Mathematical solution for nonlinear cylindrical bending of sigmoid functionally graded plates

Problems of nonlinear cylindrical bending of sigmoid functionally graded plates in which material properties vary through the thickness are considered. The variation of the material properties follows two power-law distributions in terms of the volume fractions of constituents. The nonlinear strain-displacement relations in the von Kármán sense are used to study the effect of geometric nonlinearity. The governing equations are reduced to a linear differential equation with nonlinear boundary conditions, yielding a simple solution procedure. Numerical results are presented to show the effect of the material distribution on the deflections and stresses.