Large deformation and stability analysis of functionally graded pressure vessels: An analytical and numerical study

This paper develops stability and stress analysis of hyperelastic thick-walled pressure vessel made of isotropic, incompressible functionally graded material. Among all existing energy density functions, the exp–exp form including exponential terms is selected to model the hyperelastic behavior due to its appropriate compatibility with experiments. All stress components are obtained both analytically and numerically. Furthermore, the stress components for homogenous and functionally graded vessels are presented and compared with each other. The results propose that functionally graded materials properties have a great effect on all stress components distribution and more importantly on their rate of changes throughout the thickness. Also, the snap-through instability is performed. A comprehensive study is carried out on sensitivity of stresses to the parameters of the material distribution function. It is shown that the two involved parameters in the selected material distribution function have a significant influence on the stress fields in an opposite manner. These results are useful from a design viewpoint, can be utilized in various industrial applications, to control stresses and avoid failure. To verify the proposed analytical results, the finite element method is employed in some cases. The results of the finite element method simulation and analytical solutions are shown to be in a good agreement.