Nonintrusive coupling of 3D and 2D laminated composite models based on finite element 3D recovery

In order to simulate the mechanical behavior of large structures assembled from thin composite panels, we propose a coupling technique which substitutes local 3D models for the global plate model in the critical zones where plate modeling is inadequate. The transition from 3D to 2D is based on stress and displacement distributions associated with Saint-Venant problems which are precalculated automatically for a simple 3D cell. The hybrid plate/3D model is obtained after convergence of a series of iterations between a global plate model of the structure and localized 3D models of the critical zones. This technique is nonintrusive because the global calculations can be carried out using commercial software. Evaluation tests show that convergence is fast and that the resulting hybrid model is very close to a full 3D model

Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach