8th. World Congress on Computational Mechanics (WCCM8) 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30 –July 5, 2008 Venice, Italy Accurate and efficient interweaving of substructure uncertainties and component mode synthesis *H. De Gersem, D. Moens, W. Desmet and D. Vandepitte Katholieke Universiteit Leuven, Department of Mechanical Engineering Celestijnenlaan 300B, B-3001 Heverlee, Belgium hilde.degersem@mech.kuleuven.be Keywords: uncertainty, interval analysis, component mode synthesis, substructuring ABSTRACT INTRODUCTION. During the last decade, the interval finite element method (IFEM) has proven to provide the design engineer with useful information on the dynamic behaviour of mechanical structures in the early design stage [1]. Interest in this non-probabilistic approach for uncertainty handling in the product development stage is growing. However, the vertex method, the transformation method, as well as the global optimisation approach, all possible core implementations of the IFEM for dynamic analysis, require a large number of crisp eigenvalue analyses with different values of the uncertain parameters in their respective uncertainty interval. As a result, the IFEM applicability in industrial FE design simulation and validation, with large models and a substantial number of uncertain parameters, is still limited. Therefore, extensive research is dedicated to the reduction of the computational load of the interval FE method. In the present work, the interval finite element method is combined with the Craig-Bampton component mode synthesis (CMS) method [2]. This numerical reduction technique applies a Ritz-type transforma- tion to each individual component (substructure) of a built-up structure. The deformation of a component is approximated using a limited number of component modes (i.e. admissible shape functions), yielding a large reduction in degrees of freedom (dofs) for each component, and thus for the entire structure. In this manner, the computational cost of the FE analysis of large models is drastically reduced. This com- putational time reduction obtained by the CMS method also benefits the repeated FE analyses required in a non-deterministic context. A novel approach is presented, which closely interweaves the component mode synthesis technique and the interval finite element method: an approximative component reduction is applied on each uncertain component of an assembly, in each of the FE analyses required in the IFEM procedure. The approach results in an accurate and efficient method for uncertainty propagation in substructuring techniques. METHODOLOGY. In case of substructured FE models in which uncertainties are present in one or more components to be reduced, the CMS reduction procedure itself is affected by the uncertainties. For each re-analysis of the FE model in an IFEM framework, uncertainties affecting a specific component manifest themselves in, on the one hand, the component mass and stiffness matrices, and on the other hand, in the component modes, which are used in the reduction of the component matrices. In a Repeated Component Reduction (RCR) approach, these entities are recalculated in each FE re-analysis. However,