire).

this is not going to be easy or quick ! (Huge under statement !!)

 

[Aerodesign]

Hi Greg,
I am a little unclear on why a hand calc approach is being contemplated, you asked for FEA calcs. I assume this is being done for work and not academic reasons? A piecewise curved beam of variable cross section under quasi-static or dynamic loading is a tough nut to crack by hand. This problem could be set up and solved in a couple of hours using basic FEA techniques.

One problem a matrices method will not address is the fact the beam length effectively increases as the leg straightens. The load is also very rarely applied perpendicular to the gear leg - look at FAR 23 for the combinations of loading conditions required. Each one will generate complex forces - bending and torsion and shear.

Regards
JW

 

[kgjuggy]

Cheers Guyz (rb1957 and Aerodesign). Much appreciated with all the detailed knowledge proposed and shared. The hand calculation is chosen is just to have an understanding of the structural behavior.
If i would have to take assumptions, to simplify things, can i take the beam and straight rather than curved and as it looks as a trapezoidal beam, can i use the 2nd moment of area of such shapes to calculate the Bending moment.

Thanks in advance

 

[GregLocock]

As a final note, if you are just trying to estimate likely strains, the initial curvature of the leafspring is no big deal, you can use a straight beam of the same length for sizing purposes.



Cheers

Greg Locock


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[rb1957]

"of the same length" ... of the same projected length ?

 

[GregLocock]

same moment at the root

Cheers

Greg Locock


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