Boundary element formulations for the treatment of boundary value prob
lems in 2-D elasticity with random boundary conditions are presented.
it is assumed that random boundary conditions may be described as seco
nd order random fields that possess finite moments up to the second or
der. This permits the use of the mean square calculus for which the op
erations of integration and mathematical expectations commute. Spatial
ly correlated, time-independent and time-dependent boundary conditions
are considered. For time-independent boundary conditions, the stochas
tic equivalent of Somigliana's identity is used to obtain deterministi
c integral equations for mathematical expectations and covariances of
the response variables, and crosscovariances of the response variables
with respect to prescribed boundary conditions. The random held used
to describe the boundary conditions is discretized into a finite set o
f random variables defined at the element nodes. Quadratic, conforming
boundary elements are used to arrive at discretized equations for the
response statistics of unknown boundary variables. These values may t
hen be used to calculate the response statistics of internal variables
and boundary stresses. For time-dependent, spatially correlated bound
ary conditions, the stochastic equivalent of Stokes's time-domain inte
gral representation is used to obtain deterministic integral equations
for the response statistics of unknown boundary variables. An approxi
mate procedure for the calculation of the covariance matrix, that redu
ces the number of matrix operations and computer storage requirements,
is developed. The derivations for the treatment of boundary condition
s that are random in time and may be described as an evolutionary whit
e noise are also presented.