The semi-analytical evaluation for nearly singular integrals in isogeometric elasticity boundary element method

Han, Zhilin; Chen, Cheng; Hu, Zongjun; Niu, Zhongrong

doi:10.1016/j.enganabound.2018.07.016

Cited by 9 publications

(1 citation statement)

References 38 publications

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“…Padhi et al [40] presented an analytical integration method for quadratic isoparametric boundary elements in which the distance function r 2 is expressed as a combination of polynomials a + bξ + cξ 2 + dξ 3 + eξ 4 . Several semi-analytical or analytical methods have been used for elasticity problems [41][42][43] and potential problems [44]. In references [45][46][47], the line integral approach is used to transform nearly singular integrals into a sum of weakly singular integrals and regular line integrals, and this is applied in the analysis of thin-body problems.…”

Section: Introductionmentioning

confidence: 99%

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

Gong

Trevelyan

Hattori

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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We present an isogeometric boundary element method (IGABEM) capable of delivering accurate and efficient solutions in the heat transfer analysis of 2D coated structures such as those commonly found in turbomachinery. Although we consider very thin coatings (of thickness down to 10 −7 m), they are modelled explicitly as BEM zones, and this is made possible by the development of a new integration scheme (sinh +) aimed particularly at the challenging nearly singular integrals that arise. Sinh + is a hybrid of adaptive and sinh transformation approaches, and we make further extensions to the latter to improve its robustness. The scheme is tuned to deliver results of engineering accuracy in an optimal time. The scheme is adaptable, by changing a tolerance, to enable engineers to achieve a different balance between accuracy and computational efficiency as may be required for different applications. A set of numerical examples demonstrates the ability of the scheme to produce accurate temperature distributions efficiently in the presence of very thin coatings.

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Section: Introductionmentioning

confidence: 99%

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

Gong

Trevelyan

Hattori

et al. 2019

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

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The semianalytical analysis of nearly singular integrals in 2D potential problem by isogeometric boundary element method

Han

Huang

Chen

et al. 2020

Numerical Meth Engineering

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Benefited from the accuracy improvement in modeling physical problem of complex geometry and integrating the discretization and simulation, the isogeometric analysis in boundary element method (IGABEM) has been drawn a great deal of attention. The nearly singular integrals of 2D potential problem in the IGABEM are addressed by a semianalytical scheme in the present work. We use the subtraction technique to separate the integrals to singular and nonsingular parts, where the singular parts can be calculated by the analytical formulae derived by utilizing a series of integration by parts, while the nonsingular parts are calculated numerically with fewer quadrature points. Comparing the present semianalytical results with the ones of exact solutions, we find that the present method can obtain precise potential and flux densities of inner points much closer to the boundary without refining the elements nearby. Sufficient comparisons with other regularization schemes, such as the exponential and sinh transformation methods, are also conducted. The results in the numerical examples show the competitiveness of the present method, especially when calculating the nearly strongly and highly singular integrals during the simulation of the flux density.

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A semi-analytical treatment for nearly singular integrals arising in the isogeometric boundary element method-based solutions of 3D potential problems

Han

Pan²,

Chen³

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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The semi-analytical evaluation for nearly singular integrals in isogeometric elasticity boundary element method

Cited by 9 publications

References 38 publications

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

Hybrid nearly singular integration for isogeometric boundary element analysis of coatings and other thin 2D structures

The semianalytical analysis of nearly singular integrals in 2D potential problem by isogeometric boundary element method

A semi-analytical treatment for nearly singular integrals arising in the isogeometric boundary element method-based solutions of 3D potential problems

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