The Earthquake Engineering Online Archive

The use of load dependent vectors for dynamic and earthquake analyses

Leger, Pierre; Wilson, Edward L.; Clough, Ray W.

UCB/EERC-86/04, Earthquake Engineering Research Center, University of California, Berkeley, 1986-03, 263 pages (555.1/L38/1986)

This report investigates practical computer implementation aspects of the Ritz reduction method developed by Wilson, Yuan, and Dickens (WYD), its convergence characteristics, and its extension to more general forms of loading and analyses. First, a formal mathematical framework for the WYD Ritz reduction method is established by showing that the algorithm used to produce WYD Ritz vectors is similar to the method used to produce Lanczos vectors. Error norms to measure the representation of the spatial distribution of the dynamic load achieved by truncated WYD Ritz bases and to establish a relationship between WYD Ritz solutions and exact eigensolutions are developed. Computational variants to generate load-dependent vector bases for dynamic analyses are then studied. Theoretical developments and computational procedures to apply the proposed Ritz reduction method to three-dimensional earthquake response spectra analysis, to analysis of systems subjected to multi-spatial dynamic load distributions, to multilevel substructure analysis, and to nonlinear dynamic problems are presented. Comparisons between Ritz solutions and traditional eigensolutions are presented.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-86-04.pdf (16 MB)