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V.; Thai, C. H. et alin Composites : Part B, Engineering (2014), 64We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of ... [more ▼]We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of functionally graded material (FGM) plates. A new inverse tangent distributed function through the plate thickness is proposed. The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions namely B-splines or non-uniform rational B-splines (NURBS) which reach easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field with four degrees of freedom per each control point allowing an efficient solution process. [less ▲]Detailed reference viewed: 99 (3 UL) Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theoryThai, C. H. A; Bordas, Stéphane ; Ferreira, A. et alin European Journal of Mechanics A : Solids (2014), 43This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear ... [more ▼]This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear stresses are vanished at the top and bottom surfaces of the plates and shear correction factors are no longer required. A weak form of the static, free vibration and buckling models for laminated composite and sandwich plates based on ITSDT is then derived and is numerically solved using an isogeometric analysis (IGA). The proposed formulation requires C1-continuity generalized displacements and hence basis functions used in IGA fulfill this requirement. Numerical examples are provided to show high efficiency of the present method compared with other published solutions. © 2013 Elsevier Ltd. All rights reserved. [less ▲]Detailed reference viewed: 322 (4 UL) Isogeometric Analysis of Laminated Composite Plates Using the Higher-Order Shear Deformation TheoryThai, Chien H.; Nguyen-Xuan, H.; Bordas, Stéphane et alin Mechanics of Advanced Materials and Structures (2015), 22(6), 451-469Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown ... [more ▼]Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown fields (Analysis). IGA can be based on a variety of CAD descriptions, the most widely used today being non-uniform rational B-splines (NURBS). In this article, the suitability of NURBS-based isogeometric analysis within a third-order shear deformation theory for the simulation of the static, dynamic, and buckling response of laminated composite plates is investigated. The method employs NURBS basis functions to both represent the geometry (exactly) and the unknown field variables. One of the main advantages of the present method is directly inherited from IGA, that is to easily increase the approximation order. To avoid using a shear correction factor, a third-order shear deformation theory (TSDT) is introduced. It requires C1-continuity of generalized displacements and the NURBS basis functions are well suited for this requirement. Several numerical examples are used to demonstrate the performance of the present method compared with other published ones. [less ▲]Detailed reference viewed: 92 (2 UL) Isogeometric analysis of thin Reissner-Mindlin plates and shells: Locking phenomena and generalized local B-bar methodHu, Qingyuan ; Xia, Yang; Natarajan, Sundararajan et alE-print/Working paper (2017)We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are ... [more ▼]We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation is general and allows the flexible utilization of basis functions of different order as the projection bases. The present formulation is much cheaper computationally than the global $\bar{B}$ method. Through numerical examples, we show the consistency of the scheme, although the method is not Hu-Washizu variationally consistent. The numerical examples show that the proposed formulation alleviates locking and yields good accuracy for various thicknesses, even for slenderness ratios of $1 \times 10^5$, and has the ability to capture deformations of thin shells using relatively coarse meshes. From the detailed numerical study, it can be opined that the proposed method is less sensitive to locking and mesh distortion. [less ▲]Detailed reference viewed: 219 (15 UL) Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar methodHu, Qingyuan; Xia, Yang; Natarajan, Sundararajan et alin Computational Mechanics (2020), 65(5), 1323-1341We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto ... [more ▼]We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation allows the flexible utilization of basis functions of different orders as the projection bases. The introduced formulation is much cheaper computationally than the classical $$\bar{B}$$B¯ method. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of $$10^5$$105, and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking with irregular meshes. [less ▲]Detailed reference viewed: 52 (1 UL) Isogeometric analysis suitable trivariate NURBS representation of composite panels with a new offset algorithmNguyen, Vinh-Phu; Kerfriden, Pierre; Bordas, Stéphane et alin Computer-Aided Design (2014), 55Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset ... [more ▼]Trivariate NURBS (non-uniform rational B-splines) representation of composite panels which is suitable for three-dimensional isogeometric analysis (IGA) is constructed with a new curve/surface offset algorithm. The proposed offset algorithm, which is required by IGA, is non-existent in the CAD literature. Using the presented approach, finite element analysis of composite panels can be performed with the only input being the geometry representation of the composite surface. The method proposed provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. Different parts (patches) can be parametrized independently of each other and glued together, in the finite element solver, by a discontinuous Galerkin method. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework. © 2014 Elsevier Ltd. All rights reserved. [less ▲]Detailed reference viewed: 297 (4 UL) Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solidsNguyen-Thanh, N.; Nguyen-Xuan, H.; Bordas, Stéphane et alin Computer Methods in Applied Mechanics & Engineering (2011), 200(21-22), 1892-1908Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite ... [more ▼]Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method. [less ▲]Detailed reference viewed: 85 (1 UL) Isogeometric analysis: an overview and computer implementation aspectsNguyen, Vinh-Phu; Anitescu, Cosmin; Bordas, Stéphane et alin Mathematics and Computers in Simulation (2015)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 ... [more ▼]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 Matlab⃝R 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 B ́ezier 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. [less ▲]Detailed reference viewed: 902 (11 UL) Isogeometric analysis: an overview and computer implementation aspectsNguyen, Vinh-Phu; Anitescu, Cosmin; Bordas, Stéphane et alLearning material (2013)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 ... [more ▼]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. 