Journal articles: '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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Nguyen, Lieu B., Chien H. Thai, Ngon T. Dang, and H. Nguyen-Xuan. "Transient analysis of laminated composite plates using NURBS-based isogeometric analysis." Vietnam Journal of Mechanics 36, no. 4 (November 27, 2014): 267–81. http://dx.doi.org/10.15625/0866-7136/36/4/4129.

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We further study isogeometric approach for response analysis of laminated composite plates using the higher-order shear deformation theory. The present theory is derived from the classical plate theory (CPT) and the shear stress free surface conditions are naturally satisfied. Therefore, shear correction factors are not required. Galerkin weak form of response analysis model for laminated composite plates is used to obtain the discrete system of equations. It can be solved by isogeometric approach based on the non-uniform rational B-splines (NURBS) basic functions. Some numerical examples of the laminated composite plates under various dynamic loads, fiber orientations and lay-up numbers are provided. The accuracy and reliability of the proposed method is verified by comparing with analytical solutions, numerical solutions and results from Ansys software.

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Kefal, Adnan, and Erkan Oterkus. "Isogeometric iFEM Analysis of Thin Shell Structures." Sensors 20, no. 9 (May 8, 2020): 2685. http://dx.doi.org/10.3390/s20092685.

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Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated.

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Shojaee, S., and N. Valizadeh. "NURBS-based isogeometric analysis for thin plate problems." Structural Engineering and Mechanics 41, no. 5 (March 10, 2012): 617–32. http://dx.doi.org/10.12989/sem.2012.41.5.617.

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Riffnaller-Schiefer, A., U. H. Augsdörfer, and D. W. Fellner. "Isogeometric shell analysis with NURBS compatible subdivision surfaces." Applied Mathematics and Computation 272 (January 2016): 139–47. http://dx.doi.org/10.1016/j.amc.2015.06.113.

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Bauer, A. M., M. Breitenberger, B. Philipp, R. Wüchner, and K. U. Bletzinger. "Embedded structural entities in NURBS-based isogeometric analysis." Computer Methods in Applied Mechanics and Engineering 325 (October 2017): 198–218. http://dx.doi.org/10.1016/j.cma.2017.07.010.

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Lu, Jia, Guolai Yang, and Jianli Ge. "Blending NURBS and Lagrangian representations in isogeometric analysis." Computer Methods in Applied Mechanics and Engineering 257 (April 2013): 117–25. http://dx.doi.org/10.1016/j.cma.2013.01.012.

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Abdelmoety, Ahmed K., Taha H. A. Naga, and Youssef F. Rashed. "Isogeometric boundary integral formulation for Reissner’s plate problems." Engineering Computations 37, no. 1 (July 19, 2019): 21–53. http://dx.doi.org/10.1108/ec-11-2018-0507.

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Purpose This paper aims to develop a new isogeometric boundary element formulation based on non-uniform rational basis splines (NURBS) curves for solving Reissner’s shear-deformable plates. Design/methodology/approach The generalized displacements and tractions along the problem boundary are approximated as NURBS curves having the same rational B-spline basis functions used to describe the geometrical boundary of the problem. The source points positions are determined over the problem boundary by the well-known Greville abscissae definition. The singular integrals are accurately evaluated using the singularity subtraction technique. Findings Numerical examples are solved to demonstrate the validity and the accuracy of the developed formulation. Originality/value This formulation is considered to preserve the exact geometry of the problem and to reduce or cancel mesh generation time by using NURBS curves employed in computer aided designs as a tool for isogeometric analysis. The present formulation extends such curves to be implemented as a stress analysis tool.

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BEIRÃO DA VEIGA, L., D. CHO, L. F. PAVARINO, and S. SCACCHI. "BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS." Mathematical Models and Methods in Applied Sciences 23, no. 06 (March 17, 2013): 1099–142. http://dx.doi.org/10.1142/s0218202513500048.

