Buckling Analysis With Inertia Relief

[etorrecillas]

Dear fellows,

I am writing to ask if anyone has any experience with buckling analysis considering inertia relief effects.
I ran some tests with small models to check if buckling modes considering inertia relief effects or SPC approach with fictional body loads should give the same result. It was OK for small models (except for the ones containing angular velocity).

But, for a more complex model of an aircraft in flight (considering pressure loads, linear accelerations, angular accelerations and angular velocities), buckling modes get strange (ones are like rigid body motion, but not 6 modes).

I don't know if angular velocities have any effect on buckling/inertia relief calculations.

I am using MSC Nastran v 70.7. Any help is appreciated.

Best regards,

 

[jhardy1]

"I don't know if angular velocities have any effect on buckling/inertia relief calculations."

I can imagine cases where it certainly would - e.g. angular velocity puts parts of the structure into tension, thereby changing the buckling load factor / mode shape for that element. (Your solver may even find a negative buckling load factor for an element which is in tension.)

http://julianh72.blogspot.com

 

[rb1957]

true enough, but usually we're solving loads at a point in time.

are we talking about a wing structure ? a wire braced bi-plane ?? a heavy shell structure ? a fuselage ??

Quando Omni Flunkus Moritati

 

[etorrecillas]

@jhardy: That's true. I tried removing angular velocities and mode shapes are still weird (first 4 ones like rigid body). Looks like the solver can't split rigid bode modes from real buckling modes.

@rb1957: We are talking about a complete but simplified aircraft model. It is a composite glider. I will show you a picture of the model to give an idea. Please see the picture below.

I am still trying to solve this problem, but I'm a little bit stuck now.

 

[rb1957]

see i think that answers julian's concern (re structure stiffening due to velocities) ... ie IMO it doesn't.

determine all the accelerations on the a/c (glider) ... linear velocities shouldn't affect the results, rotational ones develop linear accelerations that you need to apply. maybe your FEA can tell you when something buckles, maybe your structure (stiff shells/skins, as opposed to thin Al skins) allows this (with thin Al skins you have to analyze for shear/compression buckling, ie diagonal tension).

Quando Omni Flunkus Moritati

 

[BlasMolero]

Hello!,
If you are looking for Dynamic Unstability you need to perform a Flutter Analysis.
Flutter is the dynamic aeroelastic stability problem. It can be solved in any speed regime simply by selecting the appropriate aerodynamic theory. In the linear case, the solution involves a series of complex eigenvalue solutions; the eigenvalue problem to be solved depends on the way in which the aerodynamic loads are included in the equations of motion or whether certain damping terms are included.

The manner in which the aerodynamic loads are included depends on how the dimensionless oscillatory aerodynamic coefficients are defined. When Theodorsen (1935) first developed the American method (K-method) of flutter analysis, he introduced the aerodynamics into a vibration analysis as complex inertial terms and the flutter analysis became a vibration analysis requiring complex arithmetic. At the same time, he introduced an artificial complex structural damping, proportional to the stiffness, to sustain the assumed harmonic motion. Flutter analysis is then a double eigenvalue problem in frequency and velocity, and an iterative solution, using the reduced frequency of the assumed harmonic motion as the iteration parameter, leads to the neutrally stable conditions (flutter frequencies and velocities) at which no artificial damping is required. The artificial damping is therefore seen not to be physically meaningful, other than, perhaps, at speeds near flutter speeds.

At about the same time, Frazer and Duncan (1928) in England were attempting to solve the flutter problem using aerodynamic stability derivatives in the tradition of Bryan (1911) who had studied the flight mechanics of rigid aircraft. This approach introduced the aerodynamic loads into the equations of motion as frequency dependent stiffness and damping terms. In this representation it should be noted that the aerodynamic terms are slowly varying functions of the reduced frequency, in contrast to the representation of the aerodynamics in the K-method as mass terms that are highly dependent on the reduced frequency. In what has become known as the “British” method of flutter analysis some iteration is still necessary to “line-up” the eigenvalue solution for frequency with the reduced frequency in each mode.

A description of the British method and a comparison with the American method has been given by Lawrence and Jackson (1970). A variation of the British method in which the aerodynamic loads are treated as complex springs has been developed by Hassig (1971). Hassig called his method the p-k method, and NX Nastran has adopted his terminology, although it is now applied to the British method. The NX Nastran terminology is K-method for the American method, and PK-method for the British method. NX Nastran also has a very efficient K-method, called the KE-method, but it does not provide eigenvectors and has no provisions for viscous damping type terms, such as arise in an automatic control system in the equations of motion.

To learn more visit

http://www.iberisa.com/productos/nxnastran/nx_nastran_aeroelasticity.htm#flutter

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48011 BILBAO (SPAIN)
WEB:

http://www.iberisa.com

Blog de FEMAP & NX Nastran:

http://iberisa.wordpress.com/

 

[etorrecillas]

Thanks for all contributions... Didn't get any progress up to now, but I will keep you informed.

@BlasMolero: thank you, but flutter analysis is not the point here. Of course it will be performed, using ZAERO, but the point now is in fact buckling.

Regards.

 

[etorrecillas]

Hi people,

I am here to inform that today I had good progress with this calculation.

I noticed that 2 major points are pretty important:

1-The correct specification of the SUPORT entry;
2-The request only for positive eigenvalues. For negative ones maybe some matrix turns ill-conditioned. (makes sense in my load case).

I will try more tests tomorrow with PARAM,INREL,-2 (software should specify the best support point). Let's see what happens.

 

[rb1957]

i think the eigenvalues detect instability in the structure, like euler buckling. I'm not so sure that they detect shear buckling, or diagonal tension effects.

Quando Omni Flunkus Moritati