Quantifying Domain Uncertainty in Linear Elasticity

Abstract

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 503-523, June 2024.
Abstract.The present article considers the quantification of uncertainty for the equations of linear elasticity on random domains. To this end, we model the random domains as the images of some given fixed, nominal domain under random domain mappings, which are defined by a Karhunen–Loève expansion. We then prove the analytic regularity of the random solution with respect to the countable random input parameters which enter the problem through the Karhunen–Loève expansion of the random domain mappings. In particular, we provide appropriate bounds on arbitrary derivatives of the random solution with respect to those input parameters. These enable the use of state-of-the-art quadrature methods to compute deterministic statistics of quantities of interest, such as the mean and the variance of the random solution itself or the random von Mises stress, as integrals over the countable random input parameters in a dimensionally robust way. Numerical examples qualify and quantify the theoretical findings.