Analytical and numerical analysis of solid cylinder made of radially nonuniform material under extension

Functionally Graded Materials (FGMs) are a class of engineered materials characterized by a spatial variation of composition and microstructure aiming at controlling corresponding functional (i.e. mechanical, thermal, electrical, etc.) properties. The tailored gradual variation of microstructural features may be obtained through non-uniform distributions of the reinforcement phase(s) with different properties, sizes and shapes, as well as by interchanging the role of reinforcement and matrix materials in a continuous manner. They are used in specialized industries such as: Industries dealing in automobile, defence sectors, and structural components but notably, in the aerospace industry, due to their unique response to thermal loads which are very prominent during spacecraft flights. The use of FGMs is in increasing interest, and proper modelling of FGMs is becoming a prominent development topic. This paper proposes two solutions for modelling FGMs using COMSOL Multiphysics and Maple, which are developed for each case: a numerical solution and an analytical solution to study the functional gradient material properties, such as: Young's modulus, axial stress which are assumed to vary in the radius direction according to a radial variation law known as: linear law, power law and exponential law. The solutions are compared and the results obtained are very accurate.