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ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS ; ; Bordas, Stéphane et al Scientific Conference (2019, April 11) We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼] We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲] Detailed reference viewed: 233 (16 UL)Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT) ; Tomar, Satyendra ; et al in International Journal for Numerical Methods in Engineering (2018) This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼] This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲] Detailed reference viewed: 163 (8 UL)Micro-structured materials: inhomogeneities and imperfect interfaces in plane micropolar elasticity, a boundary element approach ; Hale, Jack ; et al in Engineering Analysis with Boundary Elements (2017), 83 In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an ... [more ▼] In this paper we tackle the simulation of microstructured materials modelled as heterogeneous Cosserat media with both perfect and imperfect interfaces. We formulate a boundary value problem for an inclusion of one plane strain micropolar phase into another micropolar phase and reduce the problem to a system of boundary integral equations, which is subsequently solved by the boundary element method. The inclusion interface condition is assumed to be imperfect, which permits jumps in both displacements/microrotations and tractions/couple tractions, as well as a linear dependence of jumps in displacements/microrotations on continuous across the interface tractions/couple traction (model known in elasticity as homogeneously imperfect interface). These features can be directly incorporated into the boundary element formulation. The BEM-results for a circular inclusion in an in finite plate are shown to be in excellent agreement with the analytical solutions. The BEM-results for inclusions in finite plates are compared with the FEM-results obtained with FEniCS. [less ▲] Detailed reference viewed: 177 (12 UL)Trefftz polygonal finite element for linear elasticity: convergence, accuracy, and properties ; ; et al in Asia Pacific Journal on Computational Engineering (2017) In this paper, the accuracy and the convergence properties of Trefftz finite element method over arbitrary polygons are studied. Within this approach, the unknown displacement field within the polygon is ... [more ▼] In this paper, the accuracy and the convergence properties of Trefftz finite element method over arbitrary polygons are studied. Within this approach, the unknown displacement field within the polygon is represented by the homogeneous solution to the governing differential equations, also called as the T-complete set. While on the boundary of the polygon, a conforming displacement field is independently defined to enforce the continuity of the field variables across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and the degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity show that the proposed method yields highly accurate results with optimal convergence rates. [less ▲] Detailed reference viewed: 41 (1 UL)Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment ; ; et al in International Journal of Fracture (2016) Detailed reference viewed: 217 (21 UL)Weakening the tight coupling between geometry and simulation in isogeometric analysis Tomar, Satyendra ; ; et al Presentation (2016, June 07) In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry ... [more ▼] In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is employed for the numerical solution of the problem over the domain. However, there are situations where this tight integration is a bane rather than a boon. Such situations arise where, e.g., (1) the geometry of the domain is simple enough to be represented by low order NURBS, whereas the unknown (exact) solution of the problem is sufficiently regular, and thus, the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry, (2) the constraint of using the same space for the geometry and the numerical solution is particularly undesirable, such as in the shape and topology optimization, and (3) the solution of the problem has low regularity but for the curved boundary of the domain one can employ higher order NURBS. Therefore, we propose to weaken this constraint. An extensive study of patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution will be discussed. It will be shown, with concrete reasoning, that why patch test fails in certain cases, and that those cases should be avoided in practice. Thereafter, selective numerical examples will be presented to address some of the above-mentioned situations, and it will be shown that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces, and thus, improved accuracy of the numerical solution. [less ▲] Detailed reference viewed: 145 (9 UL)Weakening the tight coupling between geometry and simulation in isogeometric analysis Bordas, Stéphane ; Tomar, Satyendra ; et al Scientific Conference (2016, June 05) In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry ... [more ▼] In the standard paradigm of isogeometric analysis, the geometry and the simulation spaces are tightly integrated, i.e. the same non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is employed for the numerical solution of the problem over the domain. However, there are situations where this tight integration is a bane rather than a boon. Such situations arise where, e.g., (1) the geometry of the domain is simple enough to be represented by low order NURBS, whereas the unknown (exact) solution of the problem is sufficiently regular, and thus, the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry, (2) the constraint of using the same space for the geometry and the numerical solution is particularly undesirable, such as in the shape and topology optimization, and (3) the solution of the problem has low regularity but for the curved boundary of the domain one can employ higher order NURBS. Therefore, we propose to weaken this constraint. An extensive study of patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution will be discussed. It will be shown, with concrete reasoning, that why patch test fails in certain cases, and that those cases should be avoided in practice. Thereafter, selective numerical examples will be presented to address some of the above-mentioned situations, and it will be shown that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces, and thus, improved accuracy of the numerical solution. Powered by [less ▲] Detailed reference viewed: 126 (5 UL)Generalizing the isogeometric concept: weakening the tight coupling between geometry and simulation in IGA Tomar, Satyendra ; ; et al Presentation (2016, June 02) In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the ... [more ▼] In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is also employed for the numerical solution of the problem over