A Copula-based perturbation stochastic method for fiber-reinforced composite structures with correlations

Under most circumstances, there are correlations among random variables for composite structures, and these correlations can have a considerable effect on the reliability analysis result. Consequently, a Copula-based perturbation stochastic method is proposed to amend the disability of traditional perturbation stochastic method on correlation problems. As a statistical tool, Copula function meets the intrinsic demand of fiber-reinforced composite structures on variable's correlation and allows the choice of joint cumulative distribution functions (CDFs) to be separate from the marginal CDFs. With the aid of change-of-variable technique, Copula is introduced straightly into the framework to describe the relevance without any special transformation. Besides, the probability curves and reliability index of multi-variables of Gaussian and non-Gaussian can be achieved easily. Furthermore, in order to significantly improve the efficiency and capability to resist the mesh distortion compared with the traditional stochastic FEM, strain matrices are reconstructed by the edge-based smoothing technique. The overall uncertain condition coupled by stochastic fiber orientations, material parameters, and external loads is analyzed. Several examples are provided to verify the validity of the method.