Deterministic Integration Algorithms For Stochastic Response Computations Of Non-Linear Systems

In stochastic analysis, the response is described by the mean and covariance function. Direct integration algorithms for the stochastic response computation, published since the development of the finite element methods, are applicable for MDOF-systems of FE-methods with few hundred degrees of freedom (DOF). First the stochastic central difference method has been suggested, followed by the stochastic Houbolt method and the stochastic Newmark algorithm. However, all these algorithms cannot be applied efficiently for FE-models with thousands DOFs, particularly for cases in which n is considerably larger than a few hundred, because of the huge number of required operations and also due to storage requirements.The method introduced in this paper employs deterministic integration algorithms together with the Karhunen-Loéve (K-L) representation for the covariance matrix. The deterministic vectors for the K-L representation can be integrated by any available deterministic step-by-step procedure. A relatively small number m<