Elastostatics of a half-plane under random boundary excitations
- Shalimova, Irina
- Sabelfeld, Karl
2010 Mathematics Subject Classification
- 65C05 65C20 65Z05
- Elastostatics of a half-plane, Random boundary excitations, Karhunen-Loeve expansion, partially homogeneous spectral tensor
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.