Micro-scale blood particulate dynamics using a non-uniform rational B-spline-based isogeometric analysis

2014 ◽  
Vol 30 (12) ◽  
pp. 1437-1459 ◽  
Author(s):  
V. Chivukula ◽  
J. Mousel ◽  
J. Lu ◽  
S. Vigmostad
Keyword(s):  
Isogeometric Analysis ◽  
B Spline ◽  
Micro Scale

scholarly journals A priori error for unilateral contact problems with Lagrange multipliers and isogeometric analysis

2018 ◽  
Vol 39 (4) ◽  
pp. 1627-1651 ◽  
Author(s):  
Pablo Antolin ◽  
Annalisa Buffa ◽  
Mathieu Fabre
Keyword(s):  
Isogeometric Analysis ◽  
A Priori ◽  
Contact Problems ◽  
Unilateral Contact ◽  
Spline Space ◽  
Three Dimensions ◽  
B Spline ◽  
A Priori Error Estimate ◽  
The Stability ◽  
Unilateral Contact Problems

Abstract In this paper we consider a unilateral contact problem without friction between a rigid body and a deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem. For the displacement, we use the pushforward of a nonuniform rational B-spline space of degree $p$ and for the Lagrange multiplier, the pushforward of a B-spline space of degree $p-2$. These choices of space ensure the proof of an inf–sup condition and so on, the stability of the method. We distinguish between contact and noncontact sets to avoid the classical geometrical hypothesis of the contact set. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two and three dimensions and in small and large deformation frameworks demonstrate the accuracy of the proposed method.

Sensitivity Analysis of Quality of B-spline Parameterization on Isogeometric Analysis

2021 ◽  
Author(s):  
Sangamesh Gondegaon ◽  
Hari Kumar Voruganti
Keyword(s):  
Isogeometric Analysis ◽  
Heat Conduction Problem ◽  
Exact Analytical Solution ◽  
Field Variable ◽  
Control Points ◽  
B Spline ◽  
Mesh Free ◽  
Spline Basis ◽  
Evaluation Metric

Isogeometric analysis (IGA) is a mesh free technique which make use of B-spline basis functions for geometry and field variable representation. Parameterization of B-spline for IGA is the counterpart of meshing as in finite element method (FEM). The objective of parameterization is to find the optimum set of control points for B-spline modelling. The position of control points of a B-spline model has huge effect on IGA results. In this work, the effect of B-spline parameterization on IGA result is presented. One dimensional case of bar with self-weight is solved and compared with exact analytical solution. First fundamental matrix is used as evaluation metric to check the quality of parameterization for 2-D domains. A heat conduction problem of a square domain is presented to study the parameterization effect for 2-D case.

Constructing B-spline solids from tetrahedral meshes for isogeometric analysis

2015 ◽  
Vol 35-36 ◽  
pp. 109-120 ◽  
Author(s):  
Hongwei Lin ◽  
Sinan Jin ◽  
Qianqian Hu ◽  
Zhenbao Liu
Keyword(s):  
Isogeometric Analysis ◽  
B Spline ◽  
Tetrahedral Meshes

scholarly journals Spline Parameterization of Complex Planar Domains for Isogeometric Analysis

2017 ◽  
Vol 47 (1) ◽  
pp. 18-35 ◽  
Author(s):  
Sangamesh Gondegaon ◽  
Hari K. Voruganti
Keyword(s):  
Unit Circle ◽  
Isogeometric Analysis ◽  
Harmonic Functions ◽  
Geometric Model ◽  
Mean Value ◽  
Mapping Method ◽  
Control Points ◽  
Computationally Efficient ◽  
B Spline ◽  
Domain Mapping

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.

2110 Isogeometric analysis of shell models with accurate curvatures represented by B-spline surfaces B-spline

2011 ◽  
Vol 2011.21 (0) ◽  
pp. 171-175
Author(s):  
Kaiyuan Mu ◽  
Tadahiro SHIBUTANI ◽  
Kazumi MATSUI ◽  
Takashi MAEKAWA
Keyword(s):  
Isogeometric Analysis ◽  
B Spline ◽  
Spline Surfaces ◽  
Shell Models
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