| Author | Message | ||||
     Mehdi Naderi (mnader4) Member Username: mnader4 Post Number: 31 Registered: 12-2006 |
Dear All, I will apprecite if somebody helps me. The attached file is a simple conduction problem. BC are: Top and bottem of the solid natural (temp)=-h(T-Ta) convection to environment (h heat transfer coefficent is constant and Ta of environment temperature). the other sides natural(temp)=0 The answer of temperature should be completely symmetric, but it is not. Why? is it the error in the moving mesh that fpde solves the problem? Regards, Mehdi
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1012 Registered: 06-2003 |
You have applied only Y-motion to the bar. This means that as the bar bends, its X-extent remains constant and the surface length grows. The heat loss term is energy per unit area. So when the tip of the bar grows, the heat loss from the tip increases, and the tip cools. | ||||
| Mehdi Naderi (mnader4) Member Username: mnader4 Post Number: 32 Registered: 12-2006 |
Dear Mr. Nelson, Thank you so much. I applied the x-direction of motion, I think every point has motion in x and y direction, but there is still that problem. The other attached file is a word document which describes the equation of motion (just 1 page)of the beam. I do not know where is the problem. Another thing, the deflection of the beam is not symetric (deflection in -y is higher than +y). I will appreciate if you help me.
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1018 Registered: 06-2003 |
I don't believe you have done your derivation correctly. You have computed a thickness effect in the position of the surface of the bar. This would require a negative x-offset on the top of the bar, but a positive x-offset on the bottom of the bar, which you have not done. Furthermore, you have made no analysis of how your point A moves leftwards from its initial position as the bar bends. Our example problem "Samples | Steady_State | Stress | Bentbar.pde" quotes an example from Timoshenko in which both the u and v displacement are given analytically. (his mounting assumptions are different than yours, however). Perhaps you would do best to apply a sinusoidal force at the end of the bar, as the aforementioned sample and "Samples | Time_Dependent | Stress | Vibrate.pde" do, and let FlexPDE calculate the deformation. | ||||
| Mehdi Naderi (mnader4) Member Username: mnader4 Post Number: 35 Registered: 12-2006 |
Dear Mr. Nelson, I changed the equation of motion of the the beam based on Timoshenko' book, page 35-38. But ther is the same problem and answer is not symetric. I think fpde changes the coordinate (x,y) of the beam and because of that in the end of the beam where there is large deflection x and y of the beam vary while the beam fluctuating. Actually, x and y in the equation of motion are the coordinate of every point of the beam while it has no motion. How can I tell fpde to hold the original coordinate of the beam constan and based on this original coordinade change the the new position of every point according to the equation of the motion? Regards, Mehdi
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1026 Registered: 06-2003 |
At present, there is no way to "remember" the location where a given node originated. This makes application of your analytic rule difficult. If you could turn the analytic solution into a differential equation, you could apply that rule directly. | ||||
| Mehdi Naderi (mnader4) Member Username: mnader4 Post Number: 36 Registered: 12-2006 |
Dear Mr. Nelson, Thank you so much. As you know I am going to use true displacement equation for solving fluid flow and heat transfer around a fluctuating beam. I want to avoid calculation of displacement equations because without them there are a lot equatios in the program and running time is slow enough. So, I am trying to put analytical displacement equation. You said now fpde cannot remember initial coordinates. What about changing coordinate system ? Do you think it will work? Regards... | ||||
| Marek Nelson (mgnelson) Moderator Username: mgnelson Post Number: 18 Registered: 07-2007 |
I do not think changing the coordinate system will effect this issue. |
conduction
deflection of beam