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An optimal method for the solution of the constrained eigenvalue/response problem for large structures comprising rigidly‐connected substructures
Author(s) -
Garvey S. D.,
Penny J. E. T.
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330604
Subject(s) - degrees of freedom (physics and chemistry) , eigenvalues and eigenvectors , substructure , mathematics , matrix (chemical analysis) , transformation matrix , transformation (genetics) , modal , algorithm , computer science , mathematical optimization , kinematics , engineering , structural engineering , biochemistry , chemistry , physics , materials science , classical mechanics , quantum mechanics , polymer chemistry , composite material , gene
Dynamic substructuring or modal synthesis is established as a powerful means by which the computational effort required to perform dynamic analyses of large structures comprising many degrees of freedom can be reduced. For the case where the substructures are rigidly connected a method of synthesis is proposed which gives very substantial improvements in efficiency over existing methods both in terms of the number of floating‐point operations which must take place and the on‐board computer memory required. The proposed method makes use of a stable co‐ordinate transformation which reduces the mass matrix for the constrained composite‐system to the identity matrix and makes the stiffness matrix banded. The bandwidth is exactly equal to twice the total number of constraints plus 1. This is usually very small in comparison with the total number of degrees of freedom in the constrained composite‐system. The proposed method is ideal for combining a number of substructures into a single new substructure in an efficient way without necessarily disposing of any degrees of freedom. Approximate formulae are presented which give the ratios of the number of operations required for established methods compared with the number needed for the proposed method. These formulae determine when it is appropriate to use the method proposed here.