Exact large deformation and stress analysis of shrink-fit multi-layer thick-walled/sandwich pressurized hyperelastic cylinders

Abstract

The analytical closed-form solutions reflect the exact form of the dependency on the parameters and exhibit higher accuracy, extremely shorter computational times, and more problem-specific consistency in comparison to the finite-element-based results of the commercial computer codes, especially in the presence of constitutive, large deformation, and contact nonlinearities. In the present study, an analytical solution is proposed to treat the even more complicated problem of pressurized Mooney-Rivlin hyperelastic multilayer/sandwich cylinders that are composed of prestressed/shrink-fitted layers made of distinct hyperelastic materials. In contrast to the approximate finite element commercial computer codes, the material incompressibility and continuity conditions of the interfacial radial displacements and stresses can exactly be incorporated in the developed closed-form exact formulation. Moreover, an adaptive Newton-Brent robust numerical technique is employed to solve the resulting highly nonlinear equations. After verification of the results, the sensitivity of the resulting distributions of the deformations and radial, hoop, and axial stresses as well as the interfacial jumps in the hoop and axial stresses, against the stacking sequence of the layers, magnitude of the internal pressure, differences in the materials and thicknesses of the layers, and especially, the magnitudes of the shrink-fits are discussed in detail. Moreover, the influence and the effectiveness of the shrink-fit magnitude on the reduction of the resulting maximum hoop stresses are evaluated for different internal pressures. Results show that while proper shrink-fit values may mitigate the peaks of the interfacial hoop stresses of the compound multilayer hyperelastic cylinder, excessive magnitudes may lead to premature failures. Moreover, the shrink-fit/interference may lead to more uniform stress distribution and thus, more efficient pressure vessels from the design point of view.