## Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the $$\mathrm{C}^0$$-HSDT.(English)Zbl 1296.74124

Summary: 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 $$\mathrm{C}^0$$-type high-order shear deformation plate theory ($$\mathrm{C}^0$$-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.

### MSC:

 74S05 Finite element methods applied to problems in solid mechanics 74K20 Plates
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