Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches

Abstract

of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches. (2017) Highlights• We develop a new mortar method for NURBS that keeps the benefit of using more regular functions.• We propose to match the tractions in addition to the displacements at the coupling interface.• We apply the methodology to perform the non-intrusive local enrichment of NURBS patches.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we develop a mortar method for the coupling of non-conforming NURBS subdomains within a NURBS patch that keeps the benefit of using more regular functions. The idea is to use two Lagrange multipliers to match, across the coupling interface, the tractions coming from the discrete displacements in addition to the discrete displacements. It results in a strategy that is suitable with the continuity of the physical solution: when the physical solution is sufficiently smooth, the strategy enables to represent a C 1 behavior; but, when only a C 0 displacement is expected, no additional errors are introduced since only the traction force is continuous and not the whole derivative fields. Lower stress jumps at the coupling interface can then be observed which allows for a better transition of the information. As an application, a non-intrusive algorithm is also built to solve the proposed coupling method, which enables simple and flexible local enrichments of NURBS patches without losing the interest of using more regular functions. A range of numerical examples in two-dimensional linear elasticity are carried out along with comparisons with other published NURBS coupling techniques to demonstrate the performance of the proposed coupling and its interest when combined to a non-intrusive strategy.

Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling

“…3 for illustration). We follow the nomenclature introduced in [33]. From the most restrictive to the most general case, we may encounter the situations of: 1.…”

“…In this respect, the approach is different from [18] where two interfaces where used for the local/global coupling. In addition, the proposed method can treat non-conforming geometries in a more robust and non-intrusive way when compared to [32,33]. The proposed method manages all the numerical complexities that arise with multiscale aeronautical concerns: local non-linear model, non-conforming geometries, shell-to-solid coupling, fully non-planar structure, etc.…”

“…The non-intrusive coupling strategy seems to be well-established nowadays in the FEbased computational mechanics community (see, e.g., [10,[14][15][16][17][18][19][20][21][22][32][33][34]). …”

“…8), which would require to set up specific quadrature rules to integrate over pieces of coarse elements. A methodology based on the transfer of the local quadrature rule in the global computations has been proposed in [32,33] for the coupling of NURBS isogeometric models. Nevertheless, this approach appears inconsistent with the use of standard industrial FE codes.…”

“…This strongly reduces the applicability of the method in an industrial context (see the situation of holes, bolted assemblies, etc.). Recently, the authors proposed a rigorous strategy based on setting up suitable quadrature rules for the coupling of non-conforming NURBS isogeometric models [32,33], but this approach does not seem pertinent in an industrial FE context. To go even further in the non-intrusive philosophy, we propose in the present work to overcome this scientific obstacle by means of a pragmatic technique based on features already implemented in commercial codes.…”