This paper analyzes the elastic behavior of functionally graded thick truncated cones under axisymmetric hydrostatic internal pressure using Finite Element Method based on Rayleigh-Ritz energy formulation. The material transitions continuously from pure ceramic at the inner surface to pure metal at the outer surface. The figure shows tangential stress distribution at different layers of the cone for power law exponent n=0.1 and semi-vertex angle φ=15°, demonstrating how stress varies both radially through the thickness and axially along the cone length. The analysis reveals the effects of cone geometry and material gradation on displacement and stress distributions, providing insights for designing pressure vessels with optimized stress profiles.
Abstract
Finite Element Method based on Rayleigh-Ritz energy formulation is applied to obtain the elastic behavior of functionally graded thick truncated cone. The cone has finite length, and it is subjected to axisymmetric hydrostatic internal pressure. The inner surface of the cone is pure ceramic and the outer surface is pure metal, and the material composition varying continuously along its thickness. Using this method, the effects of semi-vertex angle of the cone and the power law exponent on distribution of different types of displacements and stresses are considered.
Keywords: functionally graded materials, truncated cone, Rayleigh-Ritz method, finite element analysis, hydrostatic pressure, stress distribution