title: FE modelling and model updating of laser weld joints
Creators: name: Abu Hussain, Nurulakmar
Publisher: name: University of Liverpool Repository
Year: 2023

description: Assembled structures are typically constructed by structural elements that are connected together by structural joints. For example, thousands of spot weld joints are used in a typical automotive structure in order to provide connections between layers of thin metal sheets used to form the structure. The spot weld joints also significantly contribute to the vehicles structural stiffness and dynamic characteristics; hence it is very important to have an acceptable FE model of the joints in order to evaluate the dynamic behaviour of such structures. It appears that most of the studies regarding spot weld joints have concentrated on spot welds made by the more conventional Resistance Spot Welding, while to the author's best knowledge, there is no reported works on modelling the dynamic behaviour of structures with laser welds, which is the main objective of this thesis. Existing elements available in commercial FE software are researched and a suitable element is chosen to represent the laser weld joints for its dynamic predictions. A set of laser spot welded structures are manufactured and FE model representing the structures is developed systematically, starting from modelling and updating the substructures to the development of the FE model of the welded structures. Experimental modal analysis is conducted in order to obtain the modal parameters from the test structures, which are then employed in validating and improving the correlation between the developed FE models and their experimental counterparts. Variability that exists in the test structures is also investigated and non-deterministic (or stochastic) model updating is carried out by using the perturbation method. Parameter selection for the stochastic model updating is studied first using two sets of very different structures: the first set consists of nominally identical (simple) flat plates, while the second set comprises of (more complicated) formed structures. The stochastic updating procedure is conducted with different combinations of parameters, and it is found that geometrical features (such as thickness) alone cannot converge the predicted outputs to the measured counterparts, hence material properties (for instance, Young's modulus and shear modulus) must be included in the updating process. Then, the stochastic model updating is also conducted on the welded structures, using two approaches of parameter weighting matrix assignments. Results from one of the approaches demonstrate good correlation between the predicted mean natural frequencies and their measured data, but poor correlation is obtained between the predicted and measured covariances of the outputs. In another approach, different parameter weighting matrices are assigned to the means and covariances updating equations. Results from this approach are in very good agreement with the experimental data and excellent correlation between the predicted and measured covariances of the outputs is achieved. Finally, the developed deterministic FE model of the welded structures is used in damage identification exercise, consisting of two parts: (I) identification of defects, and (2) identification of real damage in the welded structure. In the first part, a defective structure is selected from the set of nominally identical structures and FE model updating procedure is performed in order to quantify the defects in the defective structure. In this exercise, only the natural frequencies are employed in the identification procedure and the identified defects are found to be reasonable and in agreement with the findings from visual inspection conducted prior to the identification work. In identifying real damage in the welded structure, the identification procedure is conducted based on the natural frequencies and the mode shapes information of the damaged structure. The damage is characterised by the reductions in the Young's modulus of the weld patches to indicate the loss of material/stiffness at the damage region. Based on the updating results, it can be concluded that the identification procedure has successfully identified, localised and quantified the damage. The identification procedure also brings the predicted natural frequencies closer to their measured counterparts, with a very good correlation is achieved between the numerical and experimental modes.