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# Interpolating Isogeometric Boundary Node Method and Isogeometric Boundary Element Method Based on Parameter Space

Hongyin Yang1,2, Jiwei Zhong1,*, Ying Wang3, Xingquan Chen2, Xiaoya Bian2

1 State Key Laboratory for Health and Safety of Bridge Structures, Wuhan, 430034, China
2 School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan, 430074, China
3 Wuhan Airport Economic Zone Construction Investment and Development Group Co., Ltd., Wuhan, 430000, China

* Corresponding Author: Jiwei Zhong. Email:

(This article belongs to this Special Issue: Recent Developments of Isogeometric Analysis and its Applications in Structural Optimization)

Computer Modeling in Engineering & Sciences 2020, 124(3), 807-824. https://doi.org/10.32604/cmes.2020.010936

## Abstract

In this paper, general interpolating isogeometric boundary node method (IIBNM) and isogeometric boundary element method (IBEM) based on parameter space are proposed for 2D elasticity problems. In both methods, the integral cells and elements are defined in parameter space, which can reproduce the geometry exactly at all the stages. In IIBNM, the improved interpolating moving leastsquare method (IIMLS) is applied for field approximation and the shape functions have the delta function property. The Lagrangian basis functions are used for field approximation in IBEM. Thus, the boundary conditions can be imposed directly in both methods. The shape functions are defined in 1D parameter space and no curve length needs to be computed. Besides, most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly. Numerical examples have demonstrated the accuracy of the proposed methods.

## Keywords

Yang, H., Zhong, J., Wang, Y., Chen, X., Bian, X. (2020). Interpolating Isogeometric Boundary Node Method and Isogeometric Boundary Element Method Based on Parameter Space. CMES-Computer Modeling in Engineering & Sciences, 124(3), 807–824.

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