Relevant bibliographies by topics / Nurbs Isogeometric analysis

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  1. Journal articles
  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Nurbs Isogeometric analysis'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Nurbs Isogeometric analysis"

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Zhang, Wen Lei, Rong Mo, Neng Wan, and Qin Zhang. "Isogeometric Analysis of Heat Transfer in Fluids." Applied Mechanics and Materials 105-107 (September 2011): 2174–78. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2174.

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This paper is devoted to the numerical simulation of heat transfer in fluids. We develop a numerical formulation based on isogeometric analysis that permits straightforward construction of higher order smooth NURBS approximation. Firstly, we introduce the partial differential equation (PDE) which servers as basis for the whole paper. Then, we introduce Lagrange multiplier method to deal with essentional boundary contions accroding to the nature of NURBS basis function. After getting the Equivalent integral equation, the isogeometric solving format is established based on the idea of isoparametric which is the necessary fundamentals of Isogeometric Analysis. We also discuss the programming algorithm of isogeometric analysis based on Matlab. Finally, a numerical example in two dimensions is presented that illustrate the effectiveness and robustness of our approach.
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Gan, Buntara Sthenly. "Isogeometric Analysis of Euler-Bernoulli Beam Element." Journal of Advanced Civil and Environmental Engineering 1, no. 2 (October 31, 2018): 57. http://dx.doi.org/10.30659/jacee.1.2.57-70.

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Abstract: The Isogeometric analysis is a computational geometry based on a series of polynomial functions (Non-Uniform Rational B-Spline, NURBS) which are assembled to represent the exact geometry. In the Isogeometric analysis, the curvature geometry of the beam element can be represented exactly. The conventional beam element can be developed by using the Isogeometric approach which is based on Euler-Bernoulli principle which is under the assumption that the dimension of the beam cross section is small compared with the length of the beam. The geometric shape of the beam and the shape functions formulation of the element can be formulated by using the Isogeometric approach. This paper highlights the application of the NURBS for the Euler-Bernoulli beam element in the context of finite element analysis. Examples are given to verify the effectiveness of the Isogeometric approach in static and free vibration problems.
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AURICCHIO, F., L. BEIRÃO DA VEIGA, T. J. R. HUGHES, A. REALI, and G. SANGALLI. "ISOGEOMETRIC COLLOCATION METHODS." Mathematical Models and Methods in Applied Sciences 20, no. 11 (November 2010): 2075–107. http://dx.doi.org/10.1142/s0218202510004878.

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We initiate the study of collocation methods for NURBS-based isogeometric analysis. The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three dimensions. The numerical results obtained confirm theoretical results and illustrate the potential of the methodology.
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Beirão da Veiga, L., D. Cho, and G. Sangalli. "Anisotropic NURBS approximation in isogeometric analysis." Computer Methods in Applied Mechanics and Engineering 209-212 (February 2012): 1–11. http://dx.doi.org/10.1016/j.cma.2011.10.016.

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Schmidt, Robert, Roland Wüchner, and Kai-Uwe Bletzinger. "Isogeometric analysis of trimmed NURBS geometries." Computer Methods in Applied Mechanics and Engineering 241-244 (October 2012): 93–111. http://dx.doi.org/10.1016/j.cma.2012.05.021.

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HAH, ZOO-HWAN, HYUN-JUNG KIM, and SUNG-KIE YOUN. "A HIERARCHICALLY SUPERIMPOSING LOCAL REFINEMENT METHOD FOR ISOGEOMETRIC ANALYSIS." International Journal of Computational Methods 11, no. 05 (October 2014): 1350074. http://dx.doi.org/10.1142/s0219876213500746.

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In isogeometric analysis, the tensor-product form of Nonuniform Rational B-spline (NURBS) represents spline surfaces. Due to the nature of the tensor-product, the local refinement in isogeometric analysis has many issues to be resolved. Attempts have been made in this regard, such as T-splines and hierarchical approaches. In this work, a local refinement method for isogeometric analysis based on a superimposing concept is proposed. Local refinements are performed by superimposing hierarchically-created finer overlay meshes onto the regions of high error rather than a change of analysis basis (from NURBS to some other spline space). To employ the superimposing concept as a local refinement strategy in isogeometric analysis, a hierarchical framework to construct overlay meshes is developed, and compatibility conditions across the interfacial boundaries of different levels of meshes is discussed. Through numerical examples, the effectiveness and validity of the proposed method are demonstrated.
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Truong, Hoang H., Chien H. Thai, and H. Nguyen-Xuan. "Isogeometric analysis of two-dimensional piezoelectric structures." Vietnam Journal of Mechanics 35, no. 1 (April 10, 2013): 79–91. http://dx.doi.org/10.15625/0866-7136/35/1/2895.

