Exact solutions to magneto-electro-thermo-elastic fields for a cracked cylinder composite during thermal shock

Abstract

This report derives the exact solutions for the problem of a magneto-electro-elastic cylinder with a penny-shaped and embedded crack subjected to transient thermal load. Thermal cracking is analysed in the theoretical framework of linear magneto-electro-thermo-elasticity. The heat conduction equation for a magneto-electro-thermo-elastic cylinder with a finite size is solved using the standard method of separation variables. The coupling magneto-electro-thermo-elastic fields are determined in a stationary case via the Hankel integral transform. Based on Abel’s integral equation and the dual integral equation, the mathematical formulations for the permeable crack conditions are derived. Solutions to the elastic, electric, and magnetic intensity factors are obtained. Due to the explicitness of these solutions, they are very interesting for the design and analysis of magneto-electro-thermo-elastic composites.