同心球壳-球体系感应磁场的解析解

考虑薄壳体和非薄壳体结构的感应磁场可提高舰艇感应磁场数值建模精度,开发相应的磁场数值程序包时,磁场解析解模型是验证程序包数值准确性的有效手段。同心球壳-球体系模型是验证同时考虑薄壳体和非薄壳体感应磁场数值准确性的理想模型。基于分离变量法推导了该模型感应磁场的解析解,以积分方程法和有限元法为参照,解析解误差均在5%以内,表明了导出解析解表达式的准确性。

Analytical Solution of the Induced Magnetic Field of Concentric Shell Sphere and Solid Sphere System

The magnetic field numerical model for a naval vessel can be more accurate when the induction field of thin shell structures and non-thin shell structures are both considered. A numerical software program should be developed for induced magnetic field, the analytical model is an effective mean to validate the accuracy of the numerical software program. The concentric shell sphere and solid sphere system model is suitable mean for checking the accuracy of the numerical indeucd magnetic field of thin shell strutures and non-thin shell structures. Based on the separated variable method, the analytical solution of the concentric shell sphere and solid sphere system model is deduced. Taking the results from the integral equation method(IEM) and finite element method(FEM) as references, the errors of analytical solution are both less than 5%, which demonstrates the deduced analytical solution correctly.