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Employing Enriched Meshfree MLSRK Method to Analyze 2D Linear Elastic Fracture Mechanics Problems

Namakian, Reza | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42320 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shoja, Hossein
  7. Abstract:
  8. The so-called moving least square reproducing kernel method (MLSRKM), which is a meshfree Galerkin method, has two special properties in comparison with its prior version, say moving least square method (MLSM): (i) stability in preserving completeness conditions to the desired order for a discrete reproducing formula due to implementation of shifted and scaled basis, (ii) use of more accurate quadrature weights in a discrete reproducing form, especially along boundaries. However, because of employing shifted basis in MLSRKM, some of enrichment techniques, specifically in the context of linear elastic fracture mechanics (LEFM) problems, cannot be applied to this method. Therefore, we are going through to introduce a new enrichment technique called fully enriched window or weight functions (FEWFs) to analyze 2D LEFM problems such that this technique is applicable to all kernel-based methods. Moreover, it will be demonstrated that the proposed technique compared to its existing version not only yields more accurate results in estimating stress intensity factors (SIFs) and crack mouth opening displacement (CMOD) but also preserves path-independency property of calculated SIFs via J¬-integral. It will be also shown that FEWFs technique produces very accurate results and can be regarded as a truly efficient one compared to the other enrichment techniques. Furthermore, for the case where the crack line is not aligned with the quadrature cells, a simple and convenient numerical integration technique is suggested
  9. Keywords:
  10. Linear Elastic Fracture Mechanics ; Numerical Integration ; J-Integral ; Stress Intensity Factor ; Crack Opening Displacement ; Fully Enriched Window Functions (FEWFs)Technique ; Moving Least Square Reproducing Kernel Particle Method (MLSRKPM)

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