Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C0-HSDT

• CS-MIN3 is extended to geometrically nonlinear analysis of FGPs.
• Nonlinear formulation is based on the C0-HSDT and the von Kármán strains.
• Thermal and mechanical loads are considered and a two-step procedure is performed.

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-MIN3 is extended to geometrically nonlinear analysis of functionally graded plates (FGPs) subjected to thermo-mechanical loadings. In the FGPs, the material properties are assumed to vary through the thickness by a simple power rule of the volume fractions of the constituents. The nonlinear formulation is based on the C0-type high-order shear deformation plate theory (C0-HSDT) and the von Kármán strains, which deal with small strains and moderate rotations. In the analysis process, both thermal and mechanical loadings are considered and a two-step procedure is performed including a step of analyzing the temperature field along the thickness of the plate and a step of analyzing the geometrically nonlinear behavior of the FGPs subjected to both thermal and mechanical loadings. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of available other numerical results.