Geometrically nonlinear analysis of arbitrarily straight-sided quadrilateral FGM plates

The problem of large deformation of arbitrarily straight-sided quadrilateral functionally graded material (FGM) plates is studied. The analysis is carried out using the IMLS-Ritz method. Because the plate considered is of moderate thickness, the first-order shear deformation theory (FSDT) is employed. Based on the IMLS-Ritz approximation, the discrete nonlinear governing equation for the large deformation is derived. The nonlinear solution to the quadrilateral FGM plates is obtained by solving the discrete equation through the hybrid arc-length iterative procedure with the modified Newton-Raphson method. The validity and accuracy of the numerical results are established through convergence and comparison studies. The effects of plate thickness-to-width ratio, geometry and volume fraction ratio on the large deformation behavior of the FGM plates under various boundary conditions are examined.