The Earthquake Engineering Online Archive

A reduction scheme for problems of structural dynamics

Hughes, Thomas J. R.; Hilber, Hans M.; Taylor, Robert L.

UCB/SESM-1975/09, Dept. of Civil Engineering, University of California, Berkeley, 1975-09-01, 35 pages

A method for reducing the size of finite element systems in dynamics is presented. The technique is based upon a variational theorem in which it is admissible to describe the inertial properties of structures by way of independent displacement, velocity and momentum fields. This theorem allows us to construct reduced systems for problems in structural mechanics which retain the full rate of convergence of systems employing "consistent" mass matrices. In particular, we are able to make precise the engineering intuition regarding the "inefficiency" of rotatory degrees-of-freedom in dynamics, i.e. for the common beam, plate and shell elements, rotatory degrees-of-freedom may be entirely eliminated while retaining full rate of convergence. An error analysis of the scheme and numerical examples are presented.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-75-09.pdf (3 MB)