Robert Napier Simpson
University of Glasgow
Partition of unityComputer Aided DesignMathematical optimizationEngineeringMathematical analysisFinite element methodMesh generationExtended finite element methodIsogeometric analysisApplied mathematicsMathematicsComputer scienceFracture (geology)Boundary knot methodBasis functionBoundary (topology)Boundary element methodStructural engineeringComputational mechanicsDiscretizationSingular boundary method
Publications 29
#1Robert Napier Simpson (Glas.: University of Glasgow)H-Index: 12
#2Zhaowei Liu (Glas.: University of Glasgow)H-Index: 52
Last. John A. Evans (CU: University of Colorado Boulder)H-Index: 24
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Abstract We outline the construction of compatible B-splines on 3D surfaces that satisfy the continuity requirements for electromagnetic scattering analysis with the boundary element method (method of moments). Our approach makes use of Non-Uniform Rational B-splines to represent model geometry and compatible B-splines to approximate the surface current, and adopts the isogeometric concept in which the basis for analysis is taken directly from CAD (geometry) data. The approach allows for high-or...
26 CitationsSource
#1Zhaowei Liu (Glas.: University of Glasgow)H-Index: 52
#1Zhaowei Liu (Glas.: University of Glasgow)H-Index: 5
Last. Robert Napier Simpson (Glas.: University of Glasgow)H-Index: 12
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Summary We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and preclude...
17 CitationsSource
#1Robert Napier Simpson (Glas.: University of Glasgow)H-Index: 12
#2Zhaowei Liu (Glas.: University of Glasgow)H-Index: 52
Last. Zhaowei Liu (Glas.: University of Glasgow)H-Index: 5
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Abstract This work outlines the use of a black-box fast multipole method to accelerate the far-field computations in an isogeometric boundary element method. The present approach makes use of T-splines to discretise both the geometry and analysis fields allowing a direct integration of CAD and analysis technologies. A black-box fast multipole method of O ( N ) complexity is adopted that minimises refactoring of existing boundary element codes and facilitates the use of different kernels. This pa...
26 CitationsSource
#1Robert Napier Simpson (Glas.: University of Glasgow)H-Index: 12
#2Michael A. Scott (BYU: Brigham Young University)H-Index: 27
Last. Haojie Lian (Cardiff University)H-Index: 13
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An isogeometric boundary element method based on T-splines is used to simulate acoustic phenomena. We restrict our developments to low-frequency problems to establish the fundamental properties of the proposed approach. Using T-splines, the computer aided design (CAD) and boundary element analysis are integrated without recourse to geometry clean-up or mesh generation. A regularized Burton–Miller formulation is used resulting in integrals which are at most weakly singular. We employ a collocatio...
136 CitationsSource
#1Jon Trevelyan (Durham University)H-Index: 18
#2Robert Napier Simpson (Cardiff University)H-Index: 12
Last. Lucy Weggler (Saarland University)H-Index: 2
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The boundary element method (BEM) has historically offered engineers an alternative technique to finite elements that has offered attractions for certain classes of problem including infinite domains as found in acoustic scattering or those involving discontinuous and singular fields in fracture mechanics. The emergence of the isogeometric approach in computational mechanics has recently led to a rekindling of interest in the BEM for general problems in solid mechanics due the requirement for a ...
#1Haojie Lian (Cardiff University)H-Index: 13
#2Robert Napier Simpson (Cardiff University)H-Index: 12
Last. Stéphane Bordas (University of Luxembourg)H-Index: 65
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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 approximat...
22 CitationsSource
#1Robert Napier Simpson (Cardiff University)H-Index: 12
#2Stéphane Bordas (Cardiff University)H-Index: 65
Last. Jon Trevelyan (Durham University)H-Index: 18
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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 circ...
100 CitationsSource
#1Michael A. Scott (BYU: Brigham Young University)H-Index: 27
#2Robert Napier Simpson (Cardiff University)H-Index: 12
Last. Thomas W. Sederberg (BYU: Brigham Young University)H-Index: 49
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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 Bezier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edge...
272 CitationsSource
#1Haojie LianH-Index: 13
#2Stéphane BordasH-Index: 65
Last. Robert Napier SimpsonH-Index: 12
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For linear elastic problems, it is well-known that mesh generation dominates the total analysis time. Different types of methods have been proposed to directly or indirectly alleviate this burden associated with mesh generation. We review in this paper a subset of such methods centred on tighter coupling between computer aided design (CAD) and analysis (finite element or boundary element methods). We focus specifically on frameworks which rely on constructing a discretisation directly from the f...
10 Citations
#1H. Nguyen-Vinh (Bauhaus University, Weimar)H-Index: 2
#2Ilyani Akmar Abu Bakar (University of the Witwatersrand)H-Index: 4
Last. Timon Rabczuk (Bauhaus University, Weimar)H-Index: 101
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We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.
47 CitationsSource