I work in gas turbine business and I noticed following phenomena so I would like someone helps me to understand.
I noticed that component made as full ring remains circular after load with outer pressure and temperature gradient (Figure 1) and component made as connection of 2 halfrings (Figure 2) deforms as on Figure 3.
I find, as major cause of such deformation, temperature gradient which affects as on Figure 4, but replacing connection with outer momentum I can (using integrity laws - I am not very familiar with Elasticity theory) receive only circular shape, because same momentum in section results with same local radius of curvation as on Figure 5.
Please help me to understand how to get shape of deformation like on Figure 3.
I hope this problem is already solved but for the literature I can use only free material.
All Figures are in attachment
Thanks in advance to all.
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| Sketch.jpg | 365.56 KB |
| Sketch1.jpg | 36.18 KB |
Simplification of the problem
I really expected more from you guys. Let me simplify the problem.Instead of temperature gradient load, let’s analyse part of the ring in cold condition with overall angle y (y>p see attachment Sketch1 from previous comment – Figure 1) and loaded with momentums M0 at the ends. Overall angle of displacement curve has to be p. Boundary conditions are as on Figure 2 (a is angle of the curve on normal).
P.S. It is not a problem if the last constant in displacement curve over angle is not defined because in the final I am interested in ovalisation value (horizontal minus vertical radius).
I hope you can help me to receive equation of displacement curve over angle.