In this paper, we study the analysis of the large beam deformation (FGM) under the uniform transverse loading. The mechanical properties of the beam including the modulus of elasticity and the Poisson coefficient are a function of the thickness of the beam (The Power Distribution Law). Principle equations for the FG-beams are obtained using the Von-Carmen theory for large deformities. The results are obtained by minimizing the total potential energy and solving it. The numerical examples are presented for this method. In this paper, the effect of material properties on the stress basin is examined from a thickness perspective. It discusses the effects of nonlinear terms in strain-relational relations.

In this study a new numerical-analytical method for elasto-plastic and plastic modelling and simulating of FG beams is presented. The functionally graded (FG) beam composed of ten layers through the thickness and it is assumed that the mechanical properties of the beam vary through the thickness described by a simple power law distribution in terms of the volume fractions of constituents. The beam is assumed to be under transverse pressure load. In this paper a new method is presented based on linearization of the nonlinear part of the stress-strain curve of the material of the layers of the FG beam and using the elastic relations for bending analysis of beams. Numerical results for functionally graded beam are given and results of this paper for homogeneous beam are compared with other methods and good agreement is obtained between them. In addition, the effects of material properties on the stress field through the thickness of the FG beam are determined and discussed.

In this paper, deep drawing process of functionally graded sheet is investigated analytically and using finite element method. Using equations for deep drawing of isotropic sheets and governing equations of functionally graded materials, equations for deep drawing of functionally graded sheets are derived. Mechanical properties of the functionally graded sheet vary through the thickness of it according to the exponential law distribution. Punch force and axial stresses at the wall are calculated by this analytical method. Also, using this force in abaqus software, axial stresses at the wall are determined. The results of two methods were compared with each other and good agreement was obtained.