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4 - Elastostatic Problems

Published online by Cambridge University Press:  14 January 2010

Yijun Liu
Affiliation:
University of Cincinnati
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Summary

The direct BIE formulation and its numerical solutions using the BEM for 2D elasticity problems were developed by Rizzo in the early 1960s and published in Ref. [4] in 1967. Following this early work, extensive research efforts were made for the development of the BIE and BEM for solving various elasticity problems (see, e.g., Refs. [24–28]). The advantages of the BEM for solving elasticity problems are the accuracy in modeling stress concentration or fracture mechanics problems and the ease in modeling complicated elastic domains such as various composite materials.

The FMM was applied to solving elasticity problems for more than a decade. For 2D elasticity problems, Greengard et al. [68, 69] developed a fast multipole formulation for solving the biharmonic equations using potential functions. Peirce and Napier [36] developed a spectral multipole approach that shares some common features with the FMMs. Richardson et al. [70] proposed a similar spectral method using both 2D conventional and traction BIEs in the regularized form. Fukui [71] and Fukui et al. [72] studied both the conventional BIE for 2D stress analysis and the HBIE for large-scale crack problems. In his work, he first applied the complex variable representation of the kernels and then used the multipole expansions in complex variables as originally used for 2D potential problems [35, 62]. Liu [73, 74] further improved Fukui's approach and proposed a new set of moments for 2D elasticity CBIEs, which yields a very compact and efficient formulation with all the translations being symmetrical regarding the two sets of moments.

Type
Chapter
Information
Fast Multipole Boundary Element Method
Theory and Applications in Engineering
, pp. 85 - 118
Publisher: Cambridge University Press
Print publication year: 2009

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  • Elastostatic Problems
  • Yijun Liu, University of Cincinnati
  • Book: Fast Multipole Boundary Element Method
  • Online publication: 14 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511605345.005
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  • Elastostatic Problems
  • Yijun Liu, University of Cincinnati
  • Book: Fast Multipole Boundary Element Method
  • Online publication: 14 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511605345.005
Available formats
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  • Elastostatic Problems
  • Yijun Liu, University of Cincinnati
  • Book: Fast Multipole Boundary Element Method
  • Online publication: 14 January 2010
  • Chapter DOI: https://doi.org/10.1017/CBO9780511605345.005
Available formats
×