An isogeometric b-rep mortar-based mapping method for non-matching grids in fluid-structure interaction

Abstract

In this study the isogeometric B-Rep mortar-based mapping method for geometry models stemming directly from Computer-Aided Design (CAD) is systematically augmented and applied to partitioned Fluid-Structure Interaction (FSI) simulations. Thus, the newly proposed methodology is applied to geometries described by their Boundary Representation (B-Rep) in terms of trimmed multipatch Non-Uniform Rational B-Spline (NURBS) discretizations as standard in modern CAD. The proposed isogeometric B-Rep mortar-based mapping method is herein extended for the transformation of fields between a B-Rep model and a low order discrete surface representation of the geometry which typically results when the Finite Volume Method (FVM) or the Finite Element Method (FEM) are employed. This enables the transformation of such fields as tractions and displacements along the FSI interface when Isogeometric B-Rep Analysis (IBRA) is used for the structural discretization and the FVM is used for the fluid discretization. The latter allows for diverse discretization schemes between the structural and the fluid Boundary Value Problem (BVP), taking into consideration the special properties of each BVP separately while the constraints along the FSI interface are satisfied in an iterative manner within partitioned FSI. The proposed methodology can be exploited in FSI problems with an IBRA structural discretization or to FSI problems with a standard FEM structural discretization in the frame of the Exact Coupling Layer (ECL) where the interface fields are smoothed using the underlying B-Rep parametrization, thus taking advantage of the smoothness that the NURBS basis functions offer. All new developments are systematically investigated and demonstrated by FSI problems with lightweight structures whereby the underlying geometric parametrizations are directly taken from real-world CAD models, thus extending IBRA into coupled problems of the FSI type.

Isogeometric gradient‐free proportional topology optimization (IGA‐PTO) for compliance problem

“…Second, the high continuity of NURBS basis functions in the approximation of unknown variables and the distinct $$$ k $$$‐refinement mechanism 2–4 offer higher accuracy per degree of freedom compared to conventional FEMs. These two merits have been thoroughly evidenced in many studies for structural mechanics, 5–12 fracture mechanics, 13–18 and fluid mechanics 19–22 …”

“…These two merits have been thoroughly evidenced in many studies for structural mechanics, [5][6][7][8][9][10][11][12] fracture mechanics, [13][14][15][16][17][18] and fluid mechanics. [19][20][21][22] Optimization is always an attractive keyword to engineers, and inevitably the IGA framework has been applied to this problem to devise more efficient instruments for structural designs. Although the IGA approach has been soon considered for sizing and shape optimizations, [23][24][25][26][27][28][29][30][31] great endeavors are dedicated to topology optimization, which distributes a given amount of material within a prescribed domain to optimize structural performances meeting some constraints.…”