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Imposing a rolling condition


From: Raphaël Meunier
Subject: Imposing a rolling condition
Date: Wed, 6 Apr 2022 16:08:24 +0200

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

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