PSI - Issue 57

Inge Lotsberg et al. / Procedia Structural Integrity 57 (2024) 569–580 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Solid model with one element over main plate thickness t

Solid model with four elements over main plate thickness t

Solid model with mesh size 0.5t in stress direction and t in transverse direction Arrow to weld toe shows line for surface stress calculation

Fig. 5. Finite element model of doubling plate.

Fig. 6. Modelling of eccentric plates using shell elements.

3.2. Methods for hot spot stress derivation

The first hot spot analysis approach included in DNV-RP-C203 was by a linear extrapolation of stresses from 0.5t and 1.5t from the weld toe to the weld toe (t = plate thickness). When welds are not included in the finite element model, the extrapolation is made back to the point with change in geometry. This method is denoted Method A in DNV-RP-C203 (2019). It is recommended to use a txt mesh at the hot spot area here t is plate thickness. In the study performed by Fricke in 2001 it was found that read-out of stress at 0.5t showed smaller scatter in hot spot stress and comparable stress with Method A can be achieved by increasing the derived stress at 0.5t by a factor 1.12. This method is denoted Method B in DNV-RP-C203 (2019). Later a quadratic extrapolation method has been included in DNV-RP-C203 (2019) where stresses at 0.4t, 0.9t and 1.4t are used as input. The basis for this method is found in IIW documents; see Hobbacher (2009). This method is mainly intended to be used at connections with steep stress gradients. It is important that the read-out points are in three separate elements. All these three methods are based on calculation of surface stresses at the hot spot. When several elements are used over the plate thickness, one may alternatively perform a linearization of the stress through the plate thickness for derivation of hot spot stress. This methodology was included in Hobbacher (1996). The calculated stresses can be divided into a membrane stress and a bending stress. The membrane stress can be calculated as = 1 ∫ ( ) = =0 (1) where x represent position through the plate thickness t measured from the surface of the plate. σ(x) is stress in the axial direction of the plate at position x. Similarly the bending stress can be calculated as = 6 2 ∫ ( ( ) − = =0 )( 2 − ) (2) Larger structures are normally analysed by shell elements. This means that surface stresses are most relevant for hot