Keywords: component mode synthesis, mode superposition, object-oriented programming, parallel computing, Microsoft .NET.

Dynamic structural analysis often involves computing natural frequencies of vibration and the associated mode shapes. One way to reduce the time required for free vibration analysis is to divide the associated eigenproblem into smaller sub-problems. This strategy underlies the component mode synthesis (CMS) method, which divides the eigenproblem by dividing the structure into substructures or components. CMS can be readily programmed for a parallel computing platform to further reduce analysis times. While many variants of the CMS method have been proposed, there seems to be very few parallel implementations described in the literature. This paper presents an object-oriented (O-O) parallel implementation of the Craig-Bampton CMS method [1] and the related mode superposition method.

The proposed implementation takes advantage of the Microsoft .NET framework, which provides integrated support for multi-threading and distributed objects. In contrast to message passing primitives, distributed objects [2] are a natural and transparent means of parallelizing O-O programs. The objects representing the substructures of a finite element model could be distributed across a network of computers. The .NET framework sets up the necessary infrastructure so that distributed objects can communicate across the network as if they were on the same machine.

In the implementation of parallel modal analysis, CMSFreeVibAnalyzer controls the overall CMS procedure. A ComponentAnalyzer is created for each component to assemble the subsystem of equations, compute normal and constraint modes, and reduce the subsystem. After the reduced eigenproblem is solved, the ComponentAnalyzer transforms the results to obtain vibration modes based on the original degrees of freedom (d.o.f.). The product of the CMS procedure is a CompositeVibData object, which is responsible for transforming load vectors and superimposing vibration modes for the purpose of mode superposition.

Tests were carried out to demonstrate the potential of the implementation for parallel modal analysis on a network of computers. Efficiencies of 85% and 74% were achieved using two and four computers respectively. For the most time-consuming phase of eigenproblem reduction, efficiencies of 90% and 85% respectively were achieved.

There is a real potential of using the proposed implementation on widely available computing resources to speed up free vibration and response history analyses. Further research could be carried out to investigate the effectiveness of other CMS variants, the implementation of static and dynamic load balancing, and the exploitation of multi-core computers.

1

R.R. Craig, "Structural Dynamics: An Introduction to Computer Methods", John Wiley & Sons, Inc., New York, 1981.

2

W. Emmerich, "Engineering Distributed Objects", John Wiley & Sons, Ltd, Chichester, 2000.

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