Post buckling behaviour of functionally gradede beams under the influence of temperature

In this study, post-buckling behavior of functionally graded beams under the influence of temperature loading is investigated by using total Lagrangian finite element model of two dimensional continuum, three dimensional continuum and the Timoshenko beam element approximations. Material properties of the beam change in the thickness direction according to a power-law function. It is known that post-buckling problems are geometrically nonlinear problems. In this sudy, there is no retstriction on the magnitudes of deflections and rotations in the beam. Also, the temperature dependent material properties are investigated in this study. Hence, the considered problem is both geometrically and physically nonlinear one.The considered highly non-linear problem is solved by using incremental displacement-based finite element method in connection with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. As it is known, when the nonlinearity is strong, it is needed to apply the external load step by step. In this study, the above mentioned solution procedure is applied. The necessary computer programs are developed by using MATLAB program.Functionally graded materials are a new generation of composites that have many practical applications and much more attention has been given to this area in recent years. Functionally graded materials are especially used as thermal barriers: Therefore the design of functionally graded materials in the high thermal environments is very important.With the effects of material gradient property and thermal load, the relationships between deflections, thermal post-buckling configuration, critical buckling temperature and stress distributions through the thickness of the beams are illustrated in detail in post-buckling case. The difference between the results of total Lagrangian finite element model of two-dimensional continuum, three-dimensional continuum and total Lagrangian finite element model of Timoshenko beam element is investigated for functionally graded beams. Also, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case.