Buckling Analysis of Functionally Graded Beams under Combined Loadings

This paper investigates the buckling behavior of axially functionally graded (FG) material beams subjected to combined loads with various boundary conditions. The classical beam theory is employed for the analysis, and material properties are described using power law equations. The governing equation for buckling of FG beams was derived using the energy method and solved by using the generalized differential quadrature (DQ) method. The current study explores the buckling problem of FG beam under combined loadings, focusing on the interplay of gradient index, parameter $np$ and boundary conditions. The results demonstrate that the buckling resistance of functionally graded beams is enhanced with an increase in the gradient index. For functionally graded beams with a fixed parameter $np$, the critical buckling load exhibits a nonlinear increase with the gradient index. On the other hand, for functionally graded beams with a fixed material distribution, the critical buckling load decreases almost linearly with the parameter $np$, and the slope of this linear relationship is determined by the gradient index and the boundary conditions. This study provides valuable insights into the buckling behavior of functionally graded beams under combined loads, offering guidance for the design and optimization of such beams in engineering applications.