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The isogeometric analysis (IGA) that integrates Computer Aided Design(CAD) and Computer Aided Engineering (CAE) is found so far the effectively numerical tool for the analysis of a variety of practical problems. In this paper, we develop further the NURBS based isogeometric analysis framework for piezoelectric structures.The method employs the NURBS basis functions in both geometry representation and analysis. The main advantages of the present method are capable of handling the exactgeometry of conic sections and making the flexibility of refinement and degree elevationwith an arbitrary continuity of basic functions. These features results in high accuracy of approximate solutions for practical applications, especially piezoelectric problems. Three numerical examples are provided to validate excellent performance of the present method.
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BAZILEVS, Y., L. BEIRÃO DA VEIGA, J. A. COTTRELL, T. J. R. HUGHES, and G. SANGALLI. "ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHES." Mathematical Models and Methods in Applied Sciences 16, no. 07 (July 2006): 1031–90. http://dx.doi.org/10.1142/s0218202506001455.

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We begin the mathematical study of Isogeometric Analysis based on NURBS (non-uniform rational B-splines). Isogeometric Analysis is a generalization of classical Finite Element Analysis (FEA) which possesses improved properties. For example, NURBS are capable of more precise geometric representation of complex objects and, in particular, can exactly represent many commonly engineered shapes, such as cylinders, spheres and tori. Isogeometric Analysis also simplifies mesh refinement because the geometry is fixed at the coarsest level of refinement and is unchanged throughout the refinement process. This eliminates geometrical errors and the necessity of linking the refinement procedure to a CAD representation of the geometry, as in classical FEA. In this work we study approximation and stability properties in the context of h-refinement. We develop approximation estimates based on a new Bramble–Hilbert lemma in so-called "bent" Sobolev spaces appropriate for NURBS approximations and establish inverse estimates similar to those for finite elements. We apply the theoretical results to several cases of interest including elasticity, isotropic incompressible elasticity and Stokes flow, and advection-diffusion, and perform numerical tests which corroborate the mathematical results. We also perform numerical calculations that involve hypotheses outside our theory and these suggest that there are many other interesting mathematical properties of Isogeometric Analysis yet to be proved.
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Hughes, T. J. R., A. Reali, and G. Sangalli. "Efficient quadrature for NURBS-based isogeometric analysis." Computer Methods in Applied Mechanics and Engineering 199, no. 5-8 (January 2010): 301–13. http://dx.doi.org/10.1016/j.cma.2008.12.004.

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Temizer, İ., P. Wriggers, and T. J. R. Hughes. "Contact treatment in isogeometric analysis with NURBS." Computer Methods in Applied Mechanics and Engineering 200, no. 9-12 (February 2011): 1100–1112. http://dx.doi.org/10.1016/j.cma.2010.11.020.

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Dissertations / Theses on the topic "Nurbs Isogeometric analysis"

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Sun, Zhiyu. "Generating analysis-ready NURBS models of cloth for isogeometric analysis." Thesis, University of Iowa, 2015. https://ir.uiowa.edu/etd/2015.

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Non-uniform rational basis spline (NURBS) is a geometric language which has been commonly used in computer graphics and Computer Aided Design over years, due to its great flexibility and precision for handling modeled shapes. In computer-aided design, NURBS has become part of industry standards. In most CAD programs every solid model is described by NURBS and stored in NURBS data structure. Recently, the geometric basis function of NURBS is directly used in analysis, leading to the birth of a new area of computational mechanics called isogeometric analysis (IGA). Compared with the traditional finite element analysis, IGA eliminates the disconnection between analysis and design at the geometric level, showing superiority on efficiency and accuracy over the traditional finite element method. This thesis focuses on the development of an IGA preprocessor for converting an original CAD model (2D-NURBS model) to an ASG (analysis suited geometry) model. ASG means models with mesh quality suitable for analysis. Core technologies utilized during the development include the well-developed NURBS algorithm of knot insertion and knot removal, and a self-developed technology of constructing and utilizing “multi-patch tree”. The developed IGA preprocessor is utilized to process a body armour model consisting of multiple NURBS patches with overly dense meshes. After the processing, the output model has a relatively reasonable elements distribution; the uniformity of the mesh across presumably contact patch boundaries is rebuilt.
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Boss, Matthew John. "Analysis-ready isogeometric model of skeletal muscles." Thesis, University of Iowa, 2012. https://ir.uiowa.edu/etd/2827.

