Novel modal methods for transient analysis with a reduced order model based on enhanced Craig-Bampton formulation

Abstract For transient analysis of structural dynamics with reduced order model (ROM), data recovery procedures that use modal methods such as the classical mode-acceleration (MA) and modal-displacement (MD) methods are an important step in order to increase the convergence and accuracy of the solution. In this work, we propose novel MA and MD methods for highly accurate transient analysis with a reduced order model based on enhanced Craig–Bampton (ECB) formulation, which is an extension of the classical Craig–Bampton (CB) method that is a way to reduce the size of a finite element (FE) model. The performance of the proposed data recovery approach is demonstrated with two numerical examples. We also investigate the relation between the proposed and classical MA and MD methods.

[1]  Jin-Gyun Kim,et al.  An enhanced AMLS method and its performance , 2015 .

[2]  R. Guyan.  Reduction of stiffness and mass matrices , 1965 .

[3]  M. J. Wittbrodt,et al.  A critique of mode acceleration and modal truncation augmentation methods for modal response analysis , 1997 .

[4]  Damijan Markovic,et al.  High-Fidelity Flexibility-Based Component Mode Synthesis Method with Interface Degrees of Freedom Reduction , 2016 .

[5]  Jin-Gyun Kim,et al.  Evaluating Mode Selection Methods for Component Mode Synthesis , 2016 .

[6]  Razvan Stefanescu,et al.  Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems , 2017, J. Comput. Appl. Math..

[7]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[8]  Brian T. Helenbrook,et al.  Reduced order modeling for accelerated Monte Carlo simulations in radiation transport , 2015, Appl. Math. Comput..

[9]  Chao-hong Pan,et al.  A simple approach for reducing the order of equations with higher order nonlinearity , 2012, Appl. Math. Comput..

[10]  Bülent Karasözen,et al.  Model order reduction for nonlinear Schrödinger equation , 2014, Appl. Math. Comput..

[11]  R. R. Craig,et al.  On the application of the mode‐acceleration method to structural engineering problems , 1983 .

[12]  Hanmin Lee,et al.  Flexible multibody dynamics using coordinate reduction improved by dynamic correction , 2018 .

[13]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[14]  Yong-hwa Park,et al.  Partitioned Component Mode Synthesis via a Flexibility Approach , 2004 .

[15]  R. Macneal.  A hybrid method of component mode synthesis , 1971 .

[16]  Sebastiaan Fransen,et al.  Methodologies for launcher–payload coupled dynamic analysis , 2012 .

[17]  Matthew F. Barone,et al.  Construction of energy-stable projection-based reduced order models , 2014, Appl. Math. Comput..

[18]  Lijian Jiang,et al.  A reduced order method for Allen-Cahn equations , 2016, J. Comput. Appl. Math..

[19]  Soo Won Chae,et al.  A component mode selection method based on a consistent perturbation expansion of interface displacement , 2018 .

[20]  K. Choi,et al.  Continuum Design Sensitivity of Transient Responses Using Ritz and Mode Acceleration Methods , 1992 .

[21]  W. Hurty.  Dynamic Analysis of Structural Systems Using Component Modes , 1965 .

[22]  Jin-Gyun Kim,et al.  A coupled dynamic loads analysis of satellites with an enhanced Craig-Bampton approach , 2017 .

[23]  Jin-Gyun Kim,et al.  An enhanced Craig–Bampton method , 2015 .

[24]  Richard B. Lehoucq,et al.  An Automated Multilevel Substructuring Method for Eigenspace Computation in Linear Elastodynamics , 2004, SIAM J. Sci. Comput..

[25]  Alfio Quarteroni,et al.  Comparisons between reduced order models and full 3D models for fluid-structure interaction problems in haemodynamics , 2014, J. Comput. Appl. Math..

[26]  Daniel Rixen,et al.  Generalized mode acceleration methods and modal truncation augmentation , 2001 .

[27]  Young-Jun Park,et al.  A general model reduction with primal assembly in structural dynamics , 2017 .

[28]  Víctor Pereyra,et al.  Model order reduction with oblique projections for large scale wave propagation , 2016, J. Comput. Appl. Math..