Buckling Simulation of Simply Support FG Beam Based on Different beam Theories

In this paper, a new model of beam was built to study and simulate the buckling behavior of function graded beam. All equations of motion are derived using the principal of the minimum total potential energy and based on Euler-Bernoulli, first and high order shear deformation Timoshenko beam theory. The Navier solution is used for simply supported beam, and exact formulas found for buckling load. The properties of material of FG beam are assumed to change in thickness direction by using the power law formula. The dimensionless critical buckling load is calculated analytically by the FORTRAN program and numerically by ANSYS software. In the beginning, the analytical and numerical results are validated with results available in previous works and it is also has very good agreement in comparison with and some researchers. In the present study, the lower layer of the graded beam is made up of aluminum metal. As for the properties of the rest of the layers, they are calculated based on the modulus ratios studied. The effect of length to thickness ratio, modulus ratio, and power law index on the dimensionless critical buckling load of function graded beam calculating by FORTRAN and ANSYS programs are discussed. The numerical analysis of function graded beam offers accurate results and very close to the analytical solution using Timoshenko Beam theory.