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New methods are employed to develop an anatomically accurate, analysis-ready isogeometric model of skeletal muscles. Current modeling techniques for the analysis of skeletal muscles include the utilization of finite element meshing, which inherently poses a few well-known problems that provide motivation for isogeometric analysis. In addition to those issues, standard FEA meshing cannot preserve smooth geometries, therefore the accuracy of the foregoing model and analysis is reduced. Moreover, there is no easy means to characterize fiber direction in the FEA framework due to discontinuities at element boundaries. Additionally, material property distributions such as the transition of the muscle-tendon complex along the longitudinal axis through FEA are prescribed on an element by element basis, leading to abrupt, unrealistic property changes at element boundaries. The current research builds on the idea of an isogeometric tensor-product rod using harmonic coordinates and NURBS [1]. Through a direct comparison between a meshed, FEA model and the tensor-product rod model, it can be shown that the tensor-product rod model preserves smoothness, enhancing the geometric representation passed through to analysis while reducing the total DOF of the model. Muscle fibers can be easily implemented as parametric lines with muscle-specific orientations along the muscles' longitudinal axis that match distinct fiber orientations existent within common skeletal muscles. This technique not only allows for the representation of perfectly parallel-fibered structures, but also those that do not directly follow the longitudinal axis such as a helical twist. Utilizing this geometric method also provides the framework for implementing material properties using an interpolative-style scheme. Varying properties at specific longitudinal control point cross-sections near muscle termination areas can be designated to more accurately represent the muscle-tendon complex. These new techniques allow for the creation of an analysis-ready, realistic skeletal muscle model of the male human arm. The model contains 28 muscles complete with muscle-specific geometric, fiber, and heterogeneous property characterizations all compiled into a complete "digital muscle library."
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Li, Jingang. "Isogeometric Finite Element Analysis Using T-Splines." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd3159.pdf.

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Fredheim, Ole Jørgen. "Isogeometric Finite Element Analysis based on Bézier Extraction of NURBS and T-splines." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for konstruksjonsteknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15890.

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This thesis will give a theoretical overview of B-splines, as well as NURBS and T-splines which are based on B-splines, and also the concept of Bézier decomposition of these spline functions. Bézier decomposition will decompose the splines into Bernstein polynomials which are defined over the domain of one quadrature element. This theoretical background will then be used to implement a Matlab isogeometric finite element analysis program. Two different choices for implementation are explored, a isogeometric finite element solver built from scratch for use of NURBS, and the use of Bézier extraction to implement isogeometric analysis with NURBS and T-splines in an already existing finite element solver. The main focus will be on use of Bézier extraction, which will signicantly ease the implementation. Numerical studies are performed with problems of linear elasticity and heat conduction, to study the convergence of an isogeometric  analysis.The accuracy of isogeometric analysis will prove to be better than for a traditional FEA for the analyzed problems
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Nguyen, Thanh Ngan. "Isogeometric Finite Element Analysis based on Bézier Extraction of NURBS and T-Splines." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for konstruksjonsteknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-15917.

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Data transmission between finite element analysis (FEA) and computer-aided design (CAD) is ahuge bottle-neck today. Therefore, isogeometric analysis has been introduced with aim to merge these fields. While FEA utilizes Lagrange polynomials to approximate both the geometry and the solution field, isogeometric analysis employs non-uniform rational B-splines (NURBS) from CAD technology to this objective. Isogeometric analysis will therefore have the advantage in nogeometric error in the sense that the model is exact. T-splines are a recently introduced generalization of NURBS which allow local refinement, handling complex geometry in a subtle way with fewer degrees of freedom. Increasing the order of the elements in isogeometric analysis is easy and gives higher continuous basis functions than FEA, while also maintaining few degrees of freedom. In conventional isogeometric analysis the basis functions are not confined to one single element, but span a global domain, complicating implementation. The Bézier extraction operator decomposes a set of NURBS or T-spline basis functions to linear combinations of Bernstein polynomials. These polynomials bear a close resemblance to the Lagrange polynomials as they allow for generation of C0 continuous Bézier elements. A local data structure for isogeometric analysis close to traditional FEA is provided. Codes are developed to illustrate conventional isogeometric data structures as well as structures based on Bézier extraction of NURBS. Modifications are made to the latter to be able to run analysis of T-splines modelled in the CAD system Rhino, and numerical studies are performed.Generally, NURBS elements display the same convergence rate as Lagrange elements of equal order, but higher accuracy. The reasons are a smooth solution field and exact geometrical representation.
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Nilsen, Oda Kulleseid. "Simulation of crack propagation using isogeometric analysis applied with NURBS and LR B-splines." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19545.

