Vibration analysis of uncertain spot-welded structures

Spot-welded structures contain inherent variability in location and/or stiffness due to the complexity of the manufacturing process. Therefore, an analysis that includes the uncertainty generated in the joints will provide a range of response predictions, adding more value to the design process compared to deterministic results. Finite element (FE) analysis is frequently used in conjunction with Monte Carlo simulations (MCS) to predict the variability in the vibration response of assembled structures, however this is usually computationally expensive. Small numerical spot weld models must be used since real spot welded structures usually possess many spot welds and modelling each of them in detail would lead to additional computational effort, current models provide results sensitive to the element size. In this thesis, a method to quantify the variability in the dynamic characteristics of structures due to uncertainty in the location and diameter of the spot welds is proposed and experimentally validated. Component mode synthesis (CMS) is used in combination with multipont constraint (MPC) connection models in order to improve the computational efficiency of the uncertainty analysis. However, if the number of degrees of freedom (DOFs) involved in the connection is large, then the CMS size reduction is less effective. Two techniques are proposed to overcome this problem: (i) characteristic constraint modes and (ii) application of a low rank update theory to the CMS matrices. A spot weld model based on MPCs is proposed and validated as part of the original contributions of this work. This model improves convergence and minimizes the sensitivity to the element size. The application of the new method is experimentally validated in a double hat structure. Results show that the method presented is accurate when predicting the structure’s natural frequencies and it can identify which modes are sensitive to the uncertainties in the spot welds and which modes are not.EThOS - Electronic Theses Online ServiceGBUnited Kingdo