Keywords: database management systems, engineering information management, query language, matrix representation, finite element method, structural dynamics, component mode synthesis, substructures.

The present work shows how database technology can provide efficient data management for engineering analysis activities [1]. To determine the response of a certain excitation in structural dynamics, the finite element method has been used successfully for analysis of natural frequencies and mode shapes in combination with time-history analysis. In this area, object-relational database technology has been applied to store, retrieve and interact with analysis information to perform computational data analysis. For this purpose, the AMOS2 high-performance and main-memory database management system has been used. It is explored how object-relational database technology can be used to support component mode synthesis using the Craig-Brampton method [2]. The Craig-Brampton method is a computational method where the overhead for the management of data is relatively large in commercial computer-aided engineering systems in comparison to conventional analyses. The benefits in using the Craig-Brampton method lies in savings of CPU time due to reduction of nodal degrees of freedom (DOF) as well as the possibility to perform analysis of components in parallel.

Structural problems with very large numbers of DOF may suffer from long solution times as the cost for computing eigenvalues and eigenvectors are high. A substructure is a partially solved set of equations from a complete set of structural equations. In component mode synthesis a structure is divided into substructures that are each being analyzed independently for eigenvalues and eigenvectors. The complete shape patterns or load patterns of the structures can then be assembled from the mode shapes of independent super-elements. The most popular method of component mode synthesis is the Craig-Brampton method where the normal modes of the super-element are calculated by fixing the attachment DOF. The normal modes are supplemented by constraint modes, i.e. the deflection shapes of the super- element when applying a unit displacement successively to each of the attachment DOF. Substructures are especially useful in an iterative design process or when optimization is used. In such processes many changes of the structure has to be carried out and evaluated. The stored substructures can then be reused in the analysis of the complete structure without being reanalyzed. Only those substructures, in which changes have occurred, need to be reanalyzed. The Craig-Bampton method can also be used to solve very large sets of equations where the system resources are not sufficient as it is possible to divide the problem into smaller substructures.

The work shows how the Craig-Bampton method has been implemented in an object-relational database. The database has been tightly integrated with numerical algorithms for determining mass and stiffness matrices as well as the eigenvectors. It is explained how the data efficiently can be exchanged between the algorithms and the database through a tight connection. When the tight connection is used, the database is embedded with the numerical algorithm and is run in the same address space. This makes it possible to exchange data more efficiently as the communication overhead is minimal. The communication between the external application and the database is in both directions as the external algorithm can send queries to the database and the database can execute external applications though foreign functions when used in queries. A general high-level model for accessing matrix data that is independent of matrix representation is presented. The model makes it possible to develop numerical operations on the matrix data independent of the underlying representation. Therefore is a skyline matrix accessed with the same functions as a full matrix. The model is also used to express the calculations of the reduced stiffness and mass matrices in a declarative query language and thereby letting the database decide how to execute the operations and manage the memory.

1

K. Orsborn, On extensible and object-relational DBMS technology for finite element analysis, PhD thesis, Department of Computer and Information Science, Linköping Institute of Technology, 1996, ISBN 91-7871-827-9.

2

R.R Craig, M.C.C Bampton, Coupling of Substructures for Dynamic Analysis, AIAA Journal, Vol. 3, No. 7, July 1968, 1313-1319. doi:10.2514/3.7264

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