Uncertainty quantification of thermo-elastic free vibration of cracked functionally graded plates using SXFEM approach

This paper reports the study of uncertainty quantification of thermo-elastic free flexural vibration of cracked functionally graded (FG) plates for uncertain material parameters. A novel approach called stochastic extended finite element method (SXFEM) based on higher-order shear deformation theory for the thermal environment is developed. The first-order perturbation technique is incorporated in extended finite element formulation for stochastic free vibration analysis. To track the location of the crack in the domain, a level set function is implemented. The partition of unity technique is employed to make enrichment possible that is the augmentation of the primary variable with additional functions. The material modelling of functionally graded plate is done using the power law and the gradation of material properties is considered only in the thickness direction. First, the efficacy and accuracy of the presently developed formulation are checked by performing the convergence and validation study. Numerical analysis is performed to investigate the influence of the thermal environment and material uncertainty on the stochastic natural frequency of the FG plate. Numerical results are obtained for various parameters such as uncertain material properties, various temperatures, crack sizes, various boundary conditions, and gradient indices.