A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates

• A novel and simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of FGM plates is presented.
• A new simple first-order shear deformation plate theory is used.
• The effects of boundary conditions, gradient index, length-to-thickness ratio, etc. on geometrically nonlinear responses of plates are investigated.
• The proposed approach with several advantages is effective, highly accurate, free of shear-locking, etc. in geometrically nonlinear analysis.

This paper presents a novel approach based on isogeometric analysis (IGA) and a simple first-order shear deformation plate theory (S-FSDT) for geometrically nonlinear analysis of homogeneous and non-homogeneous functionally graded plates. Owing to many advantages such as (a) the S-FSDT is free of shear-locking, (b) less one unknown for the S-FSDT as compared with the conventional FSDT, (c) the awkward C1 continuity required for the generalized displacements is treated straightforwardly because of the nature of the higher-order continuity IGA method, the new formulation is thus effective in modeling the geometrical nonlinearities of plates. The S-FSDT is associated with the von Kármán strain for dealing with small strain and moderate rotation. Numerical validation is analyzed and numerical applications are considered. The obtained results are compared with reference solutions to show the accuracy and the effectiveness of the present approach. The effects of different boundary conditions, gradient index, length-to-thickness ratio, geometric shape, etc. on the geometrically nonlinear mechanical responses of functionally graded plates are investigated.