VARIATIONAL-PRINCIPLES DEVELOPED FOR AND APPLIED TO ANALYSIS OF STOCHASTIC BEAMS

In the present paper the deterministic governing equations and boundar y conditions for mean and covariance functions of the displacement for statically determinate beams with spatially varying stochastic stiffn ess are derived. The corresponding variational principles for the mean and covariance functions of the displacement are established. Based o n the governing equations or variational principles, Galerkin and Rayl eigh-Ritz methods are proposed to find probabilistic characteristics o f the response. Several problems involving stochastic stiffness are ex emplified. It is suggested that the displacements :corresponding to an associated deterministic beam, which possesses the same geometry and load as the original beam but has deterministic stiffness, be adopted as the trial functions in Galerkin or Rayleigh-Ritz formulation. Examp les show that statically determinate beams with stochastic stiffness c an be effectively analyzed by the proposed approximate methods. The ag reement between the solutions obtained by the Galerkin or Rayleigh-Rit z method and the-exact solutions is extremely good.