bending beam Log Out | Topics | Search
Moderators | Register | Edit Profile

FlexPDE User's Forum » User Postings » bending beam « Previous Next »

Author Message
Top of pagePrevious messageNext messageBottom of page Link to this message

Robert White (bobzzwhite)
New member
Username: bobzzwhite

Post Number: 1
Registered: 04-2004
Posted on Friday, April 02, 2004 - 05:14 pm:   

Hello,

I want to use the method from the bending bar example to simulate a bar of a finite z thickness. I am learning solid mechanics so please let me know if my understanding is off. In the bending bar example, the moment of inertia equation does not include the width of the bar in the inplane direction. My understanding of the setup is that the bar is in the plain stress case. And in this case, we are assuming an infinite length in the z direction, hence we are not bending a bar, but we are bending a sheet or a plane.

My question is then can we through approriate equations simulate a real beam of finite z thickness which is similiar in magnitude to the y height of the beam, and both are smaller than the x length of the beam in the 2D version of FlexPDE?
Or do we need the full 3D version?

Bob
Top of pagePrevious messageNext messageBottom of page Link to this message

Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 137
Registered: 06-2003
Posted on Thursday, April 15, 2004 - 04:18 pm:   

Our Bentbar.pde example is taken from Timoshenko, "Theory of Elasticity", p41. In that example he considers a beam of "unit thickness", so it is not true that it considers a sheet or plate. He uses plane stress coefficients, which means that the material cannot support a stress in the Z direction, consistent with thin extent in Z. In the bending of a plate or sheet, one would need a plane strain approximation, because in a material infinite in z, no displacement is allowed in the z direction.

A full description of the bending of a bar of finite extent would require a 3D analysis, if you want to actually see the spreading of the material on the compressed side, etc. If all you want is the deflection, then 2D equations that actually embody the physics of your situation would probably suffice.

However, I am not able to address the accuracy and appropriateness of various 2D approximations; you will have to search the literature.
Top of pagePrevious messageNext messageBottom of page Link to this message

Robert White (bobzzwhite)
Member
Username: bobzzwhite

Post Number: 4
Registered: 04-2004
Posted on Thursday, April 15, 2004 - 11:45 pm:   

Thank you. I am learning elasticity and I was a bit confused. Plane stress will work for an reasonable approximation of the problem. The accuracy will be ok to quite good, depending on some details which are not known yet. To get a significant improvement in the accuracy will require a different approach and a much bigger computer.

The problem I am studying is a microelectromechanical system where an electrostatic force pulls a doubly supported beam up and down. So, I am using a modified bent bar file with constraints on both ends of the beam and a force on the top and bottom of the beam.

Sometimes there is a problem with convergence in the solution. When the voltage ramp is too fast, the beam develops kinks. So instead of resembling a parabola, the center of the beam starts to look like a camel with two or more humps. Do you have any suggestions as to what is happening and how to prevent it?

I am using the stages method for DC solutions, but I really should move to a time dependent method, like the vibrate example. I don't understand what mu = 1e3 { Estimated viscosity Kg/M/sec } is derived from?

Also, why is eps=0.01*L in the files?

Thanks so much for your help. I love FlexPDE. I have be able to go from not knowing elasticity to having a partially functional model that agrees with first order theory in only a few days.

Bob
Top of pagePrevious messageNext messageBottom of page Link to this message

Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 139
Registered: 06-2003
Posted on Friday, April 16, 2004 - 04:03 pm:   

I can't find any notes on the creation of our Vibration example, so I don't know any references for the derivation given in the comments to this problem. In any case, the mu*del2(V) term is a viscous dissipation term which may not be applicable in some cases. Presumably in metals, it would not be present until the elastic limit is exceeded. The value chosen for the example would appear to be totally fictitious. This may be the cause of difficulties in your case. Try reducing the value by several orders of magnitude. Since it also serves as a numerical stabilization term, it is probably not wise to remove it altogether.

eps=0.01*L is merely a small offset to move the plots off the domain surfaces.

Add Your Message Here
Post:
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Password:
Options: Enable HTML code in message
Automatically activate URLs in message
Action:

Topics | Last Day | Last Week | Tree View | Search | Help/Instructions | Program Credits Administration