Application of Stochastic Model Updating to a Collection of Structures with Spot-Welded Joints

The application of a stochastic model updating technique using Monte-Carlo inverse propagation and multivariate multiple regression to converge a set of analytical models with randomised updating parameters upon a set of nominally identical physical structures is considered. The structure in question is a short beam manufactured from two components, one of folded steel and the other flat. The two are connected by two rows of spot welds. The main uncertainty in the model is concerned with the spot weld but there is also considerable manufacturing variability, principally in the radii of the folds. Two main types of spot weld models exist (3-4), namely those that require the stress within the weld spot to be calculated and those that do not. The former require detailed modelling so that a smooth stress field is computed, whereas in the case of the latter the estimation of stiffness and mass distributions is sufficient. When modelling spot welds, it is difficult to take into account the many local effects such as geometrical irregularities, residual stresses, material in-homogeneities and welding defects. Furthermore a detailed and complex local model of the joint characteristics is not possible in industrial applications where typically thousands of spot welds are used to manufacture automotive parts. These conceptual modelling uncertainties are incorporated in an interface finite element (5) which may be used to connect panels at spot-weld locations. The material properties of the element determine the local stiffness in the tangential and normal directions at the surface. The interface element stiffnesses are used together with other parameters to update a structural and statistical model of a short beam manufactured from two components, one of folded steel and the other flat. The other parameters are two elastic moduli of curved regions in the folded plate. Taken all together they become the randomised parameters used in the Monte-Carlo simulation. Inverse propagation is carried out using linear regression and a population of finite element models with spot welds is updated based on measurements from a set of physical test structures.