PSI - Issue 82

A.T. Andreasen et al. / Procedia Structural Integrity 82 (2026) 146–152

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A.T. Andreasen et al. / Structural Integrity Procedia 00 (2026) 000–000

FE model is linear with a Young’s modulus of 210 GPa and Poisson’s ratio of 0.3. The FE model is meshed according to the guidelines from the International Institute of Welding (Hobbacher and Baumgartner (2016)) for hot-spot stresses. A convergence study was subsequently performed to validate the mesh. In total 1,026,250 second-order elements and 1,820,113 nodes were used. The purpose of the FE model is to establish so-called influence matrices (IM’s), that describes the strain-load relationship of the structure. The loading in the FE model was applied as unit loads in the x-, y-, and z-directions, as shown in Fig. 1, and as unit moments in the corresponding directions. Thus, a total of six load steps were applied in the FE model. For each load step, the strains at the locations corresponding to the physical strain gauges attached to the real mower lifting arm, were extracted. Using the extracted strains, an influence matrix for each strain gauge could be established. An example of the influence matrix is given in Eq. (1). = & ' ( & ' ( ) ## #$ #) #* #+ #, $# $$ $) $* $+ $, ⋮ ⋮ %# %$ ⋮ ⋮ %) %* ⋮ ⋮ %+ %, + (1) Where { & , ' , ( , & , ' , ( } are the unit loads applied in the FE model, and { !"# , !"$ . . !"- } are the strain gauges at which the strains per unit loading -. are extracted. Thus, the strains at each strain gauge can be found using matrix calculations based on the applied forces. This is a direct effect of the FE model being linear. 4. Load estimation framework Using the experimentally obtained strain gauge data in combination with the high-fidelity FE model, it is possible to set up a framework for determining the loading occurring on the lifting arm. The framework assumes that the FE model accurately predicts the behaviour of the real lifting arm and that the loading occurring on the real lifting arm is linearly dependent on the strains occurring at the strain gauge locations and vice-versa. This is, of course, an assumption; however, as seen in the results it is an acceptable assumption. Thus, using the FE model and the experimental strain gauge measurements, it is possible to estimate the loading required for the FE model to predict the same simulated strains using the governing equation, Eq. (2): [ /0 ] ⋅ { /0 } = { 1&2 } (2) [ /0 ] is the influence matrix obtained from the FE model as described in Eq. (1), { /0 } are the FE forces { & , ' , ( , & , ' , ( } required to obtain the experimental strains { 1&2 } . In other words, given this IM relationship, if strains are measured at several locations, it is possible to calculate the subsequent loading necessary to inflict that measured strain. Thus, the purpose of the framework is to estimate the force vector { /0 } which is unknown and complex due to the various loading conditions that the mower experiences in the field. Given the dimensions of the influence matrix and strain vector, an overdetermined system is created as 6 load components are used to satisfy the strain response equations. As no exact solution exists for an overdetermined system, an approximate solution must be found instead. For this the linear least squares method has been used as it is a simple optimization method that is easily implemented for data analysis. Other optimization approaches could have been used instead, however, as the experimental data consists of relatively long time series with a sampling frequency of 200 Hz, a large number of load steps must be examined to determine the load vector { /0 } as a function of time. Out of the 14 strain gauges, 13 of them are denoted global gauges. These gauges are placed on the lifting arm in areas where the strains are relatively easy to estimate. Thus, locations with hard geometry changes or welds are excluded for the global gauges as the high stress gradients can influence the results. The last gauge is denoted a local strain gauge and has been placed close to a weld for validation purposes, as the stress in the weld is of interest when estimating fatigue. Only the global gauges have been used for obtaining the loads occurring on the lifting arm, as this 1 !"# !"$ ⋮ !"%