Rods in contact under pressure
Marta Zoppello (Politecnico di Torino)
Thursday 9th July, 2020 14:00-15:00 ZOOM (ID: 971 1720 8523)
Please Note: The ZOOM meeting will be password protected, as per the e-mail you received with subject: "Applied Mathematics Seminar ZOOM password".
We study the equilibrium of a mechanical system composed by two rods that bend under the action of a pressure difference; they have one fixed endpoint and are partially in contact. We obtain the balance equations of the mechanical system exploiting the principle of virtual works and the contact point is identified by a jump condition. The problem can be simplified exploiting a first integral. Numerical integration of the differential system shows how the shape of the beams and the position of the contact point depend on the applied pressure. For small pressure, an asymptotic expansion in a small parameter allows us to find an approximate solutions of polynomial form which is in surprisingly good agreement with the solution of the original system of equations, even beyond the expected range of validity. Moreover this asymptotics predicts a value of the pressure that separates the contact from the no-contact regime of the beams.