Exploiting the physical symmetry of regular mesh in substructuring analysis

✍ Scribed by Lam, Y. C. ;Xiao-Lin, Liu

• Publisher: Wiley (John Wiley & Sons)
• Year: 1992
• Tongue: English
• Weight: 696 KB
• Volume: 8
• Category: Article
• ISSN: 0748-8025
• DOI: 10.1002/cnm.1630080706

✦ Synopsis

Abstract

A new technique of multi‐level substructuring based on a regular mesh is presented. The technique takes advantage of the physical symmetry and repetitivity generated by the regular mesh. A special node‐numbering/addressing system is developed to exploit the symmetry which results in the stiffness matrices not only being symmetrical about the leading diagonal, but a regular pattern emerging with respect to the other diagonal. The same pattern exists for their inverses. A new condensation scheme is used to take full advantage of the regular patterns. As a result, only about a quarter of the stiffness matrices and their inverses need to be processed, as compared to half when using the conventional method.

Based on the technique, a two‐dimensional finite‐element analysis program FEMSUB has been implemented in the University's VAX network. Through a number of numerical tests, it is discovered that the new technique can result in savings of both core storage and computing time. The savings become more significant when the scale of a problem increases. The investigation indicates that the core storage requirement decreases when using substructures of higher levels. However, for computational efficiency, both the level of substructuring and the number of repeated substructures have an effect. Thus, a dimensionless parameter R (number of substructures used/maximum number of substructures) has been introduced to correlate the effect of the technique on computational efficiency.