Stress State of Non-Thin Nearly Circular Cylindrical Shells Made of Continuously Inhomogeneous Materials

Abstract

The stress state of dented circular non-thin cylindrical shells under certain boundary conditions at the ends is analyzed. The shells are made of continuously inhomogeneous materials and subjected to uniform internal pressure. The three-dimensional linear elasticity problem is solved using methods of separation of variables, discrete Fourier series, and stable numerical discrete orthogonalization. The shell cross-section is described by the Pascal snail equation. The material of the shell is a continuously inhomogeneous material with a gradient profile where Young’s modulus varies quadratically across the thickness of the shell. The results on the stress state of circular shells of equal perimeter with and without a dent are compared.