Strain Gradient Elasticity Solution for Functionally Graded Micro-cylinders

TL;DR

This paper develops a strain gradient elasticity model for functionally graded micro-cylinders, deriving a fourth-order differential equation and analyzing how material length and grading affect stress and displacement.

Contribution

It introduces a novel analytical solution for FG micro-cylinders using strain gradient elasticity, highlighting the influence of characteristic length and grading on stress distribution.

Findings

Characteristic length significantly affects stress distribution.

Increasing length parameter reduces maximum stresses.

FG power index impacts maximum radial and tangential stresses.

Abstract

In this paper, strain gradient elasticity formulation for analysis of FG (Functionally Graded) micro-cylinders is presented. The material properties are assumed to obey a power law in radial direction. The governing differential equation is derived as a fourth order ODE. A power series solution for stresses and displacements in FG micro-cylinders subjected to internal and external pressures is obtained. Numerical examples are presented to study the effect of the characteristic length parameter and FG power index on the displacement field and stress distribution in FG cylinders. It is shown that the characteristic length parameter has a considerable effect on the stress distribution of FG micro-cylinders. Also, increasing material length parameter leads to decrease of the maximum radial and tangential stresses in the cylinder. Furthermore, it is shown that the FG power index has a significant effect on the maximum radial and tangential stresses.