Spectral stochastic finite element vibration analysis of fiber-reinforced composites with random fiber orientation

Fiber-reinforced composites exhibit random fiber orientations due to the manufacturing tolerances. The present study concerns with a numerical investigation of the vibrational behavior of the long fiber-reinforced composites under uncertainty in fiber orientations. The basic constitutive equations of laminate theory based on the first-order shear deformation are developed in stochastic form. It is assumed that each ply-orientation exhibits individual spatial and random variations from the nominal mean value. These lead to local variations in mechanical properties such as structural stiffness and mass matrices and, accordingly, in structural responses. The finite element formulation utilizes the spectral stochastic discretization in the sense that the random fiber orientations are approximated by a truncated Karhunen–Loève expansion. The expansion provides a framework to capture the spatial and random variations. The generalized polynomial chaos with unknown deterministic coefficients is employed to represent the structural responses. The coefficients are estimated using probabilistic collocation points where any deterministic in-house code or commercial FEM package can be treated as a black-box for the modeling and analysis of structure. A numerical case study is used to illustrate the features of the method, where impact of the uncertainty in fiber orientations on the natural frequencies and mode shapes of a 12 plies rectangular composite plate with nominal orientation of [0/90]s[0/90]s is investigated.