Random field models of geometrically imperfect structures with “clamped” boundary conditions

The subject of the paper is the stochastic modeling of geometrical imperfections of one- and two-dimensional structures. The imperfections are considered as initial deflections from a perfect axis of a bar or a mid-surface of a plate. The main goal is to define random field models whose sample paths satisfy clamped boundary conditions. The approach based on conditional random fields is adopted and formulas allowing conditioning on derivatives of the random fields are presented. Conditions for random field sample differentiability are discussed as well. The proposed approach is illustrated with a numerical example.