A stochastic finite element dynamic analysis of structures with uncertain parameters

Abstract

The real life structural systems are characterized by the inherent uncertainty in the definition of their parameters in the context of both space and time. In the present study a stochastic finite element method has been proposed in the frequency domain for analysis of structural dynamic problems involving uncertain parameters. The harmonic forces as well as earthquake-induced ground motion are treated as random process defined by respective power spectral density function. The uncertain structural parameters are modelled as homogeneous Gaussian stochastic field and discretized by the local averaging method. The discretized stochastic field is simulated by the Cholesky decomposition of respective covariance matrix. By expanding the uncertain dynamic stiffness matrix about its reference value the Neumann expansion method is introduced in the finite element procedure within the framework of Monte Carlo simulation. This approach involves only single decomposition of the dynamic stiffness matrix for entire simulated structure. Thus a considerable saving of computing time and the facility that several stochastic fields can be simultaneously handled are the basic advantages of the proposed formulation. Numerical examples are presented to elucidate the accuracy and efficiency of the proposed method with the direct Monte Carlo simulation.