title: Structural dynamic analysis and model updating for a welded structure made from thin steel sheets
Creators: name: Abdul Rani, Muhamad
Publisher: name: University of Liverpool Repository
Year: 2013

description: Modern large, complex, engineering structures normally encompass a number of substructures which are assembled together by several types of joints. Despite, the highly sophisticated finite element method that is widely used to predict dynamic behaviour of assembled complete structures, the predicted results achieved, of assembled structures are often far from the experimental observation in comparison with those of substructures. The inaccuracy of prediction is believed to be largely due to invalid assumptions about the input data on the initial finite element models, particularly those on joints, boundary conditions and also loads. Therefore, model updating methods are usually used to improve the initial finite element models by using the experimentally observed results. This thesis is concerned with the application of model updating methods to a welded structure that consists of several substructures made from thin steel sheets that are assembled together by a number of spot welds. However, the welded structure with a large surface area is susceptible to initial curvature due to its low flexible stiffness or manufacturing or assembling errors and to initial stress due to fabrication, assembly and welding process of substructures. Nevertheless, such initial stress is very difficult to estimate by theoretical analysis or to measure. This thesis puts forward the idea of including initial curvature and/or initial stress (which have a large effect on natural frequencies) as an updating parameter for improving the performance of the finite element model of a structure made from thin steel sheets. The application of conventional iterative model updating methods which use a full finite element model has been widely practised. However when updating large, complex structures with a very large number of degrees of freedom, this application becomes impractical and computationally expensive due to the repeated solution of the eigensolution problem and repeated calculation of the sensitivity matrix. It is therefore preferable to use a substructuring scheme based model updating which is highly computationally efficient for the reconciliation of the finite element model with the test structure. However, in certain practical cases, where the confidential and proprietary issues of modelling work are of concern between the collaborating companies, in which the finite element models of the substructures could not be revealed and only the condensed matrices of the substructures are used instead, the areas of the substructures having fewer number of interface nodes would always be the first choice as the interface nodes. For welded structures, the nodes in the vicinity of spot weld element models are few and hence are usually taken as the interface nodes for connecting substructures. However, the present MSC. NASTRAN superelement model reduction procedures are known not to allow the nodes of CWELD elements to be the interface nodes of substructure. Prior to the present study, no work appears to have been done to use the nodes of CWELD elements as the interface nodes of substructures in the investigation of dynamic behaviour of welded structures. In this work, the application of branch elements as the interface elements of substructure are proposed and tested. Prior to the present study, it also appears that there has been no work done concerning the adjustment of the finite element model of the welded structure by including the effects of initial curvatures, initial stress and boundary conditions that are contributing to the modelling errors, via the combination between the Craig-Bampton CMS and model updating. This thesis presents two approaches for model updating of the welded structure: the conventional methods which use full finite element model and the substructuring scheme based model updating which uses the Craig-Bampton CMS technique. The accuracy and efficiency of both approaches are thoroughly discussed and presented and are validated with the experimentally observed results.