Reduction of substructural interface degrees of freedom in flexibility‐based component mode synthesis

Abstract

SUMMARYA flexibility-based component mode synthesis (CMS) is proposed for reduced-order modelling of dynamic behaviour of large structures. The approach employs partitioning via the localized Lagrange multiplier method. The use of the localized Lagrange multipliers leads to, unlike the classical Lagrange multipliers, a linearly independent set of interface forces without any redundancies at multiply connected interface nodes. The flexibility-based CMS method has shown significant advantages over the classical Craig-Bampton method. A key feature of the method is its substructural mode selection criterion that is independent of loading conditions. Unlike the majority of available CMS approaches, where one retains the full dimension of partition boundary degrees of freedom (DOFs), the flexibility-based method allows to reduce significantly the interface DOFs. The reduction of interface DOFs represents the major contribution of the present communication. The efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3D structure, both partitioned into several substructures.

A Mode Selection Algorithm for the Flexibility-Based Component Mode Synthesis

“…After introducing the first approach of the CMS method in 1960s, various methods have been proposed [1][2][3][4][5][6][7][8][9][10][11][12]. In particular, the flexibility based CMS (F-CMS) method was developed using localized Lagrange multipliers [13], and its extended works have been performed [14,15].…”

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

“…This paper addresses the latter case, with a restriction to the design of structural components under extreme loading conditions. Projection-based reduction methods have been extensively studied in system engineering (see the review proposed in [1]), fluid mechanics [2,3,4,5,6] and structural dynamics [7,8,9,10,11,12]. The theory and applicability of various projection-based model order reduction methods such as component mode synthesis [13,7], the reduced basis method [14,15,16], the proper orthogonal decomposition [17,18,2] which will be used in this work, the a priori hyperreduction method [19,20] or the proper generalised decomposition [21,22,23] are now well-established in the linear to mildly nonlinear cases.…”

“…It probably originates from the work of Craig and Bampton [7], who proposed a reduction by projection on a modal basis defined over predefined subdomains. This idea has been explored and improved in [27,11,12], or coupled with other reduction methods, as in the case of the proper generalised decomposition [21]. A closely related family of solvers uses this concept within local/global approaches: only part of the domain is reduced (sufficiently far away from the sources of nonlinearity) [10,28,29,6], or the global reduced model is locally enriched by a fine-scale description [30,31,32] (these two approaches are equivalent when the reduced model is used as a preconditioner for the local fine-scale problem in the former group of methods [29]).…”

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

“…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.…”