Multi-directional functionally graded materials for enhancing the durability of shell structures

Uni-directional functionally graded materials (FGMs) providing a relative change in terms of material properties have been implemented in many high-tech engineering applications, including shells and plates. As a new concept, multi-directional FGMs highlight the emergence of modern materials design in the development of multi-functional materials. Pressure vessels made of materials varying in the radial direction have been comprehensively studied. In some practical instances, however, tailored grading of material properties is required in other directions. Shells with bi-dimensional FGM properties can present practical problems arising from excessive temperature gradients and extreme deflections. In this work, asymmetric deformations of two-directional FG pressure vessels under the effect of thermo-mechanical loads are studied numerically, taking advantage of Fourier and polynomial quadrature methods. Unlike most published research on this topic, we assume that the material properties of the shell are graded in the radial and axial directions obeying an exponential formulation, leading to a more accurate simulation of the real work condition. Governing equations are formulated based on three-dimensional elasticity theory, discretised into the series form, and then the resulting equations are solved. To evaluate the accuracy and superiority of this approach, numerical results are obtained and compared with exact solutions for material properties defined by the power law and are found to be in good agreement. In the results section, it is shown that variations of the grading parameter, temperature shock, geometry profile and boundary conditions play important roles in the distribution of stress, displacement and temperature fields. In the context of the thermoelastic theory of shells and plates, the results of this work will provide a reliable database for design engineers to choose a desirable material property function, changing throughout different directions of the geometry, to mitigate thermal stresses, which should be as small and uniform as possible.