Crack analysis using an enriched MFS domain decomposition technique

Alves, Carlos J.S.; Leitão, Vitor M.A.

doi:10.1016/j.enganabound.2005.08.012

Cited by 46 publications

(15 citation statements)

References 20 publications

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“…Mathematically, Equation (18) can be arbitrarily close to the solutions of Equation (1) if the source points are sufficiently dense. Numerically, the boundary conditions in Equation (2) should be properly enforced to determine the finite unknown intensities…”

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confidence: 98%

“…It is easy to verify that Equation (18) satisfies the governing equations (1) analytically. Mathematically, Equation (18) can be arbitrarily close to the solutions of Equation (1) if the source points are sufficiently dense.…”

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confidence: 99%

“…In this situation, Karageorghis [16] and Poullikkas and Karageorghis [17] incorporated the local singular solutions with the MFS formulation to improve the numerical accuracy. This combination is called the enriched MFS in the literature [18]. When the enriched MFS is applied to Stokes flows, the famous Goodier-Tayor vortex [19,20] should be incorporated with the fundamental solution.…”

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A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

Tsai

Hsu

2011

Numerical Methods in Fluids

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SUMMARYThis paper describes the formulations of the method of fundamental solutions (MFS), which is a famous meshless numerical method representing a sought solution by a series of fundamental solutions to solve slow mixed convections in containers with discontinuous boundary data. In the derivations, the fundamental solutions were obtained by using the Hörmander operator decomposition technique. All the velocities, temperatures, pressures, stresses and thermal fluxes corresponding to the fundamental solutions were addressed explicitly in tensor forms. Although the MFS is highly accurate for smooth boundary data, its convergence becomes poor when it is applied to problems with discontinuous boundary data. To compensate for this drawback, we enriched the MFS by adding the local discontinuous solutions to the series of fundamental solutions. This enriched MFS was applied to solve the benchmark problems of a lid-driven cavity and natural convection in rectangular containers. In addition, the numerical solutions were compared with the analytical solutions. Then, the meshless numerical method was further utilized to solve mixed convections in a triangular cavity and a cavity with a cosine-shaped bottom. These numerical results demonstrated the applicability of the enriched MFS to two-dimensional mixed convections in containers with discontinuous boundary data.

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A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

Tsai

Hsu

2011

Numerical Methods in Fluids

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“…It also involves addition of Ns singular terms as functions of the analytical solution (cf. Alves and Leitão, 2006) centered at the crack tip . Taking 1 (i.e.…”

Section: E-mfs Formulationmentioning

confidence: 99%

“…A number of studies on the applications of MFS to singular problems can be found in the literature (Johnston et al, 1987;Karageorghis, 1992;Poullikkas, 1998). Based on the domain decomposition technique, Alves and Leitão (2006) applied an enriched MFS to the torsion of cracked components -another form of mode III cracks. This later work demonstrates the inadequacy of the conventional/standard MFS technique to capture the singularity at the crack tip, and addressed the shortcoming by adding extra term(s) to the conventional MFS formulation.…”

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Relative Performance of Three Mesh-Reduction Methods in Predicting Mode III Crack-Tip Singularity

Mukhtar

2017

Lat. Am. j. solids struct.

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Due to their robustness in handling the inherent singularity difficulties associated with crack analysis, mesh-reduction methods present an avalanche of formulations in the literature which, sometimes, entails modifications to their conventional/standard forms for better results. Although such formulations provide a pool of alternative choices to the analyst, increase in their number requires some relative assessment between them in order to guarantee optimum choice of analysis tool. The present study assesses the applicability and relative performance of three such mesh-reduction methods, namely the radial basis function (RBF) method, the boundary element method (BEM), and the method of fundamental solution (MFS) for mode III crack analysis. In order to have a common ground for performance comparison, these methods are, first, tested in their most basic forms and simplest conventional formulations possible. Failure of some of them to provide reliable results calls for some enrichments. Yet, unless where necessary, efforts are made to ensure that unnecessary computationally expensive formulations are avoided. Consequently, the BEM formulation is not altered in any way, and modifications to both the RBF and MFS are limited to enrichment by the addition of, at most, one singular term and/or the domain-decomposition technique. Verification is achieved using the literature results and/or those obtained by FEM in this study. Summary of the relative advantages and limitations of the methods for mode III crack analysis is given to serve as a yard-stick based on which the choice of one over the others may be influenced.

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Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transfer

Tadeu

Simões

2010

Numerical Meth Engineering

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SUMMARYThe coupling between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS) is proposed for the transient analysis of conduction heat transfer in the presence of inclusions, thereby overcoming the limitations posed by each method. The full domain is divided into sub-domains, which are modeled using the BEM/TBEM and the MFS, and the coupling of the sub-domains is achieved by imposing the required boundary conditions.The accuracy of the proposed algorithms, using different combinations of BEM/TBEM and MFS formulations, is checked by comparing the resulting solutions against referenced solutions.The applicability of the proposed methodology is shown by simulating the thermal behavior of a solid ring incorporating a crack or a thin inclusion in its wall. The crack is assumed to have null thickness and does not allow diffusion of energy; hence, the heat fluxes are null along its boundary. The thin inclusion is modeled as filled with thermal insulating material.

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Crack analysis using an enriched MFS domain decomposition technique

Cited by 46 publications

References 20 publications

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

Relative Performance of Three Mesh-Reduction Methods in Predicting Mode III Crack-Tip Singularity

Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transfer

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