Finite Element Model Updating Using Dynamic Condensation Metehods

An accurate finite element model is widely used in structural health monitoring,damage detection and optimization design,yet its analytical dynamic properties reveal enormous discrepancies from the tested data of the corresponding real structure.Therefore,the finite element model is required to be updated to ensure an accurate model to reproduce the real properties of the practical structure.The traditional model updating method,performed on the global model,is time consuming especially for the large-scale structure with numerous degrees of freedom and designed parameters.Dynamic condensation methods are advantageous to condense the large global model into a much smaller one,which helps to improve the computation efficiency.Therefore,the thesis employs the dynamic condensation methods to sensitivity analysis and sensitivity-based finite element model updating of large-scale structures.First,an improved dynamic condensation approach is derived to calculate structural eigensensitivities and later used in sensitivity-based model updating.It introduces a transformation matrix to relate the mode shape of the slave degrees of freedom to the master ones.After a simplified process,the size of the global eigenequation is condensed into a much smaller one.The eigensensitivities are calculated based on the condensed model,which are later used in the sensitivity-based finite element model updating.Applications of the proposed model updating method to an eight-storey frame and Wuhan Junshan Yangtze Bridge verify its accuracy and efficiency.Second,a dynamic condensation approach is derived to compute structural responses and response sensitivities.Similarly,it employs a transformation matrix to relate the structural responses of the slave degrees of freedom to the master ones.As a consequence,the global vibration equation is condensed into a much smaller one with a simplified process.The structural responses and response sensitivities are calculated based on the condensed vibration equation and are then later employed to conduct the finite element model updating.The computational precision and efficiency of this method are illustrated by a catilever plate.As the model updating can be an ill-posed problem if the number of designed parameters is larger than the tested data.Therefore,the L1 regularization method is employed in model updating to constrain the designed parameters.The results of a simple supported beam indicates,employing the L1 regularization approach,the proposed model updating method can accurately and efficiently identify the assumed elemental stiffness changes.Finally,an improved iterative substructuring method is derived to compute eigensolutions and eigensensitivities,which are then used to conduct the sensitivity-based finite element model updating.It condensed the global model in the modal domain.It introduces a modal transformation matrix to relate the master modes to the slave modes.After a simplified process,the size of the global eigenequation is condensed into a much smaller one.The finite element model updating is performed on the condensed model,which is improves the computational efficiency significantly.Compared to the original iterative substructuring method,the proposed method is more efficient in two aspects.It can calculate the eigensolutions and eigensensitivities simultaneously for all modes.In addition,the iterative variables in the proposed method have a much smaller order than those of the original method.Applications of the proposed method to a frame model and a practical large-scale structure verify its accuracy and efficiency in eigensolutions,eigensensitivities and finite element model updating.