Coupling a simple nonlinear membrane to point displacement Michael Alletto

• contributor: Michael Alletto
• affiliation: WRD MS
• contact: click here for email address
• OpenFOAM versions: v2112
• Published under: CC BY-NC-ND license (creative commons licenses)

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You can download the case https://gitlab.com/mAlletto/openfoamtutorials/-/tree/master/membranBCSend] here.

Introduction

In the tutorial https://wiki.openfoam.com/Coupling_a_membrane_with_pretension_to_point_displacement_Michael_Alletto we saw how to couple different physical models. In the before mentioned tutorial we coupled the equations of motion of a prestressed membrane with the displacement of the mesh. The membrane is deformed by the action of the pressure on the solid surface. The equations of motion for a prestressed membrane assume that the stress of the membrane is constant and does not change when the membrane is deformed. The question which arises is what is if we want to simulate a membrane which is in an initial undeformed and unstressed configuration and deforms by the action of the fluid pressure? How should we proceed to figure out what are the correct equations to be solved, what kind of assumptions has to be made to simplify the equation and how do we verify if our assumptions are correct? In this tutorial we will answer this question.

References

[1] Fadl Moukalled, L Mangani, Marwan Darwish, et al. The finite volume method in computational fluid dynamics, volume 113. Springer, 2016.

[2] Draga Pihler-Puzović, Anne Juel, Gunnar G Peng, John R Lister, and Matthias Heil. Displacement flows under elastic membranes. part 1. ex- periments and direct numerical simulations. Journal of Fluid Mechanics, 784:487–511, 2015.

[3] Junuthula Narasimha Reddy. Theory and analysis of elastic plates and shells. CRC press, 2006.

[4] Stephen Timoshenko, Sergius Woinowsky-Krieger, et al. Theory of plates and shells, volume 2. McGraw-hill New York, 1959.