analytical and numerical instability analysis of functionally graded low-carbon steel

An algorithm is proposed for predicting the instability of functionally graded low-carbon steel with gradient work hardening exponent (n) and strength coefficient (k). the investigated work hardening exponent and strength coefficient of the functionally graded material (fgm) vary through the cross-section as a function of radius. numerical methods like the simpson rule of integration were utilized to solve the equations. the mathematical and experimental results are compared, and it can be seen that the algorithm has a reliable consistency with the experimental results. the instability of more complicated fgms can be predicted with the present algorithm.