An enriched Scaled Boundary Finite Element Method for 3D cracks

Hell, Sascha; Becker, Wilfried

doi:10.1016/j.engfracmech.2019.04.032

Cited by 14 publications

(3 citation statements)

References 95 publications

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“…In this project, we employ the scaled boundary finite element method (SBFEM) as the basis for our analysis. The SBFEM was initially developed by Wolf and Song (1996) for the dynamic soil-structure interaction and has since evolved into a versatile solver in multiple scopes, such as elasticity and fracture mechanics (e.g., Long et al, 2014;Yang and Ooi, 2012;Hell and Becker, 2019), potential flow (Tao et al, 2007;Deeks and Cheng, 2003) and heat transfer (e.g., Bazyar and Talebi, 2015;Yu et al, 2021). In SBFEMs, solutions exhibit analytic behavior in the radial direction.…”

Section: Introductionmentioning

confidence: 99%

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

2023

Physics of Fluids

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Axisymmetric geometries, such as cylindrical elements, are widely used in offshore structures. However, the presence of sharp edges in these geometries introduces challenges in numerical simulations due to singularities. To address this issue, one possible solution is to represent the singularities using analytic eigenfunctions. This approach can provide insights into the essence of the problem and has successfully applied to two-dimensional (2D) corner problems. However, finding appropriate eigenfunctions for the three-dimensional (3D) edges remains an open challenge. This paper proposes a semi-analytic scheme for 3D axisymmetric problems utilizing a scaled boundary finite element method (SBFEM). A dimensional reduction is introduced to the 3D Laplace equation, and a 3D edge is handled on the generatrix plane while governed by a complicated equation. The algorithm for resolving the SBFEM fundamental space is improved, and the singularities are approximated using a fractional-order basis. The effectiveness of the proposed method is demonstrated through its application to solve the radiation problem of a heaving cylinder. The method accurately captures the singular velocity field at the edge tip, ensuring that the boundary condition on the body surface is strictly satisfied in the neighborhood of the singularity. Accuracy of the mean drift force is ensured by performing direct pressure integrations over the body surface using a near-field formulation, which becomes as accurate as the middle-field formulation.

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Section: Introductionmentioning

confidence: 99%

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

2023

Physics of Fluids

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“…The SBFEM has been successfully applied to various analysis types, including elastostatics [19,23,24] and dynamics [25,26]. Furthermore, it excels in modelling cracks and capturing accurate fracture parameters such as stress intensity factors [27][28][29][30][31][32]. SBFEM has also been extended to solve a wide range of problems including plate analysis [33,34], sloshing [35], electromagnetics [36], acoustics [37], elasto-plasticity [38], contact mechanics [39,40], wave propagation problems [41,42] and even multi-physics problems such as piezoelectricity [43] and fluid-structure interaction [44].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional image-based numerical homogenisation using octree meshes

Saputra

Eisenträger

Gravenkamp

et al. 2020

Computers & Structures

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“…It is well known that 2D problems can be applied in engineering as well and the results can be reliable for engineering decision. Various types of numerical methods such as Finite Element Method (FEM), Boundary Element Method (BEM), Scaled Boundary Methods (SBFEM), and mesh-less methods are commonly used in order to solve elasto-static and elasto-dynamic problems in two-dimensional problems [1][2][3] and simulating cracks and fractures in domains [4][5]. All these methods have their own advantageous and disadvantageous.…”

Section: Introductionmentioning

confidence: 99%

Solving Elasto-Static Bounded Problems with a Novel Arbitrary-Shaped Element

Khalaj-Hedayati

Khodakarami

2019

Civ Eng J

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A simple method to analysis any arbitrary domain shapes with a single element which based on Decoupled Scaled Boundary Finite Element Method is presented in this paper. The introduced element is based on boundary finite element method which helps to modelling curve and sharp boundaries with acceptable accuracy. Shape functions and mapping functions are similar to Decoupled Scaled Boundary Finite Element Method but locating center origin (LCO) is relocated in this method from corners with direct view to whole domain into shape center and formulation and behavior of the method is developed for the element. The most important advantageous of this technique is ability of solving displacement in domain by solving differential equations which causes more accurate answers in domain. We also perform well-established numerical tests and show the performance of the new element. Results shown us the accuracy and reliable answers for the introduced element. Also some benchmark examples are solved by this method and answers are compared with correct answers and plotted. High accuracy of answers with low cost of calculations and ability of the method to analysis the curve and sharp boundaries are the most important advantageous of this new element.

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An enriched Scaled Boundary Finite Element Method for 3D cracks

Cited by 14 publications

References 95 publications

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

Semi-analytic solutions to edge singularities of three-dimensional axisymmetric bodies

Three-dimensional image-based numerical homogenisation using octree meshes

Solving Elasto-Static Bounded Problems with a Novel Arbitrary-Shaped Element

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