基于拓扑优化的单边核磁共振永磁磁体研究

为了在单边核磁共振仪器外产生梯度恒定的磁场，提出利用基于拓扑优化和有限元法的优化设计方法。通过伴随变量法推导出永磁系统中拓扑设计灵敏度的解析表达式，在连续性拓扑灵敏度分析的基础上，利用罚函数法来优化单边核磁共振仪器永磁磁体的磁化方向。数值结果表明，提出的优化方法能使单边核磁共振仪器外产生梯度恒定的磁场。

Topology Optimization in the Arrangement of Permanent Magnet Array for Unilateral NMR

To obtain a constant gradient magnetic field outside unilateral nuclear magnetic resonance(NMR),optimal design method based on finite element method(FEM) and topology optimization is proposed. Topology design sensitivity in terms of design variables of permanent magnetic system is derived analytically using the adjoint variable method. Then coupled with continuum topology sensitivity analysis,penalty-function method is employed to find an optimized distribution of the direction of magnetization of the permanent magnets of unilateral NMR. Numerical study shows the effectiveness of the proposed optimal design method.