Fixed membrane wings for micro air vehicles: Experimental characterization, numerical modeling, and tailoring

Fluid–structure interaction, immersed boundary-finite element method simulations of bio-prosthetic heart valves

A moving-least-squares immersed boundary method for simulating the fluid-structure interaction of elastic bodies with arbitrary thickness

Heart valves are functionally complex, making surgical repair difficult. Simulation-based surgical planning could facilitate repair, but current finite element (FE) studies are prohibitively slow for rapid, clinically oriented simulations. Mass-spring (M-S) models are fast but can be inaccurate. We quantify speed and accuracy differences between an anisotropic, nonlinear M-S and an efficient FE membrane model for simulating both biaxial and pressure loading of aortic valve (AV) leaflets. The FE model incurs approximately 10 times the computational cost of the M-S model. For simulated biaxial loading, mean error in normal strains is <1% for both FE and M-S models for equibiaxial loading but increases for non-equibiaxial states for the M-S model (7%). The M-S model was less able to simulate shear behavior, with mean strain error of approximately 80%. For pressurized AV leaflets, the M-S model predicts similar leaflet dimensions to the FE model (within 2.6%), and the coaptation zone is similar between models. The M-S model simulates in-plane behavior of AV leaflets considerably faster than the FE model and with only minor differences in the deformed mesh. While the M-S model does not allow explicit control of shear response, shear does not strongly influence shape of the simulated AV under pressure.

http://biorobotics.harvard.edu/pubs/2011/journal/HAMMER_MassSpringForSimHeartValveTissue_AnnBME2011.pdf

Mass-Spring Model for Simulation of Heart Valve Tissue Mechanical Behavior

The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a ‘pseudo-dynamic’ approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little ‘waves’ in ‘compressed’ areas. Current work presents an efficient, sub-iteration free ‘explicit’, penalty material based, wrinkling simulation procedure suitable for the solution of ‘static’ problems. The procedure is stabilized by taking full advantage of the pseudo-dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up ‘numerical experiments’ based on the solution of test cases using dense meshes. Copyright © 2005 John Wiley & Sons, Ltd.

Simulation of light-weight membrane structures by wrinkling model

This paper summarizes the development for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation gradient is first constructed in terms of nodal variables. In particular, the use of the right Cauchy-Green deformation tensor is shown to lead to a particulary simple representation in terms of nodal quantities. This may then be used to construct general models for use in static and transient analyses.

Pere-Andreu Ubach

Papers

Finite Element Analysis of Membrane Structures

A FEM fluid–structure interaction algorithm for analysis of the seal dynamics of a Surface-Effect Ship

Adaptive breakwaters with inflatable elements for coastal protection. Preliminary numerical estimation of their performance

Advances in Shell Finite Elements