Re: Imposing a rolling condition

[Raphaël Meunier]

Dear Kostas,

 

Thank you for your response. As my intuition is not as sharp as yours, I might need a few explanations:

• md.add_nonlinear_term(mim, "(u-rot(phi)*(X-[xc;yc])).mult", HoleZone) --> This order zero term seems pretty straightforward and much more readable than in my code
• md.add_linear_term(mim, "Fy/area*Test_yc", HoleZone) --> No multiplier is involved in your formulation. Is this because we need to combine this term with the previous order 0 term -((rot(phi)*([0;1])).mult)*Test_yc (and check the sign) ?
• md.add_linear_term(mim, "([Fx/area,0]*rot_der(phi))*(X-[xc;yc])*Test_phi", HoleZone) --> Could you explain how do you come up with this term ?
• A more general question: Is it possible to formulate the whole condition as an order 0 term ?

Thanks in advance,

Best regards

Raphaël

Le mer. 6 avr. 2022 à 23:14, Konstantinos Poulios <logari81@googlemail.com> a écrit :

Dear Raphaël,

Interesting question. Prescribing Fx is a bit strange condition. I haven't checked it, but I think something like this should work:

md.add_initialized_data("Fx", 10.)
md.add_initialized_data("Fy", 100.)

md.add_initialized_data("xc", 0.)
md.add_variable("yc", 1)
md.set_variable("yc", yc)
md.add_variable("phi",1)
md.set_variable("phi", 0.)
md.add_fem_variable("u", mfu)
md.add_filtered_fem_variable("mult", mfu, HoleZone)

md.add_macro("rot(x)", "[cos(x)-1,sin(x);-sin(x),cos(x)-1]")
md.add_macro("rot_der(x)", "[-sin(x),cos(x);-cos(x),-sin(x)]")

md.add_initialized_data("area", gf.asm_generic(mim, 0, "1", HoleZone)) # Calculate the area of the region
md.add_nonlinear_term(mim, "(u-rot(phi)*(X-[xc;yc])).mult", HoleZone)
md.add_linear_term(mim, "Fy/area*Test_yc", HoleZone)                                 # check if a minus sign is needed
md.add_linear_term(mim, "([Fx/area,0]*rot_der(phi))*(X-[xc;yc])*Test_phi", HoleZone) # check if a minus sign is needed

for time in [0,0.1,0.3,0.6,0.9]:
  md.set_variable("xc", speed*time)
  md.solve("noisy")

A bit based on intuition but you can certainly learn something from analyzing this suggestion. Let us discuss it further if you cannot get it to work and have more questions. Try to avoid expressions like "speed*time" and "alpha*time" in your expressions, they seem too specific to constant velocities, they make the code more difficult to read, and they will not help you to generalize the code later. Just solve for positions/angles directly if that's what you want.

FYI, the _expression_

(u-rot(phi)*(X-[xc;yc])).mult

will expand internally to something like

 (u-rot(phi)*(X-[xc;yc])).Test_mult
+Test_u.mult
-((rot_der(phi)*(X-[xc;yc])).mult)*Test_phi
-((rot(phi)*([0;1])).mult)*Test_yc

BR

Kostas

On Wed, Apr 6, 2022 at 4:54 PM Raphaël Meunier <raphael.meunier1@gmail.com> wrote:

Dear Getfem-Users,

I am trying to impose a rolling condition on a "tire". My work is directly inspired from the "Example of wheel in contact" tutorial. In this tutorial, one wants to prescribe the rim rigidity and the vertical force. From this, I just have to add a rolling condition. Specifically I want to find the rotation speed "alpha_rot" that enables me to impose some force Fx:

gwfl_rot='-lambda_D.Test_u + ([cos(alpha_rot*time),sin(alpha_rot*time);-sin(alpha_rot*time),cos(alpha_rot*time)]*(X-[0;y_c])-(X-[0;y_c])\
+ [speed*time;alpha_y] - u).Test_lambda_D +(lambda_D.[1;0] + Fx)*Test_alpha_rot + 1E-6*alpha_rot*Test_alpha_rot'
gwfl_y='(lambda_D.[0;1] + Fy)*Test_alpha_y + 1E-6*alpha_y*Test_alpha_y'
roll_gwfl=gwfl_y+gwfl_rot

idBrick = model.add_nonlinear_term(mim, roll_gwfl, HoleZone)

Where alpha_rot and alpha_y are the "parameters" I am trying to find. This works for up to ten timesteps but then it diverges... I tried to use two multipliers instead of one which leads to worse results.

Am I on the right track ? Is there a better way to achieve this ?

Thanks in advance,

Best regards,

Raphaël