Analytical study on functionally graded thickness tubes under external inversion process

The axial crushing of Functionally Graded Thickness (FGT) tubes under external inversion process is studied analytically, and their results have been checked with experimental and Finite Element (FE) simulation results. Employing doubly curved shell theory and using rigid-perfectly plastic (R-PP) material idealization, a theoretical solution is derived for the crushing inversion load of a variable thickness distribution tube. Experimental tests are carried out by employing tubes with linearly variable thickness distribution, and their results compared with analytical model. It is seen that the obtained results from experiments and theoretical model show excellent agreement. To evaluate nonlinear thickness patterns behavior, numerical simulations are carried out using the explicit FE code LSDYNA. It was found that FE simulations and theoretical analysis have reasonable correlation. Finally, the study was extended to find out the most accurate loads of thickness functions that the proposed theoretical model is predicted. The results show that the predicted theoretical loads of concave and linear thickness distribution have more precision with respect to convex function based on the FE and experimental results.