Spectral stochastic isogeometric analysis of bending and free vibration of porous functionally graded plates

In this paper, a systematic spectral stochastic isogeometric analysis (SSIGA) process is presented for the static bending and free vibration analyses of functionally graded (FG) plates with three-dimensional (3D) random porosity. The porosity is modeled as a Beta random field, represented compactly via the Karhunen-Loève expansion. A novel hierarchical locking-free quasi-3D shear deformation theory, called spectral displacement formulation (SDF), is proposed to approach exact 3D solutions and reflect more realistic effects of the random porosity field (RPF). Isogeometric analysis is utilized to meet the C¹-continuity requirement of the SDF. The response surfaces of the porous FG plates are constructed non-invasively by the spectral collocation method. A new spectral stochastic post-processing process is developed to evaluate the probability characteristics of the responses and exclude the adverse convergence-in-probability property, which typically exists in sampling-based methods. Numerical examples illustrate the SSIGA process and demonstrate its effectiveness. The influences of the RPF parameters and the gradient index on the response statistics are investigated.