Some Aspects of the BEM Research in China

Abstract

In this paper, a short historical review of the BEM research in China is given first. The investigation on the BEM in China was started in 1978 at the Tsinghua University, based on the pioneering work published by Frank Rizzo [F. J. Rizzo, An integral equation approach to boundary value problems of classical elastostatics, Quart. Appl. Math., 25, 83-95 (1967)] and others. During the last 25 years, we have organized six national conferences on BEM, two international conferences and eight China-Japan/Japan-China symposia on BEM. The BEM investigations in the authors' group at Tsinghua are briefly introduced next. Some representative investigations by other groups in Mainland China are also introduced. The related papers and other publications are listed in the References. Historical ReviewIn China, we started the investigation on boundary element methods in 1978 at Tsinghua University. At first, the second author, Du, introduced the related papers published by Frank Rizzo, T. A. Cruse and other BEM pioneers to the researchers in China, and suggested to them to pay attentions on the development of the boundary integral equation (BIE) method. In the authors' group, we started with the elastic stress concentration problems using boundary integral equation -boundary element method, including axi-symmetric body with symmetric and asymmetric loading, and also three-dimensional elasticity problems. Another topic is the plate bending problems, which related to higher order differential operator. At that time, the paper of Frank Rizzo published in 1967 was the first literature on BEM available to us. In the first several years, we learnt that the well-known kernel functions can be generalized by superposition, integration and differentiation to obtain some useful new kernel functions for different problems, such as the torsion of circular shaft with variable diameters, axi-symmetric problems, plate bending problems and crack problems. In 1982, we published our work at Acta Mechanica Solida Sinica in Chinese [1] , and gave a workshop to more than 100 audiences organized by the editorial board of that journal.

Recent Advances and Emerging Applications of the Boundary Element Method

“…30is the basis of the displacement finite element method [152] and this is explicitly assumed by the superscript ð Þ d attached to the stress field in Eq. (30). For brevity, the body force b i is assumed to be zero (see Ref.…”

“…The aim of the present brief review in this subsection is to sit uate the collocation BEM among several developments that are based on energy concepts, as in Eqs. (30), (31), (35), and (41). Some applications of the variationally based BEM and many in depth conceptual details are given in Refs.…”

“…Some personal accounts of the historical developments of the BIE and BEM in various places of the U.S., Europe, and China were given by Rizzo [24], Cruse [25], Watson [26], Shippy [27], Mukherjee [28], Telles [29], and Yao and Du [30] in a special issue of the Electronic Journal of Boundary Elements in 2003 [31]. A comprehensive review of the heritage and early history of the BIE and BEM was given by Cheng and Cheng in 2005 [32].…”