On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis

We investigate new numerical results of thermal buckling for functionally graded plates (FGPs) with internal defects (e.g., crack or cutout) using an effective numerical method. The new formulation employs the first-order shear deformation plate theory associated with extended isogeometric analysis (XIGA) and level sets. The material properties of FGPs are assumed to vary continuously through the plate thickness obeying a power function. The internal defects are represented by the level sets, while the shear-locking effect is eliminated by a special treatment, multiplying the shear terms by a factor. In XIGA, the isogeometric approximation enhanced by enrichment is cable of capturing discontinuities in plates caused by internal defects. The internal discontinuity is hence independent of the mesh, and the trimmed NURBS surface to describe the geometrical structure with cutouts is no longer required. Five numerical examples are considered and numerical results of the critical buckling temperature rise (CBTR) of FGPs computed by the proposed method are analyzed and discussed. The accuracy of the method is demonstrated by validating the obtained numerical results against reference solutions available in literature. The influences of various aspect ratios including gradient index, crack length, plate thickness, cutout size, and boundary conditions on the CBTR are investigated.