Elastostatics of a half-plane under random boundary excitations

Abstract

A stochastic analysis of an elastostatics problem for a half-plane under random white noise excitations of the displacement vector prescribed on the boundary is given. Solutions of the problem are inhomogeneous random fields homogeneous in the longitudinal direction. This is used to model the displacements and represent their correlation tensor via spectral expansion. This approach makes it possible to derive exact representations for other functionals of interest, in particular, the vorticity, the strain tensor, and the elastic energy.