A hybrid method of component mode synthesis

MacNeal, Richard H.

doi:10.1016/0045-7949(71)90031-9

Cited by 543 publications

(165 citation statements)

References 6 publications

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“…8,9 However, whereas in those methods the reduction basis is further transformed to eliminate the interface forces, the Dual Craig-Bampton method retains the interface forces as generalised degrees of freedom and reduces the problem assembled in its dual form. This also implies that the compatibility on the interface Eq.…”

Section: B Reduced Set Of Equations Of Motionmentioning

confidence: 99%

Modal Reduction in Co-Rotated Multi-Body Dynamics Based on the Dual Craig-Bampton Method

Kadawathagedara

Rixen

2011

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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A new reduction method for dynamical analsis of multi-body systems is presented in this paper. It fundamentally differs from the ones previously published in the way kinematical constraints are handled. Our approach is based on component mode synthesis, but the specificity of articulated mechanism, in which components are assembled through connecting forces, is taken into account from the reduction level. This is achieved by using a set of modes that are consistent with this type of assembly, namely the residual flexibility modes and the free-free vibration modes. In this approach, Lagrange multipliers naturally appear as generalized reduced coordinates together with the vibration modes' amplitudes. An other specific difficulty pertaining to articulated systems is the configuration dependency of the residual flexibility modes. In order to overcome this obstacle a new strategy to handle kinematical constraints has been developed, enabling us to ignore the current direction of the constraint forces at the reduction level by splitting the constraint into local and global contributions. The derived reduced matrices are remarkably simple and the procedure is easy to implement. The validity of the approach will be investigated using the crank-slider benchmark.

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Section: B Reduced Set Of Equations Of Motionmentioning

confidence: 99%

Modal Reduction in Co-Rotated Multi-Body Dynamics Based on the Dual Craig-Bampton Method

Kadawathagedara

Rixen

2011

52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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“…CMS consists of breaking up a large structure into several substructures, obtaining reduced order system matrices of each component and then assembling these matrices to obtain the reduced order system matrices of the entire structure. Depending on the type of the boundary conditions applied on the component interface nodes, CMS can be grouped into f ixed interface methods (Craig and Bampton 1968;Hurty 1965), free interface methods (Goldman 1969;Mac Neal 1971;Markovic et al 2007;Rixen 2002;Rubin 1975) and loaded interface methods (Benfield and Hruda 1971). In this study; the CraigBampton (CB) method, a fixed interface CMS method, is considered to improve the computational efficiency of structural analyses.…”

Section: Introductionmentioning

confidence: 99%

Dynamic substructuring and reanalysis methods in a surrogate-based design optimization environment

Perdahcioglu

Geijselaers

Ellenbroek³

et al. 2011

Struct Multidisc Optim

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In light weight structure design, vibration control is necessary to meet strict stability requirements and to improve the fatigue life of structural components. Due to ever-increasing demands on products, it is generally more convenient to include vibration prerequisites in a design process instead of using vibration control devices on fixed designs. One of the main difficulties associated to design optimization of complex and/or large structures is the numerous computationally demanding Finite Element (FE) calculations. The objective of this research is to present a novel strategy for efficient and accurate optimization of vibration characteristics of structures. In the proposed strategy, a sub-structuring method is utilized. The FE model of the complete structure is partitioned, reduced and then reassembled. This increases the computational efficiency of dynamic analyses. Moreover, this method is coupled with a novel reanalysis technique to speed up the repeated structural analyses. These methods are finally embedded in a surrogate-based design optimization procedure. An academic test problem is used for the validation of this novel approach.

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“…The substructures are assembled using interface displacements, which is referred to as primal assembly. Many other methods, such as those of MacNeal [2], Rubin [3], and Craig-Chang [4], employ free interface vibration modes, (residual) attachment modes, and rigid body modes and assemble the substructures in primal fashion as well. The dual Craig-Bampton method (DCBM) [6] also employs free interface vibration modes, (residual) attachment modes, and rigid body modes to build the substructures' reduction bases, but uses interface forces to assemble the substructures, which is referred to as dual assembly.…”

Section: Introductionmentioning

confidence: 99%

“…If a single component of a system is changed, only that component needs to be reanalyzed and the system can be analyzed at low additional cost. Thus, dynamic substructuring offers a flexible and efficient approach to dynamic analysis [1,2,3,4,5,6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Time Integration of Dual Craig-Bampton Reduced Systems

Gruber¹,

Gille²,

Rixen³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In this paper, time integration procedures are demonstrated and investigated for dual Craig-Bampton reduced systems. The dual Craig-Bampton method for the reduction and successive coupling of dynamic systems employs free interface vibration modes, attachment modes and rigid body modes to build the reduction bases of the substructures, but assembles the substructures using interface forces. Thereby, the interface kinematic conditions are transformed, allowing for incompatibilities associated with the equilibrium residual in the substructure. Hence, the eigenvalues of the reduced-order model are not guaranteed to be upper bounds for the unreduced system's eigenvalues. Furthermore, the dual Craig-Bampton reduced system will always have as many negative eigenvalues as interface coupling conditions. The reduced system is unstable, rendering a straightforward time integration of the dual Craig-Bampton reduced system impossible.The feasibility of a reliable time integration of dual Craig-Bampton reduced systems is demonstrated and investigated in detail. The unstable behavior when time-integrating such systems without further modifications is illustrated and two approaches to overcome this instability are suggested: on the one hand, a modal analysis of the reduced system is performed as a subsequent step to the dual Craig-Bampton reduction. Only modes corresponding to positive eigenvalues are thereby kept for transient analysis. This allows for a stable time integration. On the other hand, a modal interface reduction during the dual Craig-Bampton reduction process is performed and only interface modes corresponding to positive eigenvalues are kept. This makes the final reduced system also positive definite. The accuracy using these two approaches is demonstrated in examples with either different initial conditions or varying external periodic excitations.

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A hybrid method of component mode synthesis

Cited by 543 publications

References 6 publications

Modal Reduction in Co-Rotated Multi-Body Dynamics Based on the Dual Craig-Bampton Method

Modal Reduction in Co-Rotated Multi-Body Dynamics Based on the Dual Craig-Bampton Method

Dynamic substructuring and reanalysis methods in a surrogate-based design optimization environment

Time Integration of Dual Craig-Bampton Reduced Systems

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