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The complex function method is employed to establish a mechanical model for pressurized thick-wall cylinders made of functionally graded materials (FGM). This model is applicable to all radial varying modes of material properties, including both continuous and discontinuous variations in Young’s modulus and Poisson’s ratio. The main concept behind this mechanical model involves dividing the thick-walled cylinder into concentric thin cylinders, each equipped with a pair of analytical functions representing stress functions. By imposing continuity conditions between adjacent thin cylinders and considering the stress boundary conditions of the entire structure, all unknown forms of analytical functions can be determined. Subsequently, by establishing the correspondence relationship between these analytical functions and stress or displacement, it becomes possible to solve for the stress or displacement at any radial position within the thick-walled cylinder. Through comparison and verification against the numerical simulation results, it can demonstrate that as long as the differential scale is sufficiently small, high accuracy can be achieved in the final result. In other words, solutions obtained for multi-layered hollow cylinder converge toward those obtained for continuously graded thick-walled cylinder. Notably, by starting from the level of stress function and avoiding complex differential and integral equations, a linear equation system can provide information on stress and displacement distributions along the radial direction. Therefore, compared to other solving methods available, this proposed approach offers simplicity and applicability.
Liu et al. (Fri,) studied this question.