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  • Author: Sangamesh Gondegaon x
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Sangamesh Gondegaon and Hari K. Voruganti

Abstract

Isogeometric Analysis (IGA) is a new analysis method for unification of Computer Aided Design (CAD) and Computer Aided Engineering (CAE). With the use of NURBS basis functions for both modelling and analysis, the bottleneck of meshing is avoided and a seamless integration is achieved. The CAD and computational geometry concepts in IGA are new to the analysis community. Though, there is a steady growth of literature, details of calculations, explanations and examples are not reported. The content of the paper is complimentary to the existing literature and addresses the gaps. It includes summary of the literature, overview of the methodology, step-by-step calculations and Matlab codes for example problems in static structural and modal analysis in 1-D and 2-D. At appropriate places, comparison with the Finite Element Analysis (FEM) is also included, so that those familiar with FEM can appreciate IGA better.

Open access

Sangamesh Gondegaon and Hari K. Voruganti

Abstract

Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no self-intersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.