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This report features the isogeometric finite element method applied to the elastodynamic problem in a brittle medium with a potential for cracking. Griffith's theory for fracturing is used. The development of the model is outlined, complete with the Euler-Lagrange equations. The cracking is described with a phase field supplemented with a history field, contrary to the usual way of building the crack directly into the geometry by modification of the basis, facilitating the use of isogeometric analysis even with simplistic basis functions such as Non-Uniform Rational B-Splines (NURBS). The introduction of the crack-phase field results in non-linearity in the coupled problem. The problem is semi-discretized, upon which the spatial sub-problem is treated with isogeometric analysis. The numerical time-stepping solution routine is built around the Newton-Raphson method, but includes both pre-conditioning and correctors and is known as the predictor/multi-corrector time integration scheme. The Jacobian of the semi-discretized system (needed for the Newton-Raphson iteration) is developed analytically. In addition to the numerical tests with NURBS as our basis, we will also test the method with Locally Refined B-splines (LR B-Splines), ensuring better resolution along the crack path. The LR B-spline represents an alternative to the more commonly used T-Spline.
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Kapoor, Hitesh. "Isogeometric Finite Element Code Development for Analysis of Composite Structures." Diss., Virginia Tech, 2013. http://hdl.handle.net/10919/50567.

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This research endeavor develops Isogeometric approach for analysis of composite structures and take advantage of higher order continuity, smoothness and variation diminishing property of Nurbs basis for stress analysis of composite and sandwich beams and plates. This research also computes stress concentration factor in a composite plate with a hole.

Isogeometric nonlinear/linear finite element code is developed for static and dynamic analysis of laminated composite plates. Nurbs linear, quadratic, higher-order and k-refined elements are constructed using various refinement procedures and validated with numerical testing. Nurbs post-processor for in-plane and interlaminar stress calculation in laminated composite and sandwich plates is developed. Nurbs post-processor is found to be superior than regular finite element and in good agreement with the literature. Nurbs Isgoemetric analysis is used for stress analysis of laminated composite plate with open-hole. Stress concentration factor is computed along the hole edge and good agreement is obtained with the literature. Nurbs Isogeometric finite element code for free-vibration and linear dynamics analysis of laminated composite plates also obtain good agreement with the literature.

Main highlights of the research are newly developed 9 control point linear Nurbs element, k-refined and higher-order Nurbs elements in isogeometric framework. Nurbs elements remove shear-locking and hourglass problems in thin plates in context of first-order shear deformation theory without the additional step and compute better stresses than Lagrange finite element and higher order shear deformation theory for comparatively thick plates i.e. a/h = 4. Also, Nurbs Isogeometric analysis perform well for vibration and dynamic problems and for straight and curved edge problems.
Ph. D.
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Aoyama, Taiki, Shota Fukumoto, and Hideyuki Azegami. "Shape optimization of continua using NURBS as basis functions." Springer, 2013. http://hdl.handle.net/2237/21124.

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Ribeiro, Carlos Fernando Morgado. "Development of computational tools for Isogeometric Analysis (IGA)." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/14421.

