While the framework of Isogeometric Analysis (IGA) has opened new perspectives for the improved interaction between design and analysis, it has also led to new challenging problems which are related to the representation of the geometry. In particular, while models in geometric design are typically given in boundary representation (BRep), the use of parameterized volumes is essential for IGA. D...

In the present paper, an approach is proposed for structural topology optimization based on combination of Radial Basis Function (RBF) Level Set Method (LSM) with Isogeometric Analysis (IGA). The corresponding combined algorithm is detailed. First, in this approach, the discrete problem is formulated in Isogeometric Analysis framework. The objective function based on compliance of particular lo...

The global (patch-wise) geometry map, which describes the computational domain, is a new feature in isogeometric analysis. This map has a global tensor structure, inherited from the parametric spline geometry representation. The use of this global structure in the discretization of partial differential equations may be regarded as a drawback at first glance, as opposed to the purely local natur...

This paper deals with the isogeometric analysis using B-splines of space rods subject to Kirchhoff-Love hypotheses. A multi-patch isogeometric approach for the numerical analysis of the three-dimensional Kirchhoff-Love rod theory is developed. We use Bezier and B-splines interpolations and we show that they are able to attain very good accuracy for rod structures, particularly for developing a ...

We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, lumenal surfaces are e...

We initiate the study of efficient quadrature rules for NURBS-based isogeometric analysis. A rule of thumb emerges, the “half-point rule”, indicating that optimal rules involve a number of points roughly equal to half the number of degrees-of-freedom, or equivalently half the number of basis functions of the space under consideration. The half-point rule is independent of the polynomial order o...

This paper presents the Fourier and wavelet characterization of vibratio...