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A Balancing Domain Decomposition by Constraints (BDDC) preconditioner for Isogeometric Analysis of scalar elliptic problems is constructed and analyzed by introducing appropriate discrete norms. A main result of this work is the proof that the proposed isogeometric BDDC preconditioner is scalable in the number of subdomains and quasi-optimal in the ratio of subdomain and element sizes. Another main result is the numerical validation of the theoretical convergence rate estimates by carrying out several two- and three-dimensional tests on serial and parallel computers. These numerical experiments also illustrate the preconditioner performance with respect to the polynomial degree and the regularity of the NURBS basis functions, as well as its robustness with respect to discontinuities of the coefficient of the elliptic problem across subdomain boundaries.

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Taheri, Alireza Hassanzadeh, Mohammad Hossein Abolbashari, and Behrooz Hassani. "Free vibration characteristics of functionally graded structures by an isogeometrical analysis approach." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 9 (October 31, 2013): 1512–30. http://dx.doi.org/10.1177/0954406213508757.

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An improved methodology based on isogeometric analysis (IGA) approach is suggested to investigate the free vibration characteristics of functionally graded structures. The proposed method, which can be considered as an extension of the isogeometric analysis method to inhomogeneous elasticity, employs a fully isogeometric formulation for construction of the geometry, approximation of the solution as well as modelling the variations of material properties. The gradations of material properties are captured using the same NURBS basis functions employed for geometric and computational modelling by utilization of an interpolation technique. It will be seen that the proposed NURBS-based analysis method constitutes an efficient tool for studying integrated modelling and vibration analysis of functionally graded structures. Some numerical examples of 2D plane elasticity problems are presented and the effects of different types of unidirectional and bidirectional material profiles on dynamic characteristics of functionally graded structures are investigated. The obtained numerical results are verified with available exact elasticity solutions or the results of commercial finite element method software. It is shown that the difficulties encountered in free vibration analysis of functionally graded structures using the conventional finite element method are considerably circumvented by adopting the proposed procedure.

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Nguyen, Khuong D., Minh N. Nguyen, Hoa V. Cong, and H. Nguyen-Xuan. "Isogeometric analysis of linear isotropic and kinematic hardening elastoplasticity." Vietnam Journal of Mechanics 39, no. 1 (March 30, 2017): 51–68. http://dx.doi.org/10.15625/0866-7136/7817.

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Material nonlinearity is of great importance in many engineering problems. In this paper, we exploit NURBS-based isogeometric approach in solving materially nonlinear problems, i.e. elastoplastic problems. The von Mises model with linear isotropic hardening and kinematic hardening is presented, and furthermore the method can also be applied to other elastoplastic models without any loss of generality. The NURBS basis functions allow us to describe exactly the curved geometry of underlying problems and control efficiently the accuracy of approximation solution. Once the discretized system of non-linear equilibrium equation is obtained, the Newton-Raphson iterative scheme is used. Several numerical examples are tested. The accuracy and reliability of the proposed method are verified by comparing with results from ANSYS Workbench software.

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da Veiga, L. Beirão, A. Buffa, G. Sangalli, and R. Vázquez. "Mathematical analysis of variational isogeometric methods." Acta Numerica 23 (May 2014): 157–287. http://dx.doi.org/10.1017/s096249291400004x.

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This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error estimates in several cases of interest. The theory presented also includes estimates for T-splines, which are an extension of splines allowing for local refinement. In particular, we focus our attention on elliptic and saddle point problems, and we define spline edge and face elements. Our theoretical results are demonstrated by a rich set of numerical examples. Finally, we discuss implementation and efficiency together with preconditioning issues for the final linear system.

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Li, Xinkang, Jifa Zhang, and Yao Zheng. "NURBS-Based Isogeometric Analysis of Beams and Plates Using High Order Shear Deformation Theory." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/159027.

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Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is developed for static analysis of beams and plates using the third-order shear deformation theory (TSDT). TSDT requires C1-continuity of generalized displacements; quadratic, cubic, and quartic NURBS basis functions are utilized to satisfy this requirement. Due to the noninterpolatory nature of NURBS basis functions, a penalty method is presented to enforce the essential boundary conditions. A series of numerical examples of thick and thin beams and plates with different boundary conditions are presented. Results are compared with analytical solutions and other numerical methods. First-order shear deformation theory (FSDT) is also employed and compared with TSDT in the stress analysis. The effects of aspect ratios and boundary conditions are discussed as well.

