Modal computation of jointed structures

Research output: Types of ThesesDoctoral Thesis


Motivation: The mechanical characteristics of complex elastic structures, which are assembled of substructures, are significantly influenced by the local and non-linear constitutive behavior of the involved joints, like bolted joints, spot welded joints and others. Established computational techniques, which are mostly based on the direct finite element method (FEM) or on classical modal reduction procedures, lead to an inefficent balance between computational time and accuracy. Results: In the present thesis a novel problem oriented extension of existing and well proven mode bases (e.g. Component Modes) is suggested, which we call ‘joint interface modes’ (JIMs). In a modal analysis, utilizing JIMs, the joint state can be approximated with a sufficient accuracy, so that a local and non-linear contact model based on physical parameters can be applied with high computational efficiency. For the computation of the JIMs, the local continuity of forces acting on the two surfaces that are connected by the joint is explicitly accounted for. This leads to a convergence, which is more than twice as fast as other approaches known from the literature. Two different approaches to compute the JIMs are derived and compared to each other. In case of a bolted joint an additional convergence acceleration is obtained by a linearization of the JIMs about the time-invariant bolt preload. Numerical studies with joints of different complexity have been performed and it turned out that excellent accuracy is obtained by a number of JIMs, which is significantly smaller than the number of nodal degrees of freedom, necessary for a FE analysis. Jointed structures can be equivalently represented either by separate mode bases for each substructure or one mode base of the entire structure. Both methods have been compared to each other with respect to computational effort and efficiency. Deformations of linear elastic structures can be approximated by a superposition of time-invariant modes. Non-linearities, like e.g. joints, have to be imposed either by fictitious strains or forces. A general method has been developed in order to deter-mine such forces for a linear elastic model, which do not influence the rigid body motion and give the same deformations as the underlying non-linear problem. Benefits: Based on JIMs, it is possible to perform dynamic computations of jointed elastic structures with almost the same accuracy as the full FEM within a significant reduction of computational time (factor 10 to 100 and more). For the application engineer the joint is represented by physically meaningful parameters like bolt preload or surface roughness. The proposed method can be directly implemented in commercially available FE- or multibody simulation software.
Original languageEnglish
Publication statusPublished - 2008

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