On the Ergodicity Assumption in an Applied Mechanics Problem

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.