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Beirão Da Veiga, L., T. J. R. Hughes, J. Kiendl, C. Lovadina, J. Niiranen, A. Reali, and H. Speleers. "A locking-free model for Reissner–Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS." Mathematical Models and Methods in Applied Sciences 25, no. 08 (April 28, 2015): 1519–51. http://dx.doi.org/10.1142/s0218202515500402.

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We study a reformulated version of Reissner–Mindlin plate theory in which rotation variables are eliminated in favor of transverse shear strains. Upon discretization, this theory has the advantage that the "shear locking" phenomenon is completely precluded, independent of the basis functions used for displacement and shear strains. Any combination works, but due to the appearance of second derivatives in the strain energy expression, smooth basis functions are required. These are provided by Isogeometric Analysis, in particular, NURBS of various degrees and quadratic triangular NURPS. We present a mathematical analysis of the formulation proving convergence and error estimates for all physically interesting quantities, and provide numerical results that corroborate the theory.

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TRAN, Dang Tien, and Takashi MAEKAWA. "3103 Methods to generate 3D NURBS solids for isogeometric analysis." Proceedings of Design & Systems Conference 2013.23 (2013): _3103–1_—_3103–6_. http://dx.doi.org/10.1299/jsmedsd.2013.23._3103-1_.

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Chen, Tao, Rong Mo, and Zhong Wei Gong. "Imposing Essential Boundary Conditions in Isogeometric Analysis with Nitsche’s Method." Applied Mechanics and Materials 121-126 (October 2011): 2779–83. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.2779.

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Isogeometric Analysis combines the NURBS technology and finite element approaches into a unified framework. Regrettably, the NURBS basis functions don’t interpolate at the control points, which lead to the difficulty for imposing the essential boundary conditions. A new approach inspired by Nitsche’s notion was proposed in order to remedy this issue. The essential boundary constraints are enforced by the consistent penalty terms. It has some notable advantages than the other methods, such as (i) the symmetric and positive definite bilinear formulation when the stiffness matrix is symmetric and the stabilization parameter is large enough; (ii) the well-conditioning coefficient matrix of the linear system. Finally, the numerical experiment was performed to verify the optimal rate of convergence of the present method.

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Schollmeyer, Andre, and Bernd Froehlich. "Direct Isosurface Ray Casting of NURBS-Based Isogeometric Analysis." IEEE Transactions on Visualization and Computer Graphics 20, no. 9 (September 1, 2014): 1227–40. http://dx.doi.org/10.1109/tvcg.2014.2327977.

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Yin, Shuohui, Tiantang Yu, Tinh Quoc Bui, and Minh Ngoc Nguyen. "Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis." Engineering Computations 32, no. 2 (April 20, 2015): 519–58. http://dx.doi.org/10.1108/ec-09-2013-0220.

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Purpose – The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs. Design/methodology/approach – A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Kármán strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents. Findings – The present model for analysis of the geometrically nonlinear behavior of thin and moderately thick FGPs exhibited high accuracy. The shear locking phenomenon is avoided without extra numerical efforts when cubic or high-order NURBS basis functions are utilized. Originality/value – This paper shows that IGA is particularly well suited for the geometrically nonlinear analysis of plates because of its exact geometrical modelling and high-order continuity.

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Li, Xinkang, Jifa Zhang, and Yao Zheng. "Static and Free Vibration Analysis of Laminated Composite Plates Using Isogeometric Approach Based on the Third Order Shear Deformation Theory." Advances in Mechanical Engineering 6 (January 1, 2014): 232019. http://dx.doi.org/10.1155/2014/232019.

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Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is applied for static and free vibration analysis of laminated composite plates by using the third order shear deformation theory (TSDT). TSDT requires C1-continuity of generalized displacements and NURBS basis functions are well-suited for this requirement. Due to the noninterpolatory nature of NURBS basis functions, a penalty method is applied to enforce the essential boundary conditions. The validity and accuracy of the present method are demonstrated through a series of numerical examples of isotropic and laminated composite plates with different shapes, boundary conditions, fiber orientations, lay-up numbers, and so forth. The obtained numerical results are compared with either the analytical solutions or other available numerical methods.