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Mestrado em Engenharia Mecânica
A few years ago drawings were made in the drawing boards and using pencils on vellum. There were no computers helping the designers in the parts modeling. After designing the object, the design was passed to the analysts. The designers and analysts were in constant communication. Nowadays, the designers used Computer Aided Design (CAD) tools in the parts modeling. For application the analysis at the geometries, initially a mesh to approximate the geometries is generated. After this, on the mesh the Finite Element Method (FEM) was applied. In complex engineering design, the generation and manipulation of meshes in FEA was estimated to take over 80% of the overall analysis time. The form to break down the barriers between engineering design and the analysis is with reconstruction the entire process, but at the same time maintaining compatibility with existing practices. Create only one geometric model is the focus of reconstruction process. This geometric model is used in the representation of the geometry, as well as in the analysis, and this concept is designated by Isogeometric Analysis (IGA). In this present work the development of the tools for generate the CAD and calculate the basis function for representation the object are proposed. Initially, the mathematical formulations for Bézier, B-Spline and NURBS, for curves and surfaces are presented. The algorithms developed to generate the curves and surfaces are demonstrated. The IGA and FEM formulation for tridimensional and bidimensional spaces are introduced. In this work, a development of a tools for application this method are proposed. The convergence of the results for FEM and IGA programs are studied and compared to the theoretical values and Abaqus comercial program. The results obtained with IGA formulation converge to the reference values.
Há alguns anos atrás, os objectos eram feitos pelos designers e a criação do desenho era feita com lápis e papel vegetal. Não existiam computadores nos gabinetes de desenho para ajudar na modelação dos objectos. Após o desenho estar concluído este era entregue aos analistas para calcularem a resistência do mesmos quando solicitados por cargas externas. Assim, o gabinete de design e o gabinete de análise estavam em constante comunicação. Nos tempos de hoje os designers utilizam as ferramentas de Computer-Aided Design (CAD) para gerar os objectos, representando assim a geometria original. Por outro lado, os analistas fazem a análise baseada no Método dos Elementos Finitos (MEF). Neste método, inicialmente, gera-se uma malha para fazer a aproximação do objecto e utiliza-se esta malha gerada na análise. A forma de combater esta barreira é a construção de um novo processo de análise, mas ao mesmo tempo manter a compatibilidade com a análise do Método de Elementos Finitos. Este novo método foca-se na geração de um modelo geométrico, sendo este modelo utilizado tanto para a representação da geometria como para a análise. A principal sustentação deste novo método é a utilização das funções de base da criação e representação dos objectos, posteriormente, utilizadas na análise dos mesmos. Este novo conceito é designado por Análise Isogeométrica. Neste trabalho é exposto o desenvolvimento de ferramentas para gerar curvas e superfícies utilizando as formulações de Bézier, B-spline e NURBS. Assim, desenvolveram-se sub-rotinas para calcular as funções de base. Inicialmente apresentaram-se as formulações matemáticas e posteriormente os algoritmos desenvolvidos para a representação das curvas e superfícies. O desenvolvimento de ferramentas de análise para problemas no espaço bidimensional e tridimensional utilizando o Método de Elementos Finitos e a Análise Isogeométrica também é abordado neste trabalho. Para ser mais fácil a sua aplicação, foi desenvolvida um interface. Por fim utilizaram-se problemas e estudaram-se as curvas de convergência dos resultados e compararando-os com as referência analíticas e com o programa Abaqus. Em termos de conclusão, os resultados obtidos com a Análise Isogeométrica convergem mais rapidamente para os valores de referência do que o Abaqus e o programa desenvolvido com base no método de elementos finitos.
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Devarajan, Balakrishnan. "Thermomechanical and Vibration Analysis of Stiffened Unitized Structures and Threaded Fasteners." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/99425.

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This dissertation discusses the thermomechanical analyses performed on threaded fasteners and curvilinearly stiffened composite panels with internal cutouts. The former problem was analyzed using a global/local approach using the commercial finite element software ANSYS while a fully functional code using isogeometric analysis was developed from scratch for the latter. For the threaded fasteners, a global simplified 3D model is built to evaluate the deformation of the structure. A second local model reproducing accurately the threads of the fasteners is used for the accurate assessment of the stresses in the vicinity of the fasteners. The isogeometric analysis code, capable of performing static, buckling and vibration analysis on stiffened composite plates with cutouts using single patch, multiple patches and level set methods is then discussed. A novel way to achieve displacement compatibility between the panel and stiffeners interfaces is introduced. An easy way of modeling plates with complicated cutouts by using edge curves and generating a ruled NURBS surface between them is described. Influence on the critical thermal buckling load and the fundamental mode of vibration due to the presence of circular, elliptical and complicated cutouts is also investigated. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout, and the position and profile of the curvilinear stiffener. The numerical examples show high reliability and efficiency when compared with other published solutions and those obtained using ABAQUS, a commercial software.
PHD
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Book chapters on the topic "Nurbs Isogeometric analysis"

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Provatidis, Christopher G. "Rational Elements (BEZIER, NURBS)." In Precursors of Isogeometric Analysis, 357–80. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-03889-2_8.

