Stepwise solution for buckling of stepwise axially graded beam with linear pattern of material gradation subjected to piecewise axial load function

The various benefits over the conventional composite laminates attract many researchers to study behaviors of the structural members made up of functionally graded materials (FGMs). These materials have continuous variation of thermo-mechanical properties due to varying the microstructure or atomic order with a specific gradient. These kinds of materials are designed to achieve specific properties for specific applications. The buckling analysis of thin beam with axial gradation required more computational efforts than transverse gradation. Current study investigates the effects of stepwise linear material gradation in the axial direction and piecewise axial compressive load function on the buckling of Euler-Bernoulli beam. The various boundary conditions at beam ends are considered. Moreover, the natural conditions at insertion point of the concentrated load are satisfied. The stepwise solution is employed to obtain characteristic equation, buckling loads and corresponding mode shapes. The numerical example is conducted and diagrams of critical and higher buckling mode shapes are depicted.

Keywords:

Buckling , Stepwise axially graded beam , Linear material gradation , Piecewise axial load function , Stepwise solution