Buckling analysis of cracked functionally graded material column with piezoelectric patches

In the current study, stability analysis of cracked functionally graded material (FGM) columns under the effect of piezoelectric patches is analytically investigated. Configuration of the patches is somehow chosen to create axial load in the column. The crack is modeled by a rotational massless spring which connects the two intact parts of the column at the crack location. After applying the boundary and compatibility conditions at the crack location and the ends of the piezoelectric patches, the governing equation of buckling behavior of the cracked FGM column is derived. The effect of important parameters on the first and second buckling load of the column such as crack parameters (location and depth), location and length of the patches and also applied voltage is studied and discussed. Results show that a crack significantly reduces the column load capacity which is dependent on location and depth of the crack. By applying static load to the column, piezoelectric patches produce local torque, and controlling this torque leads to reduced crack effects on the column. Using piezoelectric patches with proper location and length compensates the effect of the crack. Despite the first buckling load, positive voltage increases the second buckling load of the column.