Computation of three-dimensional fracture parameters at interface cracks and notches by the scaled boundary finite element method

Saputra, Albert A.; Birk, Carolin; Song, Chongmin

doi:10.1016/j.engfracmech.2015.09.006

Cited by 61 publications

(36 citation statements)

References 84 publications

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“…It has been demonstrated in these works that the high flexibility of the shape of the polygonal elements significantly simplifies the meshing process. The SBFEM has been also applied for 3D fracture problems in [57][58][59].The main objective of this paper is to present a robust, automatic and simple approach for imagebased analysis by combining the SBFEM with a quadtree or an octree mesh generation algorithm for 2D or 3D images, respectively. The quadtree or octree structure can be used to model the geometrical features of different scales efficiently.…”

mentioning

confidence: 99%

Automatic image‐based stress analysis by the scaled boundary finite element method

Saputra

Talebi

Tran

et al. 2016

Int. J. Numer. Meth. Engng

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133

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SUMMARYDigital imaging technologies such as X-ray scans and ultrasound provide a convenient and non-invasive way to capture high-resolution images. The colour intensity of digital images provides information on the geometrical features and material distribution which can be utilised for stress analysis. The proposed approach employs an automatic and robust algorithm to generate quadtree (2D) or octree (3D) meshes from digital images. The use of polygonal elements (2D) or polyhedral elements (3D) constructed by the scaled boundary finite element method avoids the issue of hanging nodes (mesh incompatibility) commonly encountered by finite elements on quadtree or octree meshes. The computational effort is reduced by considering the small number of cell patterns occurring in a quadtree or an octree mesh. Examples with analytical solutions in 2D and 3D are provided to show the validity of the approach. Other examples including the analysis of 2D and 3D microstructures of concrete specimens as well as of a domain containing multiple spherical holes are presented to demonstrate the versatility and the simplicity of the proposed technique.

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mentioning

confidence: 99%

Automatic image‐based stress analysis by the scaled boundary finite element method

Saputra

Talebi

Tran

et al. 2016

Int. J. Numer. Meth. Engng

Self Cite

133

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“…Based on this general framework provided by differential geometry, there are two ways to derive the weak form (27) in parametric coordinates ξ and to proceed then with a discretization. We start with the strong form (17) in Cartesian coordinates x and then have the following choices:…”

Section: Equivalence Of the Two Approachesmentioning

confidence: 99%

“…and we impose homogeneous boundary conditions u = 0 on ∂Ω. The function u * obviously fulfills the boundary conditions, thus it is the unique solution to (17) with f = −∆u * . We solve (17) using different parametrizations and the known analytical solution is used to compute the numerical error, which is depicted in Fig.…”

Section: Poisson's Equation On a Unit Squarementioning

confidence: 99%

Scaled boundary parametrizations in isogeometric analysis

Arioli

Shamanskiy

Klinkel

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational domain is available. The idea goes back to the Scaled Boundary Finite Element Method (SB-FEM), which has recently been extended to IGA. We take here a different viewpoint and study these parametrizations as bivariate or trivariate B-spline functions that are directly suitable for standard Galerkin-based IGA. Our main results are first a general framework for this class of parametrizations, including aspects such as smoothness and regularity as well as generalizations to domains that are not star-shaped. Second, using the Poisson equation as example, we explain the relation between standard Galerkin-based IGA and the Scaled Boundary IGA by means of the Laplace-Beltrami operator. Further results concern the separation of integrals in both approaches and an analysis of the singularity in the scaling center. Among the computational examples we present a planar rotor geometry that stems from a screw compressor machine and compare different parametrization strategies.

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“…The displacement and stress fields are described semianalytically in domains of arbitrary geometry, so rapid convergence and highly accurate solutions can be obtained. The method has been successfully applied to perform many engineering analyses such as elastostatics, elastodynamics, fracture, unbounded media, wave propagation, diffusion, soil‐structure interaction, fluid‐structure interaction, acoustic, electrostatics, electromagnetics, thin plates, sloshing analysis, and isogeometric analysis . Saputra et al presented an automatic and efficient numerical technique to perform the image‐based elastic analysis by quadtree (2D) or octree (3D) mesh based on the SBFEM.…”

Section: Introductionmentioning

confidence: 99%

A novel scaled boundary finite element formulation with stabilization and its application to image‐based elastoplastic analysis

Song

Ooi

2018

Numerical Meth Engineering

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Summary Digital images are increasingly being used as input data for computational analyses. This study presents an efficient numerical technique to perform image‐based elastoplastic analysis of materials and structures. The quadtree decomposition algorithm is employed for image‐based mesh generation, which is fully automatic and highly efficient. The quadtree cells are modeled by scaled boundary polytope elements, which eliminate the issue of hanging nodes faced by standard finite elements. A novel, simple, and efficient scaled boundary elastoplastic formulation with stablisation is developed. In this formulation, the return‐mapping calculation is only required to be performed at a single point in a polytope element, which facilitates the computational efficiency of the elastoplastic analysis and simplicity of implementation. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed technique for performing the elastoplastic analysis of high‐resolution images.

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Computation of three-dimensional fracture parameters at interface cracks and notches by the scaled boundary finite element method

Cited by 61 publications

References 84 publications

Automatic image‐based stress analysis by the scaled boundary finite element method

Automatic image‐based stress analysis by the scaled boundary finite element method

Scaled boundary parametrizations in isogeometric analysis

A novel scaled boundary finite element formulation with stabilization and its application to image‐based elastoplastic analysis

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