A Numerical Solution of a Circular Section Made of Functionally Graded Material (FGM) under a Transverse Load, with a Simple Support on the Radial Edges

The most important application of functionally graded materials (FGM) is in the aerospace industry, these materials at high temperatures are very resistant to stresses especially residual stresses. In this study, a numerical solution for a circular branch made of FGM material with simple supports on radial edges, under transverse load along the thickness line, is presented. For this purpose, based on the first-order shear deformation theory and the principle of minimum energy, the potential of the entire equations of equilibrium is obtained. These equations are not independent. It is formulated for ease in solving, re-formulation, and for a circular sector with simple supports in radial edges and are solved numerically for the various boundary conditions in the periphery edges of the sector. In fact, this study aims to singularity of stress in a near-zero radius with calculations that indicate this stress is infinite in the near-zero radius, so failure will not occur.