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Chen, Leilei, Steffen Marburg, Wenchang Zhao, Cheng Liu, and Haibo Chen. "Implementation of Isogeometric Fast Multipole Boundary Element Methods for 2D Half-Space Acoustic Scattering Problems with Absorbing Boundary Condition." Journal of Theoretical and Computational Acoustics 27, no. 02 (June 2019): 1850024. http://dx.doi.org/10.1142/s259172851850024x.

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Isogeometric Analysis (IGA), which tries to bridge the gap between Computer Aided Engineering (CAE) and Computer Aided Design (CAD), has been widely proposed in recent research. According to the concept of IGA, this work develops a boundary element method (BEM) using non-Uniform Rational B-Splines (NURBS) as basis functions for the 2D half-space acoustic problems with absorbing boundary condition. Fast multipole method (FMM) is applied to accelerate the solution of an isogeometric BEM (IGA-BEM). Several examples are tested and it is shown that this advancement on isogeometric fast multipole boundary element method improves the accuracy of simulations.

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Maleki-Jebeli, Saeed, Mahmoud Mosavi-Mashhadi, and Mostafa Baghani. "Hybrid Isogeometric-Finite Element Discretization Applied to Stress Concentration Problems." International Journal of Applied Mechanics 10, no. 08 (September 2018): 1850081. http://dx.doi.org/10.1142/s1758825118500813.

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Isogeometric analysis (IGA) employs non-uniform rational B-splines (NURBS) or other B-spline-based variants to represent both the geometry and the field variable. Exact geometry representation and higher order global continuity (at least [Formula: see text] even on elements’ boundaries) are two favorable properties that would make IGA an appropriate discretization technique in problems with responses associated with the derivatives of the primary field variable. As a category of these problems, in this paper, 2D elastostatic problems involving stress concentration sites are analyzed with a hybrid isogeometric-finite element (IG-FE) discretization. To exploit higher order continuity of NURBS basis functions, IGA discretization is applied selectively at pre-identified locations of high displacement gradients where the stress concentration occurs. In addition, considering computational efficiency, the rest of problem domain is discretized by means of linear Lagrangian finite elements. The connection of NURBS and Lagrangian domain is carried out through employing specially devised elements [Corbett, C. J. and Sauer, R. A. [2014] “NURBS-enriched contact finite elements”, Computer Methods in Applied Mechanics and Engineering 275, 55–75]. The methodology is applied in some 2D elastostatic examples. Increasing the number of DOFs and comparing convergence of the concentrated stress value using different discretizations, it is shown that the hybrid IG-FE discretizations generally have faster and more stable convergence response compared with pure FE discretizations especially at lower DOFs.

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Dvořáková, Edita, and Bořek Patzák. "ON DEVELOPMENT OF THE INTERACTIVE DESIGN TOOL BASED ON ISOGEOMETRIC ANALYSIS." Acta Polytechnica CTU Proceedings 13 (November 13, 2017): 39. http://dx.doi.org/10.14311/app.2017.13.0039.

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Isogeometric analysis is a new concept of Finite element method which has been proposed to bridge the gap between the CAD systems and the FEM solvers. In Isogeometric analysis, the same basis functions, typically splines or NURBS, are used for geometry description as well as for approximation of unknowns and thus the same model can be shared between CAD and IGA systems. This results in a higher accuracy and overall efficiency of the analysis. Many isogeometric elements have been already proposed and implemented into the existing finite element solvers, but the automatic connection with a CAD system is usually missing. Our goal is to develop such a connection and to provide a tool which would interactively run the analysis when the model changes. This approach can enormously enhance the design process as it can provide the basic knowledge about the structural behavior already in conceptual design phase.

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Chang, Feng, Weiqiang Wang, Yan Liu, and Yanpeng Qu. "A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method." Engineering Computations 33, no. 7 (October 3, 2016): 2149–64. http://dx.doi.org/10.1108/ec-10-2015-0306.

