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

Gong, Y; Dong, C; Qin, F; Hattori, G; Trevelyan, J

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


Authors

Y Gong

C Dong

F Qin

G Hattori



Abstract

The isogeometric boundary element method (IGABEM) has great potential for the simulation of elasticity problems because of its exact geometric representation and good approximation properties. These advantages can be extended to thin structures, including coatings, but the development of an accurate and efficient method to deal with the large number of nearly singular integrals existing in the IGABEM presents a great challenge for very thin sections. In this paper, we propose a new sinh scheme for weakly, strongly and hyper near-singular integrals arising in 3D IGABEM for thermoelastic problems, based on the sinh transformation method and adaptive integral method. The presented scheme is efficient, since it combines the advantages of both methods: (1) when the thickness of coatings/thin structures is moderately small, an accurate and efficient integral result will be obtained by the adaptive integral method; (2) when is very small, the nearly singular integrals are computed by the sinh scheme efficiently. With the introduction of NURBS in IGABEM, truncation errors arising in the Taylor expansion cannot be ignored. Based on the values of these errors, the computed knot spans are further divided into several sub-knot spans and different methods will be used to evaluate the integral over each sub-knot span in the new scheme. In addition, based on the analytical extension of the NURBS surface, an adaptation of the sinh transformation method is proposed which can evaluate the near-singular integrals accurately for cases in which the projection point lies outside of the considered knot span. Several numerical examples are presented to validate the accuracy and efficiency of the 3D IGABEM based on the sinh scheme in the analysis of thermoelastic problems.

Citation

Gong, Y., Dong, C., Qin, F., Hattori, G., & Trevelyan, J. (2020). 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, Article 113099. https://doi.org/10.1016/j.cma.2020.113099

Journal Article Type Article
Acceptance Date Apr 24, 2020
Online Publication Date May 19, 2020
Publication Date Aug 1, 2020
Deposit Date Apr 27, 2020
Publicly Available Date Mar 28, 2024
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 367
Article Number 113099
DOI https://doi.org/10.1016/j.cma.2020.113099

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