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 Matlab⃝R implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation 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. The open source Matlab⃝R 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 B ́ezier extraction concept that allows 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. [less ▲]Detailed reference viewed: 955 (11 UL) Isogeometric and multi-scale fractureBordas, Stéphane Presentation (2015, July 31)Detailed reference viewed: 163 (10 UL) Isogeometric boundary element analysis using unstructured T-splinesScott, M. A.; Simpson, R. N.; Evans, J. A. et alin Computer Methods in Applied Mechanics & Engineering (2013), 254We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to ... [more ▼]We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bézier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method. © 2012 Elsevier B.V. [less ▲]Detailed reference viewed: 376 (13 UL) An isogeometric boundary element method for elastostatic analysis: 2D implementation aspectsSimpson, R. N.; Bordas, Stéphane ; Lian, H. et alin Computers & Structures (2013), 118The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed ... [more ▼]The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlining an isogeometric boundary element Method (IGABEM) that only requires a representation of the geometry of the domain for analysis, fitting neatly with the boundary representation provided completely by CAD. The method circumvents the requirement to generate a boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional boundary element implementations. Examples of Matlab® code are given whenever possible to aid understanding of the techniques used. [less ▲]Detailed reference viewed: 326 (3 UL) An isogeometric boundary element method for elastostatic analysis: 2D implementation aspectsSimpson, Robert; Bordas, Stéphane ; Lian, Haojie et alin Computers & Structures (2013), 118Detailed reference viewed: 542 (19 UL) An isogeometric boundary element method for fracture modelingPeng, Xuan; Atroshchenko, Elena; Bordas, Stéphane Presentation (2015, May)Detailed reference viewed: 187 (7 UL) Isogeometric boundary element methods for linear elastic fracture mechanicsPeng, Xuan; Atroshchenko, Elena; Kerfriden, Pierre et alReport (2016)Detailed reference viewed: 385 (20 UL) Isogeometric boundary element methods for three dimensional fatigue crack growthPeng, Xuan; Atroshchenko, Elena; Kerfriden, Pierre et alReport (2015)The isogeometric boundary element method (IGABEM) based on NURBS is adopted to model fracture problem in 3D. The NURBS basis functions are used in both crack representation and physical quantity ... [more ▼]The isogeometric boundary element method (IGABEM) based on NURBS is adopted to model fracture problem in 3D. The NURBS basis functions are used in both crack representation and physical quantity approximation. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted element. The convergence study in crack opening displacement is performed for penny-shaped crack and elliptical crack. Two ways to extract stress intensity factors (SIFs), the contour $M$ integral and virtual crack closure integral, are implemented based on the framework of dual integral equations. An algorithm is outlined and validated to be stable for fatigue crack growth, thanks to the smoothness not only in crack geometry but also in stress/SIFs solution brought by IGABEM. [less ▲]Detailed reference viewed: 456 (14 UL) Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growthPeng, Xuan; Atroshchenko, Elena; Kerfriden, Pierre et alin Computer Methods in Applied Mechanics & Engineering (2016)Detailed reference viewed: 202 (12 UL) Isogeometric cohesive elements for two and three dimensional composite delamination analysisNguyen, VP; Kerfriden, Pierre; Bordas, Stéphane in Composites : Part B, Engineering (2013)Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B ... [more ▼]Isogeometric cohesive elements are presented for modeling two and three dimensional delaminated composite structures. We exploit the knot insertion algorithm offered by NURBS (Non Uniform Rational B-splines) to generate cohesive ele- ments along delamination planes in an automatic fashion. A complete computational framework is presented including pre-processing, processing and post-processing. They are explained in details and implemented in MIGFEM–an open source Matlab Isogemetric Analysis code developed by the authors. The composite laminates are modeled using both NURBS solid and rotation-free shell elements. Several two and three dimensional examples ranging from standard delamination tests (the mixed mode bending test) to the L-shaped specimen with a fillet, three dimensional (3D) double cantilever beam and a 3D singly curved thick-walled laminate are provided. To the authors’ knowledge, it is the first time that NURBS-based isogeometric analysis for two/three dimensional delamination modeling is presented. IGA provides a bi-directional system in which one can go forward from CAD to analysis and backwards from analysis to CAD. This is believed to facilitate the design of composite structures. [less ▲]Detailed reference viewed: 544 (4 UL) Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problemsKhajah, Tahsin; Antoine, Xavier; Bordas, Stéphane E-print/Working paper (2016)We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The ... [more ▼]We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical results performed with high-order basis functions (third or fourth orders) showed no visible pollution error even for very high frequencies. This property combined with exact geometrical representation makes isogeometric analysis a very promising platform to solve high-frequency acoustic problems. [less ▲]Detailed reference viewed: 133 (14 UL) Isogeometric finite element analysis using polynomial splines over hierarchical T-meshesNguyen-Thanh, Nhon; Nguyen-Xuan, Hung; Bordas, Stéphane et alin IOP Conference Series: Materials Science and Engineering (2014), 10(1), Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric ... [more ▼]Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples. [less ▲]Detailed reference viewed: 80 (0 UL)