Deformation of a circular elastic tube between two parallel bars: quasi-analytical geometrical ring models (Q1665973)

Summary: Several engineering problems are confronted with elastic tubes. In the current work, homothetic quasi-analytical geometrical ring models, ellipse, stadium, and peanut, are formulated allowing a computationally low cost ring shape estimation as a function of a single parameter, that is, the pinching degree. The dynamics of main geometrical parameters due to the model choice is discussed. Next, the ring models are applied to each cross section of a circular elastic tube compressed between two parallel bars for pinching efforts between 40\% and 95\%. The characteristic error yields less than 4\% of the tubes diameter when the stadium model was used.