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.

该报告为瞬态热载荷作用下，具有一个便士形和嵌入裂纹的磁电弹性圆柱体问题提供了精确的解决方案。在线性磁电热弹性的理论框架内分析了热裂纹。使用标准的分离变量方法，可以求解具有有限大小的磁电热弹性圆柱体的热传导方程。磁电热弹性耦合场在固定情况下通过汉克尔积分变换确定。基于Abel积分方程和对偶积分方程，推导了渗透裂纹条件的数学公式。获得了弹性，电和磁强度因子的解。由于这些解决方案的明确性，