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Jüttler, Bert. "A Primer on Splines and NURBS for Isogeometric Analysis." In Isogeometric Methods for Numerical Simulation, 1–19. Vienna: Springer Vienna, 2015. http://dx.doi.org/10.1007/978-3-7091-1843-6_1.

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Devaud, Denis, and Gianluigi Rozza. "Certified Reduced Basis Method for Affinely Parametric Isogeometric Analysis NURBS Approximation." In Lecture Notes in Computational Science and Engineering, 41–62. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65870-4_3.

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Agrawal, Vishal, and Sachin S. Gautam. "Investigating the Influence of Higher-Order NURBS Discretization on Contact Force Oscillation for Large Deformation Contact Using Isogeometric Analysis." In Advances in Applied Mechanical Engineering, 343–50. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1201-8_39.

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Kopačka, J., D. Gabriel, R. Kolman, and J. Plešek. "A Large Deformation Frictionless Contact Treatment in NURBS-based Isogeometric Analysis." In Advances in Computational Coupling and Contact Mechanics, 109–44. WORLD SCIENTIFIC (EUROPE), 2018. http://dx.doi.org/10.1142/9781786344786_0003.

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Conference papers on the topic "Nurbs Isogeometric analysis"

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Chivukula, VenkatKeshav, Jia Lu, and Sarah C. Vigmostad. "RBC Modeling Using NURBS Based Isogeometric Analysis." In ASME 2012 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/sbc2012-80532.

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The Red Blood Cell(RBC) is the transporter of oxygen to the entire human body via the circulatory system. Its journey spans across pathways which step down orders of magnitude; from large arteries which are O(cm) to tiny capillaries which are O(μm). This four-fold reduction in the diameters of the circulatory pathways necessitates the RBC to be extremely deformable. One of the most intriguing facets of the RBC is that it achieves this extreme deformability with ease; and also with a very minimal area dilatation[1]. Modeling the RBC has been an active area of research since the 1950’s. However, conventional methods to model RBCs rely on simplistic Finite Element Methods(FEM) involving mostly triangular elements. The extreme deformability of the RBCs mandate the use of a large number of elements, usually O(thousands) to accurately resolve and visualize the motion of an RBC [2], which is biconcave when unstressed and assumes myriad shapes as it travels through the microcirculation. The extremely large number of elements per cell makes the calculations highly computationally intensive for a single cell alone. This becomes particularly important when attempting to simulate the motion of a large number of cells, leading to a very computationally intensive simulation. The current paper proposes a novel method to analyze and resolve the RBC as a smooth entity using greatly reduced number of elements for resolution. This approach is based on exploiting the properties of Non-Uniform Rational B-Spline (NURBS) surfaces [3]. The results obtained from utilizing the NURBS surfaces can be considered to be a more realistic representation of the behavior of the RBC. Though this article specifically deals with the RBC, it can be applied to a deformable cell of any shape.
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Cho, Seonho, Bon-yong Koo, Minho Yoon, Seung-Wook Lee, and Youn Doh Ha. "Isogeometric Shape Design Sensitivity Analysis Using Mixed Transformation Method for Kronecker Delta Property." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47697.

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The isogeometric method is very effective in shape design optimization due to its effectiveness through the easy design parameterization and accurate sensitivities considering the higher order geometric terms. Due to non-interpolatory property of the NUBRS basis functions, however, the treatment of essential boundary condition is not as straightforward in the isogeometric analysis as in the finite element analysis. Taking advantages of the transformation method developed in meshfree methods, we investigate the isogeometric shape sensitivity analysis with the treatment of essential boundary conditions. Using the property that isogeometric basis functions do not depend on design changes, the transformed shape sensitivity equation is developed and verified for the problem having the essential boundary conditions. Numerical costs to construct the transformed basis function are not as much as the meshfree methods due to the NURBS property that only boundary nodes have their supports on the boundary. Through demonstrative numerical examples having the essential boundary conditions, the effectiveness of proposed design sensitivity analysis is verified.
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Calabrò, F., and C. Manni. "THE CHOICE OF QUADRATURE IN NURBS-BASED ISOGEOMETRIC ANALYSIS." In 3rd South-East European Conference on Computational Mechanics. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2014. http://dx.doi.org/10.7712/130113.4389.s2056.

