On finite element analysis of beams with random material properties

A procedure for the linear finite element analysis of a prismatic beam having random material property is described in this paper. Due to the fact that the material property is described by a random function along the length of the beam and the direct functional form of its variation is unknown, the integration of the strain energy expression may not be possible. This makes the problem very complex and the exact form of the stiffness matrix cannot be obtained. To analyze such structures, the stiffness matrix is derived in two parts. The first part is deterministic and the second part contains spectral moments of the power spectral density function of the random variable in addition to the geometric and material properties of the beam. The solution is obtained using the Taylor series expansion. A numerical procedure to include inter-element correlation is also described in detail. The numerical results involving the variability of the response of beams under different deterministic loads and boundary conditions are obtained and found to agree well with the published data in the literature.