On the Ergodicity Assumption in an Applied Mechanics Problem

[+] Author and Article Information
A. Scheurkogel

Department of Mathematics, Delft University of Technology, Delft, The Netherlands

I. Elishakoff

Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel

J. Appl. Mech 52(1), 133-136 (Mar 01, 1985) (4 pages) doi:10.1115/1.3168982 History: Received October 01, 1983; Revised May 01, 1984; Online July 21, 2009


A deformation of a thin uniform cylindrical shell is considered under random axisymmetric loading. Mathematically this is equivalent to the study of a quasi-linear differential equation with random inhomogeneous term and random coefficient. The approximate method of solution, based on the assumption of ergodicity of the shell slope, is first described. It is shown that sometimes this assumption is valid but when not, it may yield non-negligible errors. In particular, it is shown via the exact solution that assumption of ergodicity of the shell slope is correct if the loading is ergodic in correlation. However, this assumption may yield an error of about 20 percent if the loading in ergodic in mean-square but not in correlation.

Copyright © 1985 by ASME
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