The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip
The Linear Magnetoelastic Problem of Two Coplanar Griffith Cracks in a Soft Ferromagnetic Elastic Strip
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DOI：
10.1115/1.3162073
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发表时间：
1982-03
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影响因子：
--
通讯作者：
Y. Shindo
中科院分区：
文献类型：
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作者：
Y. Shindo
根据软铁磁弹性固体的线性理论，我们考虑了含两个共面Griffith裂纹的软铁磁弹性材料无限长条中应力强度因子的确定问题。我们假定固体是均匀的各向同性固体，它被垂直于裂纹表面的均匀静磁场渗透，并且裂纹是由恒定的内压打开的。通过使用傅立叶变换，我们减少了问题的解决两个同时三重积分方程。这些方程被简化为第一类奇异积分方程。通过将解展开为第一类Chebyshev多项式级数与其权函数的乘积形式，奇异积分方程进一步化为确定未知系数的无穷代数方程组。进行了数值计算和磁场的应力强度因子上的影响，以图形方式显示的细节。
Following a linear theory for soft ferromagnetic elastic solids, we consider the problem of determining the stress-intensity factors in an infinite strip of a soft ferromagnetic elastic material containing two coplanar Griffith cracks. We assume that the solid is a homogeneous and isotropic one and it is permeated by a uniform magnetostatic field normal to the cracks surfaces and that the cracks are opened by a constant internal pressure. By the use of Fourier transforms we reduce the problem to that of solving two simultaneous triple integral equations. These equations are reduced to a singular integral equation of the first kind. By expanding the solution into the form of the product of the series of Chebyshev polynomials of the first kind and their weight function, the singular integral equation is further reduced to the infinite system of algebraic equations for the determination of the unknown coefficients. Numerical calculations are carried out and the influence of the magnetic fields on the stress-intensity factors is graphically shown in detail.