VECTORIAL COOPERATIVE RESPONSE SURFACE METHOD FOR STOCHASTIC ANALYSIS OF STRUCTURES

Conventional response surface methods (RSM) are of scalar type and usually developed for a specific random quantity at a given point attached to a stochastic structure. A vectorial response surface method called as a cooperative response surface method (CRSM) is presented and developed for a global nodal displacement vector so as to overcome the limitation of the conventional RSM. The Karhunen-Lo鑦e series is employed to expand the stiffness matrix and nodal force vector. A preconditioner is defined as the global stiffness matrix evaluated at the mean of the random field so that a preconditioned Krylov subspace can be determined. The nodal displacement vector could be expanded in the space and a vectorial cooperative response surface is developed so that the cooperativity still holds among the components in a displacement vector. The relationship between the compatible response surface and the polynomial chaos is presented so that the sample points can be defined. The explicit expressions are developed for the mean and covariance of the displacement vector. Examples demonstrate the high accuracy, global applicability and fast convergence of the cooperative response surface method.