Cylindrical element: Isogeometric model of continuum rod

Lu, Jia; Zhou, Xianlian

doi:10.1016/j.cma.2010.08.007

Cited by 18 publications

(20 citation statements)

References 33 publications

(45 reference statements)

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“…Elements with smooth boundaries such as circular and cylindrical elements were successfully constructed using the IGA concept J. (2009); Lu and Zhou (2011).…”

Section: Introductionmentioning

confidence: 99%

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Nguyen

Bordas

2015

Isogeometric Methods for Numerical Simulation

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Isogeometric analysis (IGA) is a fundamental step forward in computational mechanics that offers the possibility of integrating methods for analysis into Computer Aided Design (CAD) tools and vice versa. The benefits of such an approach are evident, since the time taken from design to analysis is greatly reduced leading to large savings in cost and time for industry. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several fracture examples in both two-dimensions and three-dimensions are given as illustration. The open source Matlab R code which accompanies the present paper can be applied to one, two and threedimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. It also implements the Bézier extraction concept that allows FE analysis to be performed on T-spline geometries. An attempt was also made to include a review of recent developments of IGA.G. Beer, S.Bordas (Eds.), Isogeometric Methods for Numerical Simulation,

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“…Elements with smooth boundaries such as circular and cylindrical elements were successfully constructed using the IGA concept J. (2009); Lu and Zhou (2011).…”

Section: Introductionmentioning

confidence: 99%

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Nguyen

Bordas

2015

Isogeometric Methods for Numerical Simulation

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“…Furthermore, isogeometric plate/shell elements exhibit much less pronounced shear-locking compared to standard FE plate/shell elements. Elements with smooth boundaries such as circular and cylindrical elements were successfully constructed using the IGA concept [27,28].The smoothness of NURBS basis functions is attractive for analysis of fluids [29,30,31] and for fluid-structure interaction problems [32,33]. In addition, due to the ease of constructing high order continuous basis functions, IGA has been used with great success in solving PDEs that incorporate fourth order (or higher) derivatives of the field variable such as the Hill-Cahnard equation [34], explicit gradient damage models [35] and gradient elasticity [36].…”

mentioning

confidence: 99%

Isogeometric analysis: An overview and computer implementation aspects

Nguyen

Anitescu

Bordas

et al. 2015

Mathematics and Computers in Simulation

548

233

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Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. In this manuscript, through a self-contained Matlab R ⃝ implementation, we present an introduction to IGA applied to simple analysis problems and the related computer implementation aspects. Furthermore, implementation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. We also describe the use of IGA in the context of strong-form (collocation) formulations, which has been an area of research interest due to the potential for significant efficiency gains offered by these methods. The code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bézier extraction concept that allows the FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA.

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“…Benson et al, for both Kirchhoff-Love shell [47] and Reissner-Mindlin shell [9]. A NURBS-based continuum rod element was proposed by Lu [56,57], which proved to be much more efficient then the corresponding FE model. Isogeometric analysis was also applied to topology optimization by Wall et al [90], cho el al.…”

Section: Introduction To Isogeometric Analysismentioning

confidence: 99%

Cloth simulation by isogeometric analysis

Chen¹

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ACKNOWLEDGEMENTS I would first and foremost like to thank my PH.D. supervisor, Dr. Jia Lu. He is brilliant as a teacher, mentor, and research collaborator, and provided incredible support to my research.I owe a lot to my wife Rong. Without her tremendous love, support, encouragement and sacrifice on her own career, I'd never be able to finish this work. I thank my parents and my bother, for their constant love and encouragement.A special thank is given to Dr. Timothy Marler, who provided me the soft armor models and the digital models of human body. A special thank is given to Dr. ABSTRACTThis thesis aims to develop a design-oriented simulation approach for cloth analysis. Our approach is built on the framework of NURBS-based isogeometric analysis, which utilizes NURBS as the basis functions of analysis. NURBS is a class of parametric geometry to represent curves and surfaces in computer-aided design (CAD) programs. Recently, NURBS geometry has been used directly in analysis.The overall goal of this thesis is to develop a computation infrastructure that enables cloth analysis directly on NURBS geometry.The advantage of NURBS in the context of cloth modeling lies in the geometric smoothness. Using NURBS, it's easy to construct surfaces with C 1 or higher order of continuity. Compared to C 0 finite element geometry, the NURBS geometry is more effective in capturing wrinkles and folders of cloth, which are characteristics of cloth motion. The NURBS geometry enables the use of rotation-free Kirchhoff-Love shell. The rotation-free shell model not only saves freedoms, but also makes the contact/impact treatment much easier.The major contribution of this work is the development of a NURBS cloth modeling approach. The mechanical model of cloth and its implementation with NURBS geometry will be presented in detail. Proper constitutive laws are employed for fabric materials. Since NURBS geometry from CAD typically contains multiple patches and trimmed patches, a certain treatment is proposed so that geometry can be used directly in analysis.iii

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Cylindrical element: Isogeometric model of continuum rod

Cited by 18 publications

References 33 publications

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Extended Isogeometric Analysis for Strong and Weak Discontinuities

Isogeometric analysis: An overview and computer implementation aspects

Cloth simulation by isogeometric analysis

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