Response Variability Of Stochastic Finite Element Systems

The response variability of finite element systems arising from the spatial randomness of the material properties is examined. The system is subjected to static loads of a deterministic nature. The problem is analyzed using the finite element method along with a first-order Neumann expansion of the stiffness matrix of the system. The covariance matrix of the response displacement vector is calculated analytically as a function of the number of finite elements. The finite element size necessary to obtain sufficiently accurate values of the stochastic response parameters is examined thoroughly. Various conclusions are drawn concerning the convergence of the coefficient of variation of the response strain to its final value as a function of the number of finite elements. The main advantage of the method is its computational efficiency, since all the response statistics are computed analytically and not through a Monte Carlo simulation.