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cylindrical coordinate system
Posted:
Jul 10, 2012 6:22 PM
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Hi,
Thanks for reading my posting.
I am using an engineering ?Finite Element Method? program. To get better idea of what I am going to ask please see the attached picture. I am trying to stretch circumferentially a piece of cylinder (with central angle of 75 degrees) and make it a half cylinder (central angle of 180 degrees). The picture is from the solution based on Cartesian coord. Sys.
I was going to solve the problem using cylindrical coordinate system, where in the boundary conditions section I need to specify two DISPLACEMENTS for the inner surface: one in r direction (ur) and the other in phi (tangential) direction (ut). Unfortunately, the program is not asking for change in angle phi, but I asking about change in length (displacement) in phi.
I have the initial and final radii of the inner surface (and even outer radii), and also initial and final phi values. Specifying ?ur? is very simple, however, in phi direction the things seem to be vague to me as both radius and angle are changing. So what I probably need to do is to enter delta value of:
d(r*phi)= r*d(phi)+phi*dr
My question is that is it correct to evaluate this by using initial radius (the one before deformations) and also initial values of angle, phi, in the above equation. I am asking this because the above equation is general in terms of r and phi, and I was asking myself should I use r=Ri or r=ri (where ri is the inner radius after deformation), and also should I use phi before deformation or after deformation.
Any comments is highly appreciated.
Thanks
MZ
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