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Calibri 83ffff̙̙3f3fff3f3f33333f33333.CTU Delft Repositoryg r4uuidrepository linktitleauthorcontributorpublication yearabstract
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departmentresearch group programmeprojectcoordinates)uuid:f9736e8bd00f4e25b45648bd65b43788Dhttp://resolver.tudelft.nl/uuid:f9736e8bd00f4e25b45648bd65b43788RModel order reduction and substructuring methods for nonlinear structural dynamicsWu, L.nvan Keulen, A. (promotor); Tiso, P. (copromotor); Delft University of Technology (degree granting institution)Dynamic analysis of largesize finite element models has been commonly applied by mechanical engineers to simulate the dynamic behavior of complex structures. The everincreasing demand for both detailed and accurate simulation of complex structures forces mechanical engineers to pursue a balance between two conflicting goals during the simulations: low computational cost and high accuracy. These goals become extremely difficult for geometric nonlinear structural dynamical problems. When geometrical nonlinearities are introduced, the internal force vector and Jacobians are configuration dependent, and the corresponding updates are computationally expensive. This thesis presents nonlinear model order reduction techniques that aim to perform detailed dynamic analysis of multicomponent structures with reduced computational cost, without degrading the accuracy too much. Special attention is given to flexible multibody system dynamics.<br/><br/>For multicomponent structures featuring many interface degrees of freedom, standard substructuring dynamics can be combined with interface reduction techniques to obtain compact reduced order models. Chapter~2 summarized a variety of interface reduction techniques for the wellknown CraigBampton substructuring method. These approaches are reviewed and compared in terms of both computational cost and accuracy. A multilevel interface reduction method is presented as a more generalized approach, where a secondary CraigBampton reduction is performed when the subsystems are assembled within localized subsets. The multilevel interface reduction method provides an accurate representation of the full linear model with significantly lower computational cost. <br/><br/>In Chapter~3, we extend the CraigBampton method to geometric nonlinear problems by augmenting the systemlevel interface modes and internal vibration modes of each substructure with their corresponding modal derivatives. The modal derivatives are capable of describing the bendingstretching coupling effects exhibited by geometric nonlinear structures. Once the reduced order model is constructed by Galerkin projection, the upcoming challenge is the computation of the reduced nonlinear internal force vectors and tangent matrices during the time integration. The evaluation of these objects scales with the size of the full order model, and it is therefore expensive, as it needs to be repeated multiple time within every time step of the time integration. To address this problem, we directly express the reduced nonlinear vectors and matrices as a polynomial function of the modal coordinates, using substructurelevel higherorder tensors with much smaller size. This enhanced CraigBampton method offers flexibility for reduced modal basis construction, as modal derivatives need to be computed only for substructures actually featuring geometrical nonlinearities, and do not need the prior knowledge of the nonlinear response of the full system with training load cases.<br/><br/>For flexible multibody systems, each body undergoes both overall rigid body motion and flexible behavior. To describe the dynamic behavior of each body accurately, the floating frame of reference is commonly applied. In Chapter~4, the enhanced CraigBampton method, as proposed in Chapter~3, is embedded in the floating frame of reference. We consider here structures modeled with vonKarman beam elements. Interface reduction methods are in this context unnecessary since the adjacent bodies ar<e connected through a single node. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.<br/><br/>For more complex geometries, like wind turbine blades, extremely simplified beam models can not capture the complexity of the real threedimensional structure, and therefore the dynamic behavior might not be accurately modeled. In Chapter~5, we present an enhanced Rubin substructuring method for threedimensional nonlinear multibody systems. The standard Rubin reduction basis is augmented with the modal derivatives of both the freeinterface vibration modes and the attachment modes to include bendingstretching coupling effects triggered by the nonlinear vibrations. When compared to the enhanced CraigBampton method proposed in Chapter~4, the enhanced Rubin method better reproduces the geometrical nonlinearities occurring at the interface, and, as a consequence, higher accuracy can be achieved.<br/><br/>In Chapter~6, the overall conclusions are drawn and recommendations for further study are provided.<brymodel order reduction; geometrical nonlinearities; component mode synthesis; multibody system dynamics; modal derivativesendoctoral thesis9789461869357%Structural Optimization and Mechanics)uuid:4e298eb32f14405b9f9bf289ce35e204Dhttp://resolver.tudelft.nl/uuid:4e298eb32f14405b9f9bf289ce35e204]Nonlinear model order reduction for flexible multibody dynamics: A modal derivatives approachWu, L.; Tiso, P.An effective reduction technique is presented for flexible multibody systems, for which the elastic deflection could not be considered small. We consider here the planar beam systems undergoing large elastic rotations, in the floating frame description. The proposed method enriches the classical linear reduction basis with modal derivatives stemming from the derivative of the eigenvalue problem. Furthermore, the Craig Bampton method is applied to couple the different reduced components. Based on the linear projection, the configurationdependent internal force can be expressed as cubic polynomials in the reduced coordinates. Coefficients of these polynomials can be precomputed for efficient runtime evaluation. The numerical results show that the modal derivatives are essential for the correct approximation of the nonlinear elastic deflection with respect to the body reference. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.\geometric nonlinearity; floating frame of reference; modal derivatives; CraigBampton methodjournal articleSpringer.Mechanical, Maritime and Materials Engineering&Precision and Microsystems Engineering)uuid:c04ed78ee9a440c684497ec129e3a91cDhttp://resolver.tudelft.nl/uuid:c04ed78ee9a440c684497ec129e3a91cQModal Derivatives based Reduction Method for Finite Deflections in Floating FrameModel order reduction techniques are widely applied in the floating frame of reference. The use of linear vibration modes, however, is not applicable when the elastic deformations become finite. In this paper, the nonlinear elastic formulation, where the higherorder terms will be included in the strain energy expression to consider the bendingstretching coupling effect, is applied in the floating frame of reference. In this case, the complexity of the formulation diminishes the advantages of the floating frame of reference formulation because of the relatively high computational cost. Therefore, the linear reduction basis of vibration modes is augmented with the relevant modal derivatives to accurately reproduce the nonlinear elastic deformation on the reduced basis. The numerical results presented in this paper demonstrate that the proposed approach can be applied to accurately investigate problems featuring arbitrary large rigid body rotations and finite elastic displacements.;modal derivatives; floating frame; geometric nonlinearitiesconference paperCIMNE
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