A novel method for solving the displacement and stress fields of an infinite domain with circular holes and/or inclusions subject to a screw dislocation

Chen, Jeng‐Tzong; Chou, K. H.; Lee, Y. T.

doi:10.1007/s00707-010-0404-8

Cited by 12 publications

(16 citation statements)

References 18 publications

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“…5. Chen et al [16] had used the Trefftz methods by using degenerate kernels and Fourier series to formulate the angular-type fundamental solution and then to successfully solve an infinite domain with circular holes and/or inclusions subject to a screw dislocation. However in this paper we do not need the degenerate form of the fundamental solution and we can solve the problem in Cartesian coordinate system with utilizing the angular basis functions.…”

Section: The Methods Of Angular Basis Functions (Abf)mentioning

confidence: 99%

Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Young

Huang

et al. 2015

Engineering Analysis with Boundary Elements

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Section: The Methods Of Angular Basis Functions (Abf)mentioning

confidence: 99%

Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Young

Huang

et al. 2015

Engineering Analysis with Boundary Elements

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“…It is well known that the real and the imaginary parts of any analytical complex function are harmonic. Then the functions r λ cos λθ and r λ sin λθ, λ ∈ ℝ are harmonic from z λ , where z ¼ (x+iy) (Chen et al, 2010;Li and Lu, 2000). Due to the fact that Laplace equation is linear, any linear combinations of these functions can satisfy the Laplace equation.…”

Section: Extending the Ebf Methodsmentioning

confidence: 99%

“…As a result, this treatment conforms to incorporating the form of singularity thoroughly. Examples of such treatment can be found in different studies (Chen et al, 2010;Li et al, 1987Li et al, , 2004Li et al, , 2006Li et al, , 2007Lu et al, 2004;Lu and Li, 2005;Poullikkas et al, 1998;Xanthis et al, 1981).…”

Section: Ec 322mentioning

confidence: 99%

Extending the method of exponential basis functions to problems with singularities

Mossaiby

Bazrpach

Shojaei

2015

Engineering Computations

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Purpose -The purpose of this paper is to aim at extending the method of exponential basis functions (EBF) to solve a class of problems with singularities. Design/methodology/approach -In the procedure of EBF a summation of EBF satisfying the governing differential equation with unknown constant coefficients is considered for the solution. These coefficients are determined by the satisfaction of prescribed boundary conditions through a collocation approach. The applied basis functions are available in the case of linear partial differential equations (PDEs) with constant coefficients. Moreover, the method contributes to yield highly accurate results with ultra convergence rates for problems with smooth solution. This leads EBF to offer many advantages for a variety of engineering problems. However, owing to the global and smooth nature of the bases, the performance of EBF deteriorates in problems with singularities. In the present study, some exponential-like influence functions are developed, and a few of them are added to original bases. Findings -The new bases are capable of forming the constitutive terms of the asymptotic solution near the singularity points and alleviate the aforementioned limitation. The appealing feature of this method is that all the advantages of EBF such as its simplicity and efficiency are completely preserved. Research limitations/implications -In its current form, EBF can only solve PDEs with constant coefficients. Originality/value -Application of the method to some benchmark problems demonstrates its robustness over some other boundary approximation methods. This research may pave the road for future investigations corresponding to a wide range of practical engineering problems.

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“…Shells and plates with holes and through cracks of various types were investigated in [1,2,[6][7][8][9][10][11]13]. For the solution of the three-dimensional problem of surface cracks in the plate, Rice and Levy [14] proposed an approximate approach, namely, the so-called line-spring model, which enables one to consider the problem in the two-dimensional statement.…”

Section: Introductionmentioning

confidence: 99%

Mutual Influence of Collinear Surface Cracks and a Circular Hole in the Isotropic Plate

Dovbnya

Krupko

2014

J Math Sci

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We study the mutual influence of collinear surface cracks and a circular hole on the stress state of an isotropic plate. To solve this problem, we use the method of boundary integral equations and the linespring model. The obtained system of singular integral equations is solved numerically by the method of mechanical quadratures. We also study the influence of various parameters on the concentration of stress-strain state in the plate.

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A novel method for solving the displacement and stress fields of an infinite domain with circular holes and/or inclusions subject to a screw dislocation

Cited by 12 publications

References 18 publications

Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Angular basis functions formulation for 2D potential flows with non-smooth boundaries

Extending the method of exponential basis functions to problems with singularities

Mutual Influence of Collinear Surface Cracks and a Circular Hole in the Isotropic Plate

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