Computations of Singular Stresses Along Three-Dimensional Corner Fronts by a Super Singular Element Method

Ping, Xuecheng; Chen, Mengcheng; Zhu, Wei; Xiao, Yihua; Wu, Weixing

doi:10.1142/s0219876217500657

Cited by 5 publications

(10 citation statements)

References 52 publications

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“… T u and T ε are displacement and strain transformation matrix, respectively. It should be pointed out that strain transformation matrix rather than stress transformation matrix is used in Equation ; this treatment method is different from that of Ping et al Since U and E in Equations and have been solved by the finite element eigenanalysis method, only the unknown stress intensity parameters, β , need to be solved later.…”

Section: Expressions Of the Singular Stress Fields Near A Circumferenmentioning

confidence: 99%

“…The finite element formulation of the SCFE can be derived from Equations and and the H‐R variational functional, and the following element stiffness matrix for the SCFE is finally obtained:

K_{s} = G^{T} H^{- 1} boldG,

in which

boldH = \frac{1}{2} \int_{Γ_{normalc}} ([], {(n {boldE}_{normalc})}^{T} U_{c} + {(U_{c})}^{T} ((), boldn E_{c})) normald A,

boldG = \int_{Γ_{normalc}} {({nE}_{c})}^{T} N_{h} normald A,

U_{c} = ([], \begin{array}{c} ((), 1 - η) T_{u} boldU / 2 & ((), 1 + η) T_{u} boldU / 2 \end{array})

E_{c} = ([], \begin{array}{c} ((), 1 - η) {DT}_{ε} boldE / 2 & ((), 1 + η) {DT}_{ε} boldE / 2 \end{array})

in which Γ c is a combination of all Γ c i , n contains the unit normal vectors, N h is a matrix of interpolation function, and the natural coordinate η represents the location of a normal plane along the corner front. The interested readers can refer to Ping et al…”

Section: Formulation Of a Mafem For The Circumferential Corner Problemmentioning

confidence: 99%

“…Once the displacement u i ( x , y , z ) is solved from Equation , the stress intensity parameter

β_{c} = {[\begin{matrix} center \\ {boldβ}_{1}^{normalT} & {boldβ}_{2}^{normalT} \end{matrix}]}^{T}

can be obtained from the following expression:

β_{c} = H^{- 1} {Gu}_{i} ((), x, y, z),

in which β 1 and β 2 are stress intensity parameters at two end faces of a SCFE . Compared with conventional FEMs with extremely refined meshes near the corner front, it is no need to use a large number of nodes within the SCFE domain in our current method.…”

Section: Formulation Of a Mafem For The Circumferential Corner Problemmentioning

confidence: 99%

“…One of the SCFEs is plotted in Figure 2, the element is l 1 in width, l 2 in height, and l f in thickness. The finite element formulation of the SCFE can be derived from Equations (9) and (10) and the H-R variational functional, 39,40 and the following element stiffness matrix for the SCFE is finally obtained:…”

Section: Formulation Of a Mafem For The Circumferential Corner Problemmentioning

confidence: 99%

“…Until now, no other else solved GSIFs along 3D corner fronts using 3D singular element model expect the authors. At current stage, the singular element method of Ping and Chen is limited to a straight corner front, a new singular element model for finite element analysis of circumferential corner problems still need to be established.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Intensity of stress singularity for the circumferential V‐shape corner front of a three‐dimensional diamond‐like defect

Ping

Zhang

Guo

et al. 2020

Fatigue Fract Eng Mat Struct

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Three‐dimensional diamond‐like defects with circumferential V‐shape corner fronts are often contained in engineering materials. In this paper, generalized stress intensity factors are calculated for this type of defect using a modified advanced finite element method. A super corner front element model in the global coordinates is established to capture the stress singularities along the circumferential corner front. Three‐dimensional numerical series eigen‐solutions in the element have been transformed from asymptotic expressions in the local curvilinear coordinates. The element is suitable for a sharp V‐shape corner with arbitrary opening and inclination angle. Singular stress fields near various shapes of diamond‐like defects are systematically investigated. The interaction of an embedded defect with free surface or another identical defect is also investigated. The numerical results can be used as stress intensity parameters to predict fatigue strength at circumferential corner front of a diamond‐like defect.

show abstract

Section: Expressions Of the Singular Stress Fields Near A Circumferenmentioning

confidence: 99%

“…The finite element formulation of the SCFE can be derived from Equations and and the H‐R variational functional, and the following element stiffness matrix for the SCFE is finally obtained:

K_{s} = G^{T} H^{- 1} boldG,

in which

boldH = \frac{1}{2} \int_{Γ_{normalc}} ([], {(n {boldE}_{normalc})}^{T} U_{c} + {(U_{c})}^{T} ((), boldn E_{c})) normald A,

boldG = \int_{Γ_{normalc}} {({nE}_{c})}^{T} N_{h} normald A,

U_{c} = ([], \begin{array}{c} ((), 1 - η) T_{u} boldU / 2 & ((), 1 + η) T_{u} boldU / 2 \end{array})

E_{c} = ([], \begin{array}{c} ((), 1 - η) {DT}_{ε} boldE / 2 & ((), 1 + η) {DT}_{ε} boldE / 2 \end{array})

Section: Formulation Of a Mafem For The Circumferential Corner Problemmentioning

confidence: 99%

“…Once the displacement u i ( x , y , z ) is solved from Equation , the stress intensity parameter

β_{c} = {[\begin{matrix} center \\ {boldβ}_{1}^{normalT} & {boldβ}_{2}^{normalT} \end{matrix}]}^{T}

can be obtained from the following expression:

β_{c} = H^{- 1} {Gu}_{i} ((), x, y, z),

Section: Formulation Of a Mafem For The Circumferential Corner Problemmentioning

confidence: 99%

Section: Formulation Of a Mafem For The Circumferential Corner Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Intensity of stress singularity for the circumferential V‐shape corner front of a three‐dimensional diamond‐like defect

Ping

Zhang

Guo

et al. 2020

Fatigue Fract Eng Mat Struct

View full text Add to dashboard Cite

show abstract

A new computational approach for three-dimensional singular stress analysis of interface voids

et al. 2020

View full text Add to dashboard Cite

On the three-dimensional singular stress field near the corner front of revolution-shaped inclusions

et al. 2021

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Computations of Singular Stresses Along Three-Dimensional Corner Fronts by a Super Singular Element Method

Cited by 5 publications

References 52 publications

Intensity of stress singularity for the circumferential V‐shape corner front of a three‐dimensional diamond‐like defect

Intensity of stress singularity for the circumferential V‐shape corner front of a three‐dimensional diamond‐like defect

A new computational approach for three-dimensional singular stress analysis of interface voids

On the three-dimensional singular stress field near the corner front of revolution-shaped inclusions

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