Isogeometric Analysis of Multi-patch Geometry

Isogeometric analysis (IGA) aims at bridging the gap between Computer Aided Design (CAD) and Computer Aided Engineering (CAE) by utilizing Non-uniform rational B-splines (NURBS), which is used for geometric description, as the basis for approximating the solution in CAE environment. However, IGA is not always straightforward, like in case of complex geometries which are generally described using multiple NURBS surfaces/patches also called as Multi-patch Geometry.

The patches in multi-patch geometry needs to be coupled for analysis suitability, this posses a problem due to the required order of continuity and also the conformity between the patches. Here, conformity means whether the patch interfaces are conforming or non-conforming i.e matching or non-matching edges at the interface. The coupling of patches with C1 or higher continuity requirements and for non-conforming patches, is not a trivial matter, and requires use of methods such as Nitsche’s method, mortar methods, domain decomposition, Finite element tearing and interconnecting method etc.

In case of conforming patches with C0 continuity requirement, we can couple the patches by assigning the same degree of freedom at the interface of the patches. We have accomplished this by creating a data structure and method that is called when the control points of a patch is updated. A plate with a hole is shown here without the C0 coupling and with it. We can see that the C0 coupling is automatically established.

Plate with a hole
Plate with a hole: without C0 coupling

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