Applicability of Empirical Tolerance Limit for Wrinkled-Membrane Distortions

摘要

This paper evaluates the applicability of the stochastic method to membrane-wrinkling problems. The stochastic method is used to compute a conservative upper bound of structural responses for membrane-wrinkling problems based on measurements at selected points. An empirical tolerance limit, which is defined as the value that exceeds the possible structural responses for at least a proportion of beta among all values with a confidence level of 50% (P beta/50), was applied. The spatial distribution of the wrinkled-membrane distortion, presented by point-to-point variation in the out-of-plane displacement at various points on the membrane surface, was investigated through a wrinkling analysis based on shell theory. A practical method for computing a conservative upper bound of the wrinkled-membrane distortions based on measurements at selected points was then proposed and evaluated for the wrinkling phenomena in three membrane models: a rectangular membrane under shear and tension loadings, a stretched circular membrane with a rotating center hub, and a square membrane subjected to corner tension loads. The calculated upper bounds approximately enveloped the wrinkled-membrane profile, confirming that this method provides a new and simple statistical approach for estimating highly nonlinear wrinkling behavior.