No abstract

A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces

This work introduces an indirect Boundary Element Method (BEM) within a NURBSbased isogeometric framework for solving three-dimensional acoustic problems in the frequency domain. Developments of isogeometric boundary elements so far have focused on the direct BEM. Yet, a multitude of common problems in acoustics involves openboundary surfaces, which require a more involved, indirect, boundary element formulation. The current work presents an indirect variational BEM which makes use of NURBS shape functions. Additionally, a novel technique for coupling (strongly) non-conforming patches is introduced to allow the analysis of more complex geometries. The proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial-based indirect BEM. Also two open-boundary problems are studied, including analyses over wider frequency ranges, and one industrial-type, complex geometry containing multiple non-conforming patches. The proposed method is found to be not only significantly more efficient than its polynomialbased counterpart, but also very robust against strong non-conformities in the NURBS descriptions.

With the emergence of isogeometric analysis (IGA), the Galerkin rotation-free discretization of Kirchhoff-Love shells is facilitated, enabling more efficient thin shell structural analysis. High-order shape functions used in IGA also allow the collocation of partial differential equations, avoiding the time-consuming numerical integration of the Galerkin technique. The goal of the present work is to apply this method to NURBS-based isogeometric Kirchhoff-Love plates and shells, under the assumption of small deformations.Since Kirchhoff-Love plate theory yields a fourth-order formulation, two boundary conditions are required at each location on the contour, generating some conflicts at the corners where there are more equations than needed. To remedy this overdetermination, we provide priority and averaging rules that cover all the possible combinations of adjacent edge boundary conditions (i.e. the clamped, simplysupported, symmetric and free supports). Greville and alternative superconvergent points are used for NURBS basis of even and odd degrees, respectively. For square, circular, and annular flat plates, convergence orders are found to be in agreement with a-priori error estimates. The proposed isogeometric collocation method is then validated and benchmarked against a Galerkin implementation by studying a set of problems involving Kirchhoff-Love shells.

This paper presents a flexible method for coupling NURBS patches in isogeometric Kirchhoff-Love shell analysis. The required C 1 -continuity in such a shell formulation significantly complicates the patch coupling (as compared to typical C 0 -cases). In the present work, the C 0 -part of the coupling is a global coupling in a weak sense, whereas the C 1 -continuity is enforced by a strong point-wise coupling in well-chosen collocation points along the interface. The coupling conditions can be derived using only mesh information, without the need for suitable penalty or stabilisation parameters. They are expressed using a master-slave formulation between the interface variables. A static condensation approach to enforce these continuity constraints results in a reduced system matrix. The proposed method can be employed for both conforming and non-conforming patch configurations, and for G 1 -continuous structures as well as for patches meeting at a kink. This is demonstrated for a set of problems of (dynamic) shell analysis, including both eigenvalue and boundary-value problems.