A fast multipole boundary element method based on higher order elements for analyzing 2-D elastostatic problems. (1st September 2021)

• Record Type: Journal Article
• Authors: Bin, Hu; Zhongrong, Niu; Cong, Li; Zongjun, Hu
• Is Part Of: Engineering analysis with boundary elements. Volume 130(2021)
• Page Start: 417
• Page End: 428
• Publication Date: 2021-09-01
• Subjects: 2-D elasticity -- BEM -- Fast multipole -- Higher order element -- Nearly singular integral; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.06.001
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: A new fast multipole boundary element method (FM-BEM) is proposed to analyze 2-D elastostatic problems by using linear and three-node quadratic elements. The use of higher-order elements in BEM analysis results in more complex forms of the integrands, in which the direct Gaussian quadrature is difficult to calculate the singular and nearly singular integrals. Herein, the complex notation is first introduced to simplify all integral formulations (including the near-field integrals) in FM-BEM for 2-D elasticity. In direct evaluation of the near-field integrals, the nearly singular integrals on linear elements are calculated by the analytic scheme, and those on quadratic elements are evaluated by a robust semi-analytical algorithm. Numerical examples show that the present method possesses higher accuracy than the FM-BEM with constant elements. The computed efficiency of FM-BEM with higher order elements for analyzing large scale problems is still O ( N ), where N is the number of linear system of equations. In particular, the proposed FM-BEM is available for solving thin structures.