Flexibility-based finite element analysis for structures with random material properties

In this paper, we propose a flexibility-based finite element formulation fo r beams with stochastic bending stiffness. We formulate the element-level f inite element equilibrium equation in terms of the element flexibility, so that the stochasticity appears on the right side of the equilibrium equatio n as the random flexibility. As a result, the unknown internal forces, whic h are dependent on the stochastic bending stiffness for statically indeterm inate beams, appear explicitly in the global finite element equilibrium equ ations. The internal forces associated with the mean stiffness are used to approximate the unknown internal forces in the process of computation. With the new formulation, the mean and covariance of the displacement for stoch astic beams can be directly calculated in terms of mean and covariance func tion of the flexibility, which can be evaluated from one-dimensional probab ility density function and the correlation function of the stiffness by the Monte Carlo simulation. The numerical example is given to illustrate the a dvantages of the new formulation over the conventional perturbation solutio n.