軟鐵磁彈性半平面受機械力激發之擾態磁感

Magnetic fields generated by a mechanical singularity in a magnetized elastic half plane

任承緯(Cheng-Wei Ren)

指導教授 ： 葉超雄

國立臺灣大學/工學院/土木工程學研究所/博士(2008年)

https://doi.org/10.6342/NTU.2008.10239

摘要

本論文採用Pao與Yeh於1973年發表的軟鐵磁彈性線性化理論，主要推導異向性磁化半平面受機械力或差排所激發的擾態磁感。
1987年，Yeh引用此理論推得了等向性磁化半平面受集中力、力雙極及力偶所激發的擾態磁感的封閉解。1988年他的學生黃國將延伸此問題至外加傾斜磁感應場的情況，惟所述的問題皆為等向性的材料。本文再擴大此課題，除了補充等向性磁化半平面受差排受激發的擾態磁感外，並討論異向性磁化半平面受外加傾斜磁感應場因基本機械力、廣義機械力及差排所激發的擾態磁感，再進一步討論當基本械械力與廣義機械力為任意方向時的情形。
基於Lin與Yeh（2002）假設擾態磁感對變形影響很小則含裂縫之等向性磁化半平面受均勻磁感及機械張應力的問題可等價成受磁荷載及機械張應力的純彈性問題，再利用差排密度函數方法透過編制Fortran程序後解得沿裂縫分布的差排密度，由此給出裂縫尖端的應力強度因子並進一步利用所推得等向性磁化半平面受集中差排所激發的擾態磁感為基本解沿裂縫長度積分後得到半平面邊界處的擾態磁感分布。

關鍵字

Pao－Yeh線性化磁彈性理論 ； 擾態磁感 ； 橫向等向性 ； 半平面 ； 裂縫 ； 差排密函數方法

並列摘要

The linear theory for a soft ferromagnetic elastic solid with multi-domain structure, which has been developed by Pao and Yeh (1973) is adopted to investigate some topics like magnetic inductions generated by generalized mechanical forces in the transversely isotropic magnetized elastic half-plane and oblique edge crack subjected to uniform magnetic induction and uniform mechanical tension.
By applying the Fourier transform technique, the exact solutions for the generated magnetic induction due to various mechanical singularities such as single force, a dipole, single couple and dislocations are obtained in a closed form.
A problem of magnetic induction generated by an oblique crack which is embedded in a magnetoelasticity half-plane is solved in two steps. Firstly, we change the original problem to a purely elastic case, i.e. the magnetic field is transformed to loading form the boundary conditions. Then, by applying the distributed dislocation technique, we can get the dislocation density function along the crack. Finally, we use this function as weight to integrate along the crack with green function solved in the first chapter, the magnetic induction along the free surface can be obtained numerically. The stress intensity factor can be obtained at the same time.

並列關鍵字

Pao-Yeh linearized magnetoelastic theorem ； perturbation of magneitc induction ； transversely isotropic ； half-plane ； crack ； distributed dislocation technique

參考文獻

劉晉奇. (2005). 含界面裂紋之雙磁電彈楔形結構反平面破壞分析, 博士論文, 成功大學.

Yeh, C. S., Teng, T. J., Shyu, W. S. and Ren, C. W. (2007). The stress distribution around the cavity of magneto-elastic medium subjected to magnetic field. Journal of Aeronautics, Astronautics and Aviation, 39(3), 215-223.

Hutter, K. and van de Ven, A. A. F. (1978). Field matter interactions in thermoelastic solids. Springer-Verlag, New York.

Alshits, V. I., Darinskii, A. N. and Lothe, J. (1992). On the existence of surface-waves in half-infinite anisotropic elastic media with piezoelectric and piezomagnetic properties. Wave Motion, 16(3), 265-283.

Bagdasarian, G. Y. and Hasanian, D. J. (2000). Magnetoelastic interaction between a soft ferromagnetic elastic half-plane with a crack and a constant magnetic field. International Journal of Solids and Structures, 37(38), 5371-5383.