Discrete and Continuous Models for Dry Masonry Columns
Publication: Journal of Engineering Mechanics
Volume 123, Issue 4
Abstract
The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length–block-height (L/h) ratios bigger than 2π. The theory based on systematic differential approximation remains accurate up to L/h= 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h< 2π. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Apr 1, 1997
Published in print: Apr 1997
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