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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3. Theory 3.1. Structural stress

In vehicle engineering, thin-walled components are often modelled as 2D surfaces with uniform thickness, to which plate theory can be applied. In finite element modelling, thin or curved surfaces can be approximated using shell elements, which are governed by plate equations at their nodes, where forces, moments, and displacements from which stress and strain are calculated. The following section focuses on the underlying methodology introduced by P.Dong, describing the structural stress method for weld fatigue evaluation (Dong, 2001). Consider a weld, described by two shell elements joined along one edge, which indicates the weld, as shown in Fig. 4. According to P.Dong’s structural stress method since all forces from element i to element j need to pass these two nodes, and since it is known that the weld throat distance a does not impact the weld life assuming that it is sufficiently large, this means that a valid stress can be defined for the weld using only these two nodes that does take into account the non-linear behaviour at the weld toe. To calculate the structural stresses, the nodal forces and moments from the FE-solution need to be available for each node that is to be analysed. These forces and moments are denoted as y i z i F F F M M M     where i indicates the node number and , , X Y Z refer to the global coordinates, and , , x y z for local element coordinates. , x i , y i , z i , x i , , , , , , ,

Figure 4. Visualization of single structural elements (a) line force (Liu et al., 2024), (b) line moment (Liu et al., 2024), (c) Mesh of same element subdivided into n elements Fig. 4 shows elements of the weld line. Since node i and node k both belong to both elements, a structural stress is associated with each node from the thickness:

f

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m

y   

(1)

x

t

t

s

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where y f and x m are local line forces and moments, respectively. These local line forces are based on the element local coordinates for each element, which means that the node k could in this case have 2 different s  , depending on which element thickness is used. In the current study, the minimum thickness of the two elements is used to ensure a strictly conservative stress output. To acquire these line forces, the local L matrix is defined which transforms nodal reaction forces to line forces and moments: