A simple approach to the numerical simulation with trimmed CAD surfaces

Beer, Gernot; Marussig, Benjamin; Zechner, Jürgen

doi:10.1016/j.cma.2014.12.010

Cited by 38 publications

(35 citation statements)

References 7 publications

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“…For this we propose to use a mapping method introduced recently for trimmed surfaces in [9,3]. This means that the subdomain is defined by two NURBS curves and a linear interpolation between them.…”

Section: Geometry Definition For Inclusionsmentioning

confidence: 99%

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Advanced Boundary Element analysis of geotechnical problems with geological inclusions

Beer

Duenser

2016

Computers and Geotechnics

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Section: Geometry Definition For Inclusionsmentioning

confidence: 99%

“…As in the majority of previous work on the isogeometric BEM [4][5][6][7][8][9][10] we use the collocation method, i.e. we write the integral equations for a finite number, N, of source or collocation points y n :…”

Section: The Bem With Volume Effectsmentioning

confidence: 99%

Advanced Boundary Element analysis of geotechnical problems with geological inclusions

Beer

Duenser

2016

Computers and Geotechnics

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“…IGABEM has thus been subsequently extended to many fields [68][69][70][71]. PU enriched IGABEM was later proposed in [72,73] and trimmed NURBS approaches were presented in [74,75]. Accelerated solutions were proposed in [42] and Galerkin version of IGABEM in [76,77] etc.…”

Section: Dealing With Component Complexitymentioning

confidence: 99%

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Peng

Atroshchenko

Kerfriden

et al. 2017

Computer Methods in Applied Mechanics and Engineering

194

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Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

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“…Secondly, the trimmed parameter space has to be stabilized, because basis functions with small support occur which may lead to ill-conditioned system matrices. Several different approaches [15][16][17][18][19][20] have been proposed to address the former issue. However, the latter has hardly been considered in the literature so far.…”

Section: Stable Basis For Trimmed Geometriesmentioning

confidence: 99%

Integration of Design and Analysis Through Boundary Integral Equations

Marussig

Zechner

Beer

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The direct integration of Computer Aided Geometric Design (CAGD) models into a numerical simulation improves the accuracy of the geometrical representation of the problem as well as the efficiency of the overall analysis process.In this work, the complementary features of isogeometric analysis and boundary integral equations are combined to obtain a coalescence of design and analysis which is based on a boundary-only discretization. Following the isogeometric concept, the functions used by CAGD are employed for the simulation. An independent field approximation is applied to obtain a more flexible and efficient formulation. In addition, a procedure is presented which allows a stable analysis of trimmed geometries and a straightforward positioning of collocation points.Several numerical examples demonstrate the characteristics and benefits of the proposed approach. In particular, the independent field approximation improves the computational efficiency and reduces the storage requirements without any loss of accuracy. The proposed methodology permits a seamless integration of the most common design models into an analysis of linear elasticity problems. 6526Benjamin Marussig, Jürgen Zechner, Gernot Beer, and Thomas-Peter Fries INTRODUCTIONIsogeometric analysis aims to close the existing gap between the design process and analysis such that a simulation can be performed without generating a mesh. Consequently, the accuracy and efficiency of the overall simulation process is improved, since meshing is timeconsuming [1, 2] and introduces additional (geometrical) approximation errors. In addition, the basis functions used by design models, i.e. NURBS, provide further benefits such as high continuity [3,4].However, during the last years, it has become clear that a true integration of design and analysis is far from trivial due to several reasons: first of all, most engineering design models are based on a boundary representation (B-Rep) rather than a volume description. Secondly, three dimensional B-Rep models are usually defined by a non-conforming partition of NURBS surfaces, i.e. their mathematical parametrizations have no explicit relation to each other. Thirdly, each boundary surface is based on a tensor product structure which is a very efficient representation but has limitations due to its four sided nature. As a result, almost all NURBS based design models use trimming procedures to increase the flexibility of tensor product surfaces. This means that only a certain area of a surface is visualized while the underlying mathematical parametrization remains unchanged.In this work, a coherent framework is presented which allows a seamless integration of trimmed NURBS models into an analysis. In general, the governing equations of the problem are expressed by means of boundary integral equations which are discretized by a numerical approximation method. Here, the boundary element method (BEM) is used since it is the most versatile approach. However, it should be pointed out that other schemes like the Nyst...

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A simple approach to the numerical simulation with trimmed CAD surfaces

Cited by 38 publications

References 7 publications

Advanced Boundary Element analysis of geotechnical problems with geological inclusions

Advanced Boundary Element analysis of geotechnical problems with geological inclusions

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Integration of Design and Analysis Through Boundary Integral Equations

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