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Purpose As one of the earliest high-level programming languages, Fortran with easy accessibility and computational efficiency is widely used in the engineering field. The purpose of this paper is to present a Fortran implementation of isogeometric analysis (IGA) for thin plate problems. Design/methodology/approach IGA based on non-uniform rational B-splines (NURBS) offers exact geometries and is more accurate than finite element analysis (FEA). Unlike the basis functions in FEA, NURBS basis functions are non-interpolated. Hence, the penalty method is used to enforce boundary conditions. Findings Several thin plate examples based on the Kirchhoff-Love theory were illustrated to demonstrate the accuracy of the implementation in contrast with analytical solutions, and the efficiency was validated in comparison with another open method. Originality/value A Fortran implementation of NURBS-based IGA was developed to solve Kirchhoff-Love plate problems. It easily obtained high-continuity basis functions, which are necessary for Kirchhoff formulation. In comparison with theoretical solutions, the numerical examples demonstrated higher accuracy and faster convergence of the Fortran implementation. The Fortran implementation can well solve the time-consuming problem, and it was validated by the time-consumption comparison with the Matlab implementation. Due to the non-interpolation of NURBS, the penalty method was used to impose boundary conditions. A suggestion of the selection of penalty coefficients was given.

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Le, Em Tuan, Khuong Duy Nguyen, and Hoa Cong Vu. "An isogeometric analysis approach for twodimensional steady state heat transfer problems." Science and Technology Development Journal 18, no. 2 (June 30, 2015): 164–74. http://dx.doi.org/10.32508/stdj.v18i2.1090.

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The purpose of this article is studied the application of isogeometric analysis (IGA) to two-dimensional steady state heat transfer problems in a heat sink. By using high order basis functions, NURBS basis functions, IGA is a high rate convergence approach in comparison to a traditional Finite Element Method. Moreover, the development of this method decreased the gaps between CAD and mathematical model and increased the continuity of mesh.

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Le-Manh, Tuan, and Jaehong Lee. "Postbuckling of laminated composite plates using NURBS-based isogeometric analysis." Composite Structures 109 (March 2014): 286–93. http://dx.doi.org/10.1016/j.compstruct.2013.11.011.

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Adam, C., T. J. R. Hughes, S. Bouabdallah, M. Zarroug, and H. Maitournam. "Selective and reduced numerical integrations for NURBS-based isogeometric analysis." Computer Methods in Applied Mechanics and Engineering 284 (February 2015): 732–61. http://dx.doi.org/10.1016/j.cma.2014.11.001.

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Gondegaon, Sangamesh, and Hari K. Voruganti. "Static Structural and Modal Analysis Using Isogeometric Analysis." Journal of Theoretical and Applied Mechanics 46, no. 4 (December 1, 2016): 36–75. http://dx.doi.org/10.1515/jtam-2016-0020.

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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.

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Niiranen, Jarkko, Sergei Khakalo, and Viacheslav Balobanov. "Isogeometric finite element analysis of mode I cracks within strain gradient elasticity." Rakenteiden Mekaniikka 50, no. 3 (August 22, 2017): 337–40. http://dx.doi.org/10.23998/rm.65124.

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A variational formulation within an H2 Sobolev space setting is formulated for fourth-order plane strain/stress boundary value problems following a widely-used one parameter variant of Mindlin's strain gradient elasticity theory. A corresponding planar mode I crack problem is solved by isogeometric Cp-1-continuous discretizations for NURBS basis functions of order p \ge 2. Stress eld singularities of the classical elasticity are shown to be removed by the strain gradient formulation.

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Nguyen, Khuong Duy, Tien Manh Nguyen, Chien Trung Vo, Hung Xuan Nguyen, and Hoa Cong Vu. "Analyze thermo-mechanical problem by isogeometric analysis for structures used functionally graded material." Science and Technology Development Journal 20, K3 (June 30, 2017): 53–59. http://dx.doi.org/10.32508/stdj.v20ik3.1092.

