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Volumetric T-Spline Modeling
Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018
With the rapid development of 3D scanning data acquisition and automatic geometric modeling techniques, the obtained geometries are usually represented in the form of polygonal meshes. Note that the scanned data can be slices of images like CT and MRI as we discussed in the previous chapters, or they can be points cloud acquired from Reverse Engineering. Besides polygonal meshes, spline models are popularly used to represent free-form surfaces, especially in computer aided design (CAD), computer aided manufacturing (CAM), and computer aided engineering (CAE). Unlike piecewise-linear elements, splines can accurately represent a wide range of geometric objects with high order continuity. In recent years, a spline-based analysis method named “isogeometric analysis” was developed [42, 104, 179], which integrates design with analysis directly and has many advantages over the traditional finite element method (FEM). Isogeometric analysis utilizes the same basis functions to construct the geometry and the solution space, it basically incorporates the isoparametric idea into FEM. To improve geometric accuracy and surface continuity, and to achieve compatibility with CAD systems and isogeometric analysis, one of the most significant challenges facing isogeometric analysis researchers is developing analysis-suitable volumetric spline parameterizations such as solid NURBS and T-splines from boundary representations.
Computational Methods in Cardiovascular Mechanics
Published in Michel R. Labrosse, Cardiovascular Mechanics, 2018
F. Auricchio, M. Conti, A. Lefieux, S. Morganti, A. Reali, G. Rozza, A. Veneziani
Isogeometric analysis was introduced in 2005 by Hughes and coworkers, with the main goal of bridging the gap between computer-aided design (CAD) and the FEM-based engineering analysis process. Its basic paradigm consists of adopting the same basis functions used for geometry representations in CAD systems, such as NURBS (e.g., for the approximation of field variables), in an isoparametric fashion. This leads to a cost-saving simplification of the typically expensive mesh generation and refinement processes required by standard FEA; this was the original motivation for IGA. Moreover, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per degree of freedom and an enhanced robustness compared with standard FEA in a number of applications. Solids and structures are prime examples (see, e.g., Cottrell et al., 2006; Cottrell et al., 2007; Elguedj et al., 2008; Lipton et al., 2010; Schillinger et al., 2012; Caseiro et al., 2015) and also include effective beam, plate, and shell elements (see, e.g., Kiendl et al., 2009; Benson et al., 2010; Echter et al., 2013; Kiendl et al., 2015). Isogeometric analysis has also been successful in fluid mechanics and fluid–structure interaction (see, e.g., Bazilevs et al., 2007; Akkerman et al., 2008; Gomez et al., 2010; Hsu and Bazilevs, 2012; Hsu et al., 2015) and has opened the door to geometrically flexible discretizations of higher-order partial differential equations (PDEs) in primal form (see, e.g., Auricchio et al., 2007; Gomez et al., 2008; Kiendl et al., 2016). Thanks to its more-than-promising results, IGA has attracted a lot of attention and is now regarded as one of the most prominent research areas in modern computational mechanics. Within this context, we focus here on two recent applications that show the potential of IGA for structural biomechanical simulations: aortic valves and SMA stents.
EdgeCFD: a parallel residual-based variational multiscale code for multiphysics
Published in International Journal of Computational Fluid Dynamics, 2020
Adriano M. A. Cortes, Erb F. Lins, Gabriel M. Guerra, Rômulo M. Silva, José L. D. Alves, Renato N. Elias, Fernando A. Rochinha, Alvaro L. G. A. Coutinho
There has been a continuous development of CFD tools to face the above challenges. We refer here to several CFD finite element codes designed for high performance, such as Alya (Vázquez et al. 2016), PHASTA (Sahni et al. 2009) and FreeFEM (Hecht 2012). Note that Alya and PHASTA have been used successfully in production runs with hundreds of thousands of cores. On the other hand, to help developers, general finite element libraries that support the development of parallel multiphysics applications are becoming increasingly popular. Among then, libMesh (Kirk et al. 2006), that has been used in around 1000 scientific works, MOOSE (Gaston et al. 2009), tailored for CFD applications in the nuclear industry, FEniCS (Logg, Mardal, and Wells 2012), deal.II (Arndt et al. 2019), and more recently, libraries that support isogeometric analysis like PetIGA (Dalcin et al. 2016).
Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects
Published in Mechanics of Advanced Materials and Structures, 2022
Arash Rahmani, Shirko Faroughi, Michael I. Friswell, Alireza Babaei
Yin et al. [57] developed a new isogeometric Timoshenko beam model to study static bending and free vibration of micro-beams using MCST and surface elasticity theory. They employed a novel computational approach based on isogeometric analysis. Norouzzadeh et al. [58] studied the nonlinear bending analysis of nanobeams using a comprehensive nonlocal strain gradient Timoshenko beam model without any simplification. Also, they proposed a non-classical isogeometric analysis to obtain the numerical results.
Free vibration analysis of variable stiffness laminated composite beams
Published in Mechanics of Advanced Materials and Structures, 2021
Z. Kheladi, Sidi Mohammed Hamza-Cherif, M. E. A. Ghernaout
In this section, we give a brief overview on the main features of the isogeometric approach. The principle idea of the isogeometric analysis IGA is to use functions from computer-aided design CAD like B-Splines to represent the geometry and to construct an approximate numerical solution in the fashion of a finite element discretization. This approach is useful because it merges design and analysis into one model.