Скачать или смотреть [29/06/2021] Severo Ochoa Coffee Talk by G. Scovazzi; "The shifted boundary method for embedded..."

"The shifted boundary method for embedded solid mechanics"

A new embedded/immersed framework for computational solid mechanics is presented, with the aim of vastly speeding up the cycle of design and analysis in complex geometry. In many problems of interest, the proposed approach bypasses the complexities associated with generation of CAD representations and subsequent body-fitted meshing, since it only requires a relatively simple surface representation of the geometries to be simulated, such as, for example, STL files widely used in computer graphics (i.e., collections of disconnected triangles in three dimensions). Most finite element embedded boundary methods are of difficult implementation, due to the need to perform complex cell cutting operations at boundaries, and the consequences that these operations may have on the overall conditioning of the ensuing algebraic problems. The “shifted boundary method” (SBM) eliminates the need to perform cell cutting. Boundary conditions are imposed on a surrogate discrete boundary, lying on the interior of the true boundary interface. We then construct appropriate field extension operators, with the purpose of preserving accuracy when imposing the boundary conditions. An extensive set of computational experiments in two and three dimensions is included, to demonstrate optimal convergence of the error and robustness in complex geometry simulations.