Stress analysis of thick pressure vessel composed of functionally graded incompressible hyperelastic materials

• Analytical solution of pressurized thick spheres made of FG rubber is presented.
• Member of Ericksen׳s family of universal solutions has been used.
• Material properties vary in radial direction by power law function.
• Influence of inhomogeneity on thestress components distribution has been studied.
• Effect of the outer to inner radius ratio in stress components has been studied.

The present paper develops stress analysis of functionally graded hyperelastic thick spherical shell subjected to internal and external pressure. Hyperelastic behavior is modeled by using modified neo-Hookean strain energy function with variable material parameters. The material constants of strain energy function are graded along the radial direction based on a power law function. Material inhomogeneity parameter (m(m) is a power in the mentioned power law function. Material constant of strain energy function calculated from experimental data by using Levenberg-Marquardt nonlinear regression method. Stress components and stretches of spherical shell have been obtained for axisymmetric radial condition. Following this, profiles of extension ratio and stress components are plotted as a function of radius of sphere in the undeformed configuration for different material inhomogeneity parameter (m)(m). The obtained results show that the inhomogeneity properties of FGMs have a significant influence on the displacement, stretch and stresses distribution along the radial direction. Sensitivity of stress components and displacement field to applied pressure and outer to inner radius ratio of vessel (structure parameter) are also investigated and leads to the fact that outer to inner radius ratio has a great effect on the deformation field and stress components and is a useful parameter from a design point of view which can be tailored to specific applications to control the stress. Thus with selecting a proper mm value and structure parameter (B/A)(B/A), engineers can design a specific FGM hollow sphere that can meet some special requirements.

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