Large variation finite element method for beams with stochastic stiffness

The behavior of beams with stochastic stiffness subjected to either deterministic or stochastic loading is studied via finite element method. The results are contrasted with exact solution to check the accuracy of the FEM for the case of large variations. It represents a generalization of the previous study in which the stiffness matrix was decomposed as a product of three matrices, two of which are numerical ones and the third matrix involves the uncertain stiffness analytically. To illustrate the proposed method, we evaluate the mean and the auto-correlation functions of the displacement of beams under various boundary conditions. Two statically determinate beams (clamped-free or simply-supported) and two statically indeterminate beams (clamped–simply-supported or clamped are both ends) are investigated in this study. The beams are subjected to a deterministic uniform pressure or a stochastic excitation.