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Calabò, Francesco, and Carla Manni. "THE CHOICE OF QUADRATURE IN NURBS-BASED ISOGEOMETRIC ANALYSIS." In 3rd South-East European Conference on Computational Mechanics. Athens: ECCOMAS, 2013. http://dx.doi.org/10.7712/seeccm-2013.2056.

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Montanari, Mattia, Petros Siegkas, Antonio Pellegrino, and Nik Petrinic. "NURBS-BASED ISOGEOMETRIC ANALYSIS FOR BALLISTIC EVALUATION OF TITANIUM PLATES." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2394.9281.

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Duckitt, Sam, Chiara Bisagni, and Shahrokh Shahpar. "Parametric Bird Strike Study of a Transonic Rotor Using Isogeometric Analysis." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57464.

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This paper investigates the use of isogeometric analysis (IGA) to study high velocity impact on a transonic compressor rotor resulting from a bird strike. An approach is developed for creating volumetric NURBS blade models which are suitable for IGA. A newly implemented 3D solid NURBS element within the development version of LS-Dyna is validated against finite elements for the NASA rotor 37 under a steady centrifugal load. The smoothed particle hydrodynamics (SPH) method is then used to simulate impact from a bird strike. As a preliminary assessment for multi-disciplinary optimisation (MDO), with the objective to improve aerodynamic performance whilst satisfying mechanical constraints from impact, a number of different blade designs are created by modifying the NURBS control points directly. Hence the control points used in analysis can also be used in the design space. This approach eliminates the need for re-meshing, highlighting the advantages that IGA can bring to design optimisation, since without filtering, moving finite element nodes can result in non-smooth geometries. NURBS parametrisations are also more efficient resulting in fewer design variables, thereby accelerating the optimisation process. The effect of blade sweep, lean, twist and thickness on the impact response are investigated. The results in this paper show the promise that IGA holds in this field but some limitations of the current LS-Dyna implementation are also discussed.
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Shen, Le, and Yang Xia. "Isogeometric Analysis of Pipe System in Nuclear Power Plant." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66147.

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The security of pipe system is an important problem in nuclear power plant. The displacement field and vibration frequency of the pipeline system under given loads and displacement boundary conditions are calculated with isogeometric analysis. Comparisons with commercial softwares are given to prove its effectiveness. In isogeometric analysis the non-uniform rational B-spline (NURBS) basis functions are used to accurately describe the geometry of pipeline, which can be imported directly from the geometry model designed by computer aided design (CAD) tools for numerical analysis. The quarter bend pipes are described precisely with only limited control points and the approximation by straight line elements in finite element method based simulation is replaced. Present simulation with isogeometric analysis can simplify the modelling process of pipeline system and improve the efficiency of the simulation with great accuracy.
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Zhang, Ran, Gang Zhao, Wei Wang, Xiaoxiao Du, and Mayi Guo. "NURBS-based Isogeometric Analysis for Small Deformation of Viscoplastic and Creep Problems." In CAD'20. CAD Solutions LLC, 2020. http://dx.doi.org/10.14733/cadconfp.2020.116-120.

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Guo, Yujie, and Hornsen Tzou. "Frequency Control of Shell Structures With Light-Activated Shape Memory Polymers Based on Isogeometric Analysis." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67693.

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The frequency control of LaSMP laminated shell structures in the framework of isogeometric analysis is presented. LaSMP is a novel smart material which realizes shape memory function and stiffness variation via light exposures. This dynamic properties of stiffness provides a natural way for the noncontact actuation of shell structures. Isogeometric analysis utilizes high order and high continuity NURBS as basis functions which is an ideal candidate for the analysis of shell structures where curved geometries can be captured exactly. A variationally consistent Nitsche’s method is proposed for the coupling between Kirchhoff-Love shell patches to prevent hinge-like motion. The accuracy and efficiency of the proposed isogeometric approach are demonstrated via several numerical examples. The results show that, with LaSMPs, broadband frequency control of shell structures can be realized which further opens a door for the dynamic control of engineering-related LaSMP shell structures.
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Kapoor, Hitesh. "Free Vibration and Linear Dynamics Analysis of Composite Plate Using NURBS Isogeometric Finite Element Analysis." In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-1952.

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