The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.
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ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
September 4–7, 2007
Las Vegas, Nevada, USA
Conference Sponsors:
- Design Engineering Division and Computers and Information in Engineering Division
ISBN:
0-7918-4805-1
PROCEEDINGS PAPER
Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates
Muhammad Treifi,
Muhammad Treifi
University of Manchester, Manchester, UK
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Derek K. L. Tsang,
Derek K. L. Tsang
University of Manchester, Manchester, UK
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S. Olutunde Oyadiji
S. Olutunde Oyadiji
University of Manchester, Manchester, UK
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Muhammad Treifi
University of Manchester, Manchester, UK
Derek K. L. Tsang
University of Manchester, Manchester, UK
S. Olutunde Oyadiji
University of Manchester, Manchester, UK
Paper No:
DETC2007-35563, pp. 399-405; 7 pages
Published Online:
May 20, 2009
Citation
Treifi, M, Tsang, DKL, & Oyadiji, SO. "Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates." Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 4: ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications and the 19th Reliability, Stress Analysis, and Failure Prevention Conference. Las Vegas, Nevada, USA. September 4–7, 2007. pp. 399-405. ASME. https://doi.org/10.1115/DETC2007-35563
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