Null-field Integral Equations for Stress Field around Circular Holes under Antiplane Shear

Chen, Jeng‐Tzong; Shen, Wen-Cheng; Wu, An‐Chien

doi:10.1016/j.enganabound.2005.08.013

Cited by 49 publications

(33 citation statements)

References 12 publications

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“…where the A(x) and B(x) can be found for the Laplace [4][5][6][7][8], Helmholtz [9], biharmonic [5] and biHelmholtz operators and the superscripts " i " and " e " denote the interior ( s x ≥ ) and exterior ( s x < ) cases, respectively. To classify the interior and exterior regions, Figure 2 shows for one-, two-and three-dimensional cases.…”

Section: Expansions Of the Fundamental Solution And Boundary Densitymentioning

confidence: 99%

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Null-field integral equations and their applications

Chen¹,

Chen²

2007

WIT Transactions on Modelling and Simulation, Vol 44

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In this paper, a null-field equation approach is proposed to deal with boundary value problems containing circular boundaries. The mathematical tools, degenerate kernels and Fourier series, are utilized in the null-field integral formulation. Although we employ the null field equations, we can exactly collocate the point on the real boundary. Thus, the singularity is novelly avoided since the kernel is expressed in a degenerate form. Five gains of well-posed model, singularity free, boundary layer effect free, exponential convergence and mesh-free approach are achieved. To demonstrate the validity of the present formulation, some applications are considered: (1) torsion problem, (2) bending problem, (3) SH wave impinging successive canyons. It is found that previous results by other investigators are not consistent with ours. After comparing with other independent solutions, the accuracy and efficiency of our approach is acceptable.

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Section: Expansions Of the Fundamental Solution And Boundary Densitymentioning

confidence: 99%

“…In this paper, we review the recent development of the null-field integral equation approach [4][5][6][7][8][9] for boundary value problems (BVPs) with circular boundaries. The key idea is the expansion of kernel functions and boundary densities in the null-field integral equations.…”

Section: Introductionmentioning

confidence: 99%

Null-field integral equations and their applications

Chen¹,

Chen²

2007

WIT Transactions on Modelling and Simulation, Vol 44

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“…A dual integral formulation that has regularized the singularities for the Laplace potential problem with a corner was derived by Chen and Hong (1994) using the contour approach surrounding the singularity. Very recently, the problem of the boundary layer effect has also been investigated by Chen et al (2006aChen et al ( , 2006b, who have derived null-field integral equations for a medium containing circular cavities. By introducing the concept of degenerate kernels, Chen et al (2006a) transformed the singular integrals into series sum when the null-field point was moved to the boundary.…”

Section: Introductionmentioning

confidence: 99%

Regularization of nearly singular integrals in the boundary element analysis for interior anisotropic thermal field near the boundary

Shiah

Shih²

2007

Journal of the Chinese Institute of Engineers

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In this paper the previously developed scheme of integration by parts to treat the boundary thermal field is applied to calculate the interior thermal field. Also, the scheme is extended further to regularize the strongly singular integral appearing in the boundary integral equation for interior calculations of the heat fluxes. Moreover, the present work develops a semi-analytical integration scheme to regularize the hypersingular integral for the interior heat-flux calculations. All formulations are derived for elements of arbitrary orders with general interpolation. At the end, the veracity of the scheme is illustrated by numerical examples.

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“…Liang et al (2003Liang et al ( , 2004) discussed a series of solutions for surface motion amplification of the underground twin tunnels under P, SV waves. Chen et al (2006) presented the Null-field integral equations for stress field around circular holes under anti-plane shear waves. Zhou et al (2009) applied a semi-analytical method to discuss the dynamic response of twin-parallel elliptic tunnels embedded in an infinite poroelastic medium.…”

Section: Introductionmentioning

confidence: 99%

Dynamic interaction of twin vertically overlapping lined tunnels in an elastic half space subjected to incident plane waves

2016

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The scattering of plane harmonic P and SV waves by a pair of vertically overlapping lined tunnels buried in an elastic half space is solved using a semi-analytic indirect boundary integration equation method. Then the effect of the distance between the two tunnels, the stiffness and density of the lining material, and the incident frequency on the seismic response of the tunnels is investigated. Numerical results demonstrate that the dynamic interaction between the twin tunnels cannot be ignored and the lower tunnel has a significant shielding effect on the upper tunnel for high-frequency incident waves, resulting in great decrease of the dynamic hoop stress in the upper tunnel; for the low-frequency incident waves, in contrast, the lower tunnel can lead to amplification effect on the upper tunnel. It also reveals that the frequency-spectrum characteristics of dynamic stress of the lower tunnel are significantly different from those of the upper tunnel. In addition, for incident P waves in low-frequency region, the soft lining tunnels have significant amplification effect on the surface displacement amplitude, which is slightly larger than that of the corresponding single tunnel.

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Null-field Integral Equations for Stress Field around Circular Holes under Antiplane Shear

Cited by 49 publications

References 12 publications

Null-field integral equations and their applications

Null-field integral equations and their applications

Regularization of nearly singular integrals in the boundary element analysis for interior anisotropic thermal field near the boundary

Dynamic interaction of twin vertically overlapping lined tunnels in an elastic half space subjected to incident plane waves

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