FINITE-ELEMENT METHOD FOR STOCHASTIC BEAMS BASED ON VARIATIONAL-PRINCIPLES

This paper proposes a new version (fundamentally different from the ex isting ones) of finite element method for the mean and covariance func tions of the displacement for bending beams with spatially random stif fness. Apart from the conventional finite element method for stochasti c problems, which utilizes either perturbation or series expansion tec hnique or the Monte Carlo simulation, the present method is based on t he newly established variational principles. The finite element scheme is formulated directly with respect to the mean function and covarian ce function, rather than perturbed components of the displacement. It takes into account an information on joint probability distribution fu nction of the random stiffness to obtain the covariance function of th e displacement. Therefore, the accurate solution can be obtained even if the coefficient of variation of the random stiffness is large, in c ontrast to conventional technique. Several examples are given to illus trate the advantage of the proposed method, compared with the conventi onal ones.