the domain. However, in certain situations, such as, when the geometry of the domain can be represented by low order NURBS but the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry; or in the shape and topology optimization where the constraint of using the same space for the geometry and the numerical solution is not favorable, this tight coupling is disadvantageous. Therefore, we study the effect of decoupling the spaces for the geometry representation and the numerical solution, though still using the prevalent functions in CAD/CAGD. To begin with, we perform the patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution. This shows that certain cases, perhaps intuitive, should be avoided in practice because patch test fails. The above-mentioned situations are further explored with some numerical examples, which shows that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces. [1] J. Cottrell, T.J.R. Hughes, and Y. Bazilevs. Isogeometric Analysis: Toward Integration of CAD and FEA, volume 80. Wiley, Chichester, 2009. [2] T.J.R. Hughes, J. Cottrell, and Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194:4135–4195, 2005. [less ▲] Detailed reference viewed: 138 (11 UL)Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth ; ; et al in Computer Methods in Applied Mechanics & Engineering (2016) Detailed reference viewed: 160 (12 UL)Generalizing the isogeometric concept: weakening the tight coupling between geometry and simulation in IGA Bordas, Stéphane ; Tomar, Satyendra ; et al Scientific Conference (2016, May 30) In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the ... [more ▼] In the standard paradigm of isogeometric analysis [2, 1], the geometry and the simulation spaces are tightly integrated, i.e. the non-uniform rational B-splines (NURBS) space, which is used for the geometry representation of the domain, is also employed for the numerical solution of the problem over the domain. However, in certain situations, such as, when the geometry of the domain can be represented by low order NURBS but the numerical solution can be obtained with improved accuracy by using NURBS of order higher than that required for the geometry; or in the shape and topology optimization where the constraint of using the same space for the geometry and the numerical solution is not favorable, this tight coupling is disadvantageous. Therefore, we study the effect of decoupling the spaces for the geometry representation and the numerical solution, though still using the prevalent functions in CAD/CAGD. To begin with, we perform the patch tests on various combinations of polynomial degree, geometry type, and various cases of varying degrees and control variables between the geometry and the numerical solution. This shows that certain cases, perhaps intuitive, should be avoided in practice because patch test fails. The above-mentioned situations are further explored with some numerical examples, which shows that weakening the tight coupling between geometry and simulation offers more flexibility in choosing the numerical solution spaces. [less ▲] Detailed reference viewed: 120 (3 UL)3D fatigue fracture modeling by isogeometric boundary element methods ; ; et al Scientific Conference (2016, April 01) Detailed reference viewed: 120 (1 UL)Isogeometric boundary element methods for linear elastic fracture mechanics ; ; et al Report (2016) Detailed reference viewed: 353 (20 UL)Isogeometric boundary element methods for three dimensional fatigue crack growth ; ; et al Report (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: 439 (14 UL)Multi-scale fracture, model reduction, CAD and image as a model Bordas, Stéphane ; ; Beex, Lars et al Scientific Conference (2015, June 24) Detailed reference viewed: 259 (7 UL)Geometry-Independent Field approximaTion (GIFT) for spline based FEM for Linear Elasticity: a Diffpack implementation ; ; Bordas, Stéphane et al Scientific Conference (2015, June 01) Detailed reference viewed: 326 (7 UL)An isogeometric boundary element method for fracture modeling ; ; Bordas, Stéphane Presentation (2015, May) Detailed reference viewed: 174 (7 UL)Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity ; Bordas, Stéphane in Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences (2015), 471(2179), In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate ... [more ▼] In this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip. [less ▲] Detailed reference viewed: 46 (1 UL)Multiscale computational mechanics: industrial applications Bordas, Stéphane ; ; Beex, Lars et al Presentation (2014, November 25) Detailed reference viewed: 150 (7 UL)Cardiff/Luxembourg Computational Mechanics Research Group Bordas, Stéphane ; ; Hale, Jack et al Poster (2014, November) Detailed reference viewed: 155 (6 UL)Geometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity ; ; et al in Computer Methods in Applied Mechanics & Engineering (2014) In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and ... [more ▼] In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper [20] as a key advantage on the way to the integration of Computer Aided Design (CAD) and subsequent analysis in Computer Aided Engineering (CAE). [20] claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables, without requiring the regeneration of the mesh at each change of the domain geometry. Yet, in Finite Element versions of IGA, a parameterization of the interior of the domain must still be constructed, since CAD only provides information about the boundary. The identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process, because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately, in particular when the solution is not smooth. We propose here a new paradigm called Geometry-Independent Field approximaTion (GIFT) where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight CAD integration. GIFT has the following features: (1) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the problem, e.g. the continuity of the solution field, boundary layers, singularities, whilst retaining geometrical exactness of the domain boundary. (2) For multi-patch analysis, where the domain is composed of several spline patches, the continuity condition between neighboring patches on the solution field can be automatically guaranteed without additional constraints in the variational form. (3) Refinement operations by knot insertion and degree elevation are performed directly on the spline space of the solution field, independently of the spline space of the geometry of the domain, which makes the method versatile. GIFT with PHT-spline solution spaces and NURBS geometries is used to show the effectiveness of the proposed approach. Keywords : Super-parametric methods, Isogeometric analysis (IGA), Geometry-independent Spline Space, PHT-splines, local refinement, adaptivity [less ▲] Detailed reference viewed: 993 (29 UL) |
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