PSI - Issue 75

Carl-Fredrik Lind et al. / Procedia Structural Integrity 75 (2025) 519–529 Carl-Fredrik Lind et al./ Structural Integrity Procedia (2025)

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at the crack tip (Liu et al., 2024). If the crack length is allowed to expand until failure ( a t  ). Then the required number of cycles can be calculated, and the equivalent stress is defined as below (Liu et al., 2024):

2 t I r    2 m m

S  

(8)

( ) s

1

m

In the above formula, the intensity function is defined according to (Liu et al., 2024).This then needs to be adjusted to the following formula, which forms the basis of the master S-N curve method: ( ) h d S N C    (9) Where C d and h are empirical constants (Dong et al., 2007). Since C d governs the Wöhler curve line, it is empirical and therefore statistical. The mean value  corresponds to a 50 % likelihood of fatigue failure at N cycles, with the remainder being normally distributed. 3.3. DBSCAN cluster method A key factor in determining the effectiveness of the method presented in the current study is the ability to group all nodes that are considered weld nodes (that is, they form part of a weld line and are used in Eq.(4)) based on their adjacency to each other. This requires a clustering method implemented by Ghanadi et al. (Ghanadi et al., 2024) to identify clusters of coordinates. The primary reason for the usage of the DBSCAN method is that the number of clusters does not need to be known, allowing for a more robust and general program. Consider an ungrouped set of points (nodes)   1, 2,..., ,... i n W  with respective coordinates   , , T i i i x y z i   i x . Under a tolerance  , that defines the maximal distance between points in a group, and a parameter MinPts here called min m , that is the minimal number of points to form a cluster. Let C be a cluster of points. For points , i k to belong to C if and only if the number of points in C (including , i k ) is larger than the MinPts parameter m min , and either the distance between points i, k is smaller than  or there are nodes w j C  such that there exists a chain of points i → j 1 → ... → j w → j w +1 → ...j n → k where for all such w the distance between is smaller than  (Ester et al., 1996). 4. Stress and life calculations If the mesh is designed for P. Dong’s method, welds should consist of shell elements connected either directly, via constraint equations, or through beam elements. To ensure accurate structural stress calculation, only one beam element is allowed per node, though multiple beams can connect from a node to different components. Consider all nodes in the model in a set N and assume that we also have a set W N  of nodes that belong to a weld (all weld joints in the structure) and are analysable using P. Dongs method. Assume that for every node id i W  , the following is known: the coordinate vector with global coordinates   , , T i i i X Y Z  i x , the nodal forces , , , , , T X i Y i Z i F F F     i F and moments , , , , , T X i Y i Z i M M M     i M . Assume that we also know the thickness i t and element normal unit vector e n of the shell elements associated with the nodes in W . If there are more than one element associated with a node, the minimum thickness of the elements is used for that node. In order to gain the life for each node from P. Dongs' method, the structural stress is calculated (Liu et al., 2024), which involves building L matrix from Eq.(2) and subsequently knowing which nodes are adjacent to the node i . To find this a set i M is created, which contains the ids of every node that belongs to any element that node i belongs to, then create the subset w M so that