Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures

Abstract

Hybrid nearly singular integration for three-dimensional isogeometric boundary element analysis of coatings and other thin structures.', Computer methods in applied mechanics and engineering., 367 . p. 113099.

Numerical Aspects of Isogeometric Boundary Element Methods: (Nearly) Singular Quadrature, Trimmed NURBS and Surface Crack Modeling

“…This also complicates the singular and nearly-singular behaviors in the integrand of BEM. Efforts have been made to tackle this problem [30,31]. In this work, we investigate the conformal transformation technique [29] to the improve the (hyper-)singular integration in detail, then an L − 1/5 transformation is implemented to handle nearly singular integration.…”

New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow

“…Other variable transformation considered for the approximation of weakly near singular integrals include the radial variable transformation (Hayami and Matsumoto, 1994), the distance transformation (Ma and Kamiya, 2002;Xie et al, 2013) and the sinh transformation (Johnston et al, 2007;Xie et al, 2021). The quadrature scheme presented in Gong et al (2020) combines the benefits of the sinh transformation method and adaptive methods such it is capable of integral kernels of the type 1/r, 1/r 2 and 1/r 3 on near singular elements. Many other quadrature rules for weakly singular integrals on nearly singular elements can be found in the literature as for example the parameterized Gaussian quadrature (Lutz, 1992), line integral approaches (Krishnasamy et al, 1994;Liu, 1998) and analytical (Padhi et al, 2001;Zhou et al, 2008) and semi-analytical methods (Sladek et al, 2001;Niu et al, 2005;Han et al, 2022).…”

“…The quadrature rule from Telles (1987) is combined with Gauss-Legendre quadrature for linear elastic problems considering homogeneous material (Karam and Telles, 1988;Simpson et al, 2012) and liquid inclusions (Dai et al, 2021) and for FSI problems considering Stokes Flow (Patiño and Nieto-Londoño, 2021). The adaptive integral method for near singular integrals (Gao and Davies, 2000) is used to solve Laplace's equation by isogeometric BE analysis for potential problems (Gong and Dong, 2017), thermal problems (Gong et al, 2018) and thermoelasticity problems (Gong et al, 2020), whereas the singularity subtraction method (Guiggiani et al, 1992) is applied in Jarvenpaa et al (2006) to electromagnetics and in Peng et al (2017) to fracture mechanics. Ata and Sahin (2018) consider the tanh-sinh quadrature rule (Borwein and Ye, 2006) for BE analysis of Stokes flow problems and Keuchel et al (2017) apply the sinhquadrature (Johnston et al, 2007) to nearly singular integrals in the Burton-Miller formulation of the Helmholtz equation for acoustic problems.…”

Coupling Heat Conduction and Radiation by an Isogeometric Boundary Element Method in 2-D Structures

“…Mondal and Mishra [22] combined the Boltzmann method with the finite volume method to deal with the coupled heat transfer and radiation with heat flow and temperature boundary conditions. Gu et al [23][24][25][26][27][28][29][30] studied the heat transfer of coating structure based on the isogeometric boundary element method, and they also used the isogeometric boundary element method by calculating the effective property of steady-state thermal conduction in 2D heterogeneities with a homogeneous interphase. Fu et al [31][32][33] studied the boundary collocation method for anomalous heat conduction analysis in functionally graded materials.…”