Abstract
We derive a hyperelastic shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid–structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the “midsurface” location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the “midsurface” location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung’s models, for the compressible- and incompressible-material cases, and for two different locations of the “midsurface.” We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.
Highlights
A shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization was introduced in [1,2,3]
We start with the formulation from [4] and derive, based on the Kirchhoff–Love shell theory and isogeometric discretization, a hyperelastic shell formulation that takes into account the out-of-plane deformation mapping
In fluid–structure interaction (FSI) analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know
Summary
A shell formulation based on the Kirchhoff–Love shell theory and isogeometric discretization was introduced in [1,2,3]. It has the advantage of not requiring rotational degrees of freedom. Extension to general hyperelastic material can be found in [4]. The formulation has been successfully used in computation of a good number of challenging problems, including wind-turbine fluid–structure interaction (FSI) [3,5,6,7,8,9], bioinspired flapping-wing aerodynamics [10], bioprosthetic heart
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