Weak Cⁿ coupling for multipatch isogeometric analysis in solid mechanics

Abstract

Summary The objective of this contribution is to design a novel methodology to enforce interface conditions preserving higher‐order continuity across the interface. In recent years, isogeometric methods using NURBS as basis functions have gained increasing attention, especially in the context of higher‐order partial differential equations. They require, in general, higher continuity across interfaces, and thus, new methodologies for domain decomposition constraints capable to deal with those requirements have to be developed. In this contribution, we introduce, in a first step, the coupling constraints using a Euclidean norm on the interface and construct new basis functions. A reformulation as saddle point system allows for a comparison with classical mortar approaches and leads finally to an extended mortar method to enforce Cn continuity.

Frontiers in Mortar Methods for Isogeometric Analysis

“…of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis") are gratefully acknowledged. Moreover, we would like to thank S. Schuß and M. Dittmann as co-authors of [20,21,67], S. Klinkel as co-author of [67] and İ. Temizer and M. Franke as co-authors of [37]. Funds provided by the Deutsche Forschungsgemeinschaft under the contract/grant numbers: HE5943/3-2, HE5943/6-1, HE5943/8-1, DI2306/1-1 and HE5943/5-1 (within the Priority Program SPP 1748, "Reliable Simulation Techniques in Solid Mechanics.…”

“…In [20], the previously introduced concept of high-order mortar coupling conditions is extended towards the application on Cauchy continua. Moreover, we investigate different evaluations of general C n continuous coupling conditions, written in terms of a saddle point system.…”

“…A wide range of issues arise, mostly related with the suitable choice of the Lagrange multiplier space. In a series of actual contributions [20,21,40,67], higher-order domain decomposition has been addressed as well, which allows for the application of higher-order PDE's in multi-patch geometries.…”

Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff‐Love theory

“…and F m is defined analogous to (5). Unfortunately, especially if the curves meet not G 1 but high regularity of the corresponding IGA test functions is required, then the coupling gets involved.…”

“…bad approximation results, if we want strong global C r -smoothness with r ≥ 1; see [4]. Consequently, in literature one can find the concept of weak patch-coupling to define proper multipatch IGA spaces; see [5][6][7]. But in 2D, if one restricts oneself to a special class of parametrizations, the so-called analysis-suitable G 1 parametrizations, the strong C 1 coupling of patches is possible; cf.…”