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   An isogeometric boundary element method for elastostatic analysis: 2D implementation aspects; Bordas, Stéphane  ; et alin Computers and Structures (2013), 118 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 ... [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: 407 (5 UL)Stress analysis without meshing: Isogeometric boundary-element method; ; Bordas, Stéphane in Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics (2013), 166(2), 88-99 The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The ... [more ▼] The focus of this paper is the description and numerical validation of a computational method where stress analysis can be performed directly from computer-aided design data without mesh generation. The clear benefit of the approach is that no mesh needs to be generated prior to running the analysis. This is achieved by utilising the isogeometric concept whereby computer-aided design data are used to construct not only the geometry discretisation but also the displacement and traction approximations. In this manner, significant savings can be made in the engineering design and analysis process. This paper also demonstrates that, compared with a standard boundary-element method implementation using quadratic Lagrangian shape functions, superior accuracy is achieved using the present approach for the same number of degrees of freedom. It further illustrates practical applications of the method, comparing against results obtained with a standard boundary-element method and finite-element method for verification. In addition, a propeller is analysed as a sample to show the ability of the present method to handle complex three-dimensional geometries. [less ▲] Detailed reference viewed: 486 (7 UL) A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis; Bordas, Stéphane ; et alin Computer Methods in Applied Mechanics and Engineering (2012), 209-212 The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention ... [more ▼] The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation. © 2011 Elsevier B.V. [less ▲] Detailed reference viewed: 265 (8 UL)Enriched residual free bubbles for semiconductor device simulation; Bordas, Stéphane ; et alin Computational Mechanics (2012), 50(1), 119-133 This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite ... [more ▼] This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite element (FE) implementation that are able to prevent oscillations which are seen when using the conventional Bubnov-Galerkin FE implementation. In addition, it is shown that the RfBF are able to provide stabilisation with very distorted meshes and curved interface boundaries. Comparison with the commonly used SUPG scheme is made throughout, showing that in the case of 2D problems the RfBF allow faster convergence of the coupled semiconductor device equations, especially in the case of distorted meshes. [less ▲] Detailed reference viewed: 126 (0 UL)A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis; ; et al in Computer Modeling in Engineering and Sciences (2011), 73(4), 331-355 This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture ... [more ▼] This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results. [less ▲] Detailed reference viewed: 80 (2 UL) |
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