STOCHASTIC BEM - RANDOM EXCITATIONS AND TIME-DOMAIN ANALYSIS

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.