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The objective of this paper is apply isogeometric analysis (IGA) to analyze thermoelastic behavior of functionally graded material (FGM) structures. IGA is built on NURBS basis functions used to model exact geometries with higher-order approached functions. The FGM is a type of advanced composite material has material properties is continuous distributed variation through thickness direction. The results are verified with other numerical results and results from COMSOL commercial software.

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De Lorenzis, L., İ. Temizer, P. Wriggers, and G. Zavarise. "A large deformation frictional contact formulation using NURBS-based isogeometric analysis." International Journal for Numerical Methods in Engineering 87, no. 13 (February 23, 2011): 1278–300. http://dx.doi.org/10.1002/nme.3159.

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Mi, Yongzhen, Hui Zheng, Yang Shen, and Yuanyi Huang. "A Weak Formulation for Isogeometric Analysis of Vibro-Acoustic Systems with Non-Conforming Interfaces." International Journal of Applied Mechanics 10, no. 07 (August 2018): 1850073. http://dx.doi.org/10.1142/s1758825118500734.

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This paper develops a weak formulation for steady-state dynamic analysis of vibro-acoustic systems in the isogeometric framework. The Non-Uniform Rational B-Splines (NURBS) polynomials are used as basis functions for both geometrical transformation and numerical approximation. Starting from a NURBS-based geometrical projection that transforms a general, complex domain to a regular, spectral domain, an energy-based numerical model is then built, in which NURBS are again used as wholly admissible functions to approximate the structural displacement and the acoustic sound pressure. This process eventually leads to a set of discretized equations, based on which the system’s dynamic properties can be obtained. Besides better accuracy and excellent geometrical adaptivity, the main merit of the proposed method lies in its element-free feature of system modeling, which provides a natural solution for structural-acoustic coupling with non-conforming interfaces. This non-conformity results from either non-matching control points along the boundary or distinct polynomial orders used by adjacent patches, which is inevitable for a vibro-acoustic system given its multi-physics nature. The reliability of the proposed method is validated by a benchmark example. Its accuracy and efficiency are further investigated through a more general, car-like vibro-acoustic system.

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Faroughi, S., E. Shafei, and D. Schillinger. "Isogeometric Stress, Vibration and Stability Analysis of In-Plane Laminated Composite Structures." International Journal of Structural Stability and Dynamics 18, no. 05 (May 2018): 1850070. http://dx.doi.org/10.1142/s0219455418500700.

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We present a computational study that develops isogeometric analysis based on higher-order smooth NURBS basis functions for the analysis of in-plane laminated composites. Focusing on the stress, vibration and stability analysis of angle-ply and cross-ply 2D structures, we compare the convergence of the strain energy error and selected stress components, eigen-frequencies and buckling loads according to overkill solutions. Our results clearly demonstrate that for in-plane laminated composite structures, isogeometric analysis is able to provide the same accuracy at a significantly reduced number of degrees of freedom with respect to standard [Formula: see text] finite elements. In particular, we observe that the smoothness of spline basis functions enables high-quality stress solutions, which are superior to the ones obtained with conventional finite elements.

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Gantner, Gregor, Dirk Praetorius, and Stefan Schimanko. "Adaptive isogeometric boundary element methods with local smoothness control." Mathematical Models and Methods in Applied Sciences 30, no. 02 (February 2020): 261–307. http://dx.doi.org/10.1142/s0218202520500074.

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In the frame of isogeometric analysis, we consider a Galerkin boundary element discretization of the hyper-singular integral equation associated with the 2D Laplacian. We propose and analyze an adaptive algorithm which locally refines the boundary partition and, moreover, steers the smoothness of the NURBS ansatz functions across elements. In particular and unlike prior work, the algorithm can increase and decrease the local smoothness properties and hence exploits the full potential of isogeometric analysis. We prove that the new adaptive strategy leads to linear convergence with optimal algebraic rates. Numerical experiments confirm the theoretical results. A short appendix comments on analogous results for the weakly-singular integral equation.

