Application of the p-version FEM to stress singularity field problems

Hideki Kumamoto, Takao Yoshikawa, Seiichi Yamaji

Research output: Contribution to journalArticlepeer-review


Two types of p-version finite elements were developed, which enable precise analyses of hot spot stress at a welded zone and of the stress intensity factor at a root gap by fairly coarse meshing. The stress singularity exists at the crack tip and the weld toe. Stress singularities are expressed by the term of -1/2 power of distance r from the singular point for the crack tip, and of -1/3 power for the weld toe. Displacement is expressed by 1/2 power and 2/3 power of r for the respective cases. For those displacement expressions, 2 types of polynomial function elements were developed. Their transformations from natural coordinates to actual coordinates are biased toward the singular points. To verify the performance of the elements, 2 examples were demonstrated. The first is a 2-edged long plate with a perpendicular crack on one edge, under uniaxial uniform tension at the far ends. The stress intensity factor was calculated by just 2 elements through the plate width, and compared with the conventional reference. The second example is a T-joint with fillet welding under uniaxial uniform tension at the 2 far ends of the flat plate. Hot spot stress at the welded zone was calculated with only 2 elements through the thickness. The result was compared with that by BEM with a very fine mesh. Good agreement between the results obtained by the elements and reference solutions showed that the elements could provide high precision for the welded zone. This fact implies that the newly developed polynomial elements could reduce meshing labor.

Original languageEnglish
Pages (from-to)133-138
Number of pages6
JournalInternational Journal of Offshore and Polar Engineering
Issue number2
Publication statusPublished - Jun 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Ocean Engineering
  • Mechanical Engineering


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