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Cardiff/Luxembourg Computational Mechanics Research Group Bordas, Stéphane ; ; Hale, Jack et al Poster (2014, November) Detailed reference viewed: 184 (7 UL)Geometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity ; ; et al in Computer Methods in Applied Mechanics and 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: 1115 (30 UL)GEOMETRY-INDEPENDENT FIELD APPROXIMATION FOR SPLINE-BASED FINITE ELEMENT METHODS ; ; Bordas, Stéphane in Proceedings of the 11th World Congress in Computational Mechanics (2014, July) We propose a discretization scheme where the spline spaces used for the geometry and the field variables can be chosen independently in spline-based FEM. he method is thus applicable to arbitrary domains ... [more ▼] We propose a discretization scheme where the spline spaces used for the geometry and the field variables can be chosen independently in spline-based FEM. he method is thus applicable to arbitrary domains with spline representation. (2) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the PDE, e.g. the continuity of the solution field. (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, i.e. the parameterization of the given geometry is not altered during the refinement process. Hence, the initial design can be optimized in the subsequent shape optimization stage without constraining the geometry discretization space to conform to the field approximation space. [less ▲] Detailed reference viewed: 566 (15 UL)Crack growth analysis by a NURBS-based isogeometric boundary element metyhod ; ; et al Presentation (2014, July) Detailed reference viewed: 116 (3 UL)Crack growth analysis by a NURBS-based isogeometric boundary element method ; ; et al Scientific Conference (2014, July) Detailed reference viewed: 558 (26 UL)Stress analysis, damage tolerance assessment and shape optimisation without meshing Hale, Jack ; Bordas, Stéphane ; et al Poster (2014, June 24) Detailed reference viewed: 121 (3 UL)Damage tolerance assessment directly from CAD: (extended) isogeometric boundary element methods ; ; Bordas, Stéphane Scientific Conference (2014, June) Detailed reference viewed: 292 (4 UL)A two-dimensional isogeometric boundary element method for linear elastic fracture ; ; et al Report (2014) Detailed reference viewed: 134 (5 UL)A Two-Dimensional Isogeometric Boundary Element Method For Linear Elastic Fracture ; ; et al Scientific Conference (2014, January) Detailed reference viewed: 401 (11 UL)Fundamental Solutions and Dual Boundary Element Method for Crack Problems in Plane Cosserat Elasticity ; Bordas, Stéphane in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (2014) 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 the equations (approach known as the dual BEM) allows to treat problems where parts of the boundary are overlapping, such as crack problems, 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 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. A modified method for computing the couple stress intensity factors is also proposed and evaluated. Finally, the asymptotic behavior of the solution to the Cosserat crack problems, in the vicinity of the crack tip is analyzed. [less ▲] Detailed reference viewed: 678 (13 UL)Boundary Element Method with NURBS-geometry and independent field approximations in plane elasticity ; ; et al Scientific Conference (2014) Detailed reference viewed: 341 (2 UL)Damage tolerance assessment directly from CAD: (extended) isogeometric boundary element methods (XIGABEM) ; ; Bordas, Stéphane Scientific Conference (2014) Detailed reference viewed: 403 (5 UL)A two-dimensional isogeometric boundary element method for linear elastic fracture: a path towards damage tolerance analysis without meshing ; ; et al Report (n.d.) Detailed reference viewed: 131 (7 UL)A new one point quadrature rule over arbitrary star convex polygon/polyhedron ; ; et al E-print/Working paper (n.d.) The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we ... [more ▼] The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲] Detailed reference viewed: 65 (3 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 E-print/Working paper (n.d.) 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: 274 (13 UL) |
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