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Wang, DongDong, HanJie Zhang, and JunChang Xuan. "A strain smoothing formulation for NURBS-based isogeometric finite element analysis." Science China Physics, Mechanics and Astronomy 55, no. 1 (October 28, 2011): 132–40. http://dx.doi.org/10.1007/s11433-011-4528-1.

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Im, Chan-Kyung, and Sung-Kie Youn. "The Generation of 3D Trimmed Elements for NURBS-Based Isogeometric Analysis." International Journal of Computational Methods 15, no. 07 (October 12, 2018): 1850065. http://dx.doi.org/10.1142/s0219876218500652.

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In conventional 3D NURBS-based isogeometric analysis (IGA), it is required to generate a discretized 3D model from the imported CAD model. Since a CAD file only contains surface information of the 3D object, generation of 3D mesh and trivariate basis functions are required for the IGA. In CAD system, the Boolean difference operation, so-called “trimming” is frequently employed for creating complex objects. To directly utilize the trimming information into analysis, trimmed elements need to be defined and their integration schemes are also needed. In this paper, trimmed elements searching, classification, decomposition and integration rules are presented. In the process, seven types of generalized trimmed elements are defined. Since covering all possible 3D geometries is not possible, three out of seven types of trimmed elements formed by extrusion are treated. The decomposition rule of trimmed elements is introduced and curved tetrahedral cells are adopted to integrate the trimmed elements. For numerical integration of curved tetrahedral cells, 3D NEFEM-like integration scheme has been developed. For the demonstration of the usage of the developed elements, two numerical examples of trimmed volume are treated.

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Zhang, Xiangkui, Chunning Jin, Ping Hu, Xuefeng Zhu, Wenbin Hou, Jinting Xu, Changsheng Wang, Yuewei Zhang, Zheng-Dong Ma, and Holly Smith. "NURBS modeling and isogeometric shell analysis for complex tubular engineering structures." Computational and Applied Mathematics 36, no. 4 (February 24, 2016): 1659–79. http://dx.doi.org/10.1007/s40314-016-0312-1.

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Kapoor, Hitesh, and R. K. Kapania. "Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates." Composite Structures 94, no. 12 (December 2012): 3434–47. http://dx.doi.org/10.1016/j.compstruct.2012.04.028.

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Al Akhras, H., T. Elguedj, A. Gravouil, and M. Rochette. "Isogeometric analysis-suitable trivariate NURBS models from standard B-Rep models." Computer Methods in Applied Mechanics and Engineering 307 (August 2016): 256–74. http://dx.doi.org/10.1016/j.cma.2016.04.028.

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Hughes, T. J. R., J. A. Cottrell, and Y. Bazilevs. "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement." Computer Methods in Applied Mechanics and Engineering 194, no. 39-41 (October 2005): 4135–95. http://dx.doi.org/10.1016/j.cma.2004.10.008.

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Zhang, Yongjie, Yuri Bazilevs, Samrat Goswami, Chandrajit L. Bajaj, and Thomas J. R. Hughes. "Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow." Computer Methods in Applied Mechanics and Engineering 196, no. 29-30 (May 2007): 2943–59. http://dx.doi.org/10.1016/j.cma.2007.02.009.

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Xiang, Ying, Rong Mo, Neng Wan, and Hu Qiao. "The High Precision Blade Electrochemical Machining Simulation and Cathode Optimization Based on Isogeometric Method." Applied Mechanics and Materials 339 (July 2013): 489–94. http://dx.doi.org/10.4028/www.scientific.net/amm.339.489.

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The simulation and optimization of electrochemical machining is an important means to improve processing quality. However, the fragmented nature of geometric modeling and numerical analysis model, restricts the application proportion. Aiming at this problem, it is refined that the scientific problem of coordination modeling between CAD and CAE based isogeometric method. In this paper, the unified model is established based NURBS basis functions to solve the problems that the geometric parameterization and the infliction of boundary conditions. And the optimization efficiency is promoted by improved optimization model using the convex hull characteristic of NURBS basis function. At last, a confluent design method is realized for the blade electrochemical machining process.

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Journal articles on the topic 'Nurbs Isogeometric analysis'

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