Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

Mittelstedt, Christian; Becker, Wilfried

doi:10.1016/j.ijsolstr.2005.05.059

Cited by 35 publications

(20 citation statements)

References 113 publications

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“…It was shown analytically that the asymptotic solutions obtained for sharp V-notches were also closely linked to the non-singular field of blunt notches (Lazzarin and Tovo, 1996;Filippi et al, 2002). Reliable numerical methods and procedures for the evaluation of the notch stress intensities factors have been developed (e.g., Ghahremani, 1991;Lee and Barber, 2006;Mittelstedt and Becker, 2006). In addition, several asymptotic methods for failure and durability assessment have been suggested based on various characteristics of the asymptotic stress field, such as the average stress or strain over a characteristic volume encapsulating the notch root, energy density, critical distances and energy release rates.…”

Section: In-plane Singularitiesmentioning

confidence: 99%

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

Kotousov

2010

International Journal of Solids and Structures

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Keywords:Effect of plate thickness Plain problems of elasticity Stress singularity Asymptotic methods of fracture assessment Linear-elastic fracture mechanics Notch stress intensity factor a b s t r a c t Notched plates are often found in various applications ranging from microelectronic devices to largescale civil structures. Stress analysis of plate components wherein the loading is uniformly distributed over the thickness, parallel to the plane of the plate, is normally based on plane stress or plane strain assumptions. Three-dimensional effects, such as the influence of the plate thickness on stress components, are largely ignored or considered as negligible for all practical purposes.This paper summarizes recent theoretical and numerical studies and discusses some important features of the three-dimensional singular solutions for sharp notches obtained within linear elasticity. Taking into account dimensionless considerations, the relationships between the intensities of the singular stress states corresponding to the three-dimensional linear elastic solutions and the plate thickness are established. The obtained relationships have many intriguing implications for the failure assessment of notched plates made of sufficiently brittle material. For example, based on a similar argument to the one used in classical linear-elastic fracture mechanics, it can be shown that a sufficiently thick plate with a sharp re-entrant corner should have virtually zero strength when subjected to antisymmetric (or mixed mode) loading. The theoretical conclusions drawn in this paper have direct applications to fracture testing and fracture assessment of plate components, and they set new goals for further experimental studies.

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Section: In-plane Singularitiesmentioning

confidence: 99%

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

Kotousov

2010

International Journal of Solids and Structures

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“…Recently, new finite element and boundary finite-element procedures have been developed. These procedures are able to determine for special geometries, such as a cylindrical or spherical sector, the local singular behaviour with a very high accuracy (Song and Wolf, 2002;Mittelstedt and Becker, 2006).…”

Section: Introductionmentioning

confidence: 99%

Fracture in plates of finite thickness

Kotousov

2007

International Journal of Solids and Structures

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Application of the plane theory of elasticity to planar crack or angular corner geometries leads to the concept of stress singularity and stress intensity factor, which are the cornerstone of contemporary fracture mechanics. However, the stress state near an actual crack tip or corner vertex is always three-dimensional, and the meaning of the results obtained within the plane theory of elasticity and their relation to the actual 3D problems is still not fully understood. In particular, it is not clear whether the same stress field as found from the well-known 2D solutions of the theory of elasticity do describe the corresponding stress components in a plate made of a sufficiently brittle material and subjected to in-plane loading, and what effect the plate thickness has. In the present study we adopt, so called, first order plate theory to attempt to answer these questions. New features of the elastic solutions obtained within this theory are discussed and compared with 2D analytical results and experimental studies as well as with 3D numerical simulations.

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“…They are more convenient because they better conform to the analytical field (26)(27)(28) but are still equivalent to Fleming's approach [22]. Table 2 shows the analytical coefficient relations and the results obained numerically for a material with a Poisson's ratio ν = 0.3.…”

Section: Crack In Isotropic Homogeneous Continuum (Benchmark Example)mentioning

confidence: 99%

“…[40,42,15,30,34,43]) and 3D applications (e.g. [5,32,24,13,31,9,20,26,18]). The FEM eigenanalysis is based on the approximation of the displacements by a separation of variables representation with FE-shape functions in the circumferential direction, i.e.…”

Section: Introductionmentioning

confidence: 99%

The Use of Enriched Base Functions in the Three-Dimensional Scaled Boundary Finite Element Method

Hell¹,

Becker²

2016

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

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Abstract. The Scaled Boundary Finite Element Method (SBFEM) is a semi-analytical method which combines the advantages of the Boundary Element Method (BEM) and the Finite Element Method (FEM). Like in the BEM, only the boundary needs to be discretized. On the other hand, the SBFEM is based on the virtual work principle and does not need any fundamental solutions. If the scalability condition is fulfilled, a separation of variables representation can be employed leading to a quadratic eigenvalue problem and a linear equation system which can be solved by standard methods. The SBFEM has proven its high efficiency and accuracy in the presence of stress singularities, especially in 2D fracture mechanics when the singularity is entirely located within the considered domain.However, in 3D elasticity problems, there can also be singularities on the discretized boundary itself. Then, the SBFEM suffers from drawbacks also well known from the standard FEM, i.e. moderate accuracy and bad convergence. To overcome these deficiencies in such 3D cases, we propose the enrichment of the standard separation of variables representation with analytical fields which are known to exactly fulfill the local boundary conditions:The examples of a single plane crack and two perpendicularly meeting cracks in an isotropic continuum are considered. It is demonstrated that the method's original excellent accuracy and convergence are regained, at a minimum cost of additional degrees of freedom (DOF). The normalized errors in the solution of the quadratic eigenvalue problem already become negligibly small for very coarse boundary meshes. The obtained convergence orders are often optimal and sometimes even superconvergence is observed.

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Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

Cited by 35 publications

References 113 publications

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

Effect of plate thickness on stress state at sharp notches and the strength paradox of thick plates

Fracture in plates of finite thickness

The Use of Enriched Base Functions in the Three-Dimensional Scaled Boundary Finite Element Method

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