Application of the p-version FEM to Stress Singularity Field Problems

Two types of p-version finite elements, which enable precise analyses of hot spot stress at welded zone and of stress intensity factor at root gap by fairly coarse, meshing, were developed. The stress singularity exists at the crack tip and the weld toe. The stress singularities are expressed by a 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, the two types of polynomial function elements were developed. Their transformations from natural coordinates to global coordinates are biased toward the singular points. To verify the performance of the elements, two examples were demonstrated. The first example is a two-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 two 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 far two ends of the flat plate. Hot spot stress at the welded zone was calculated with only two 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.