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20.01.2020 | Correction
Correction to: Bonded contact and general crack problems in generalized materials and their relationships
Erschienen in: Meccanica
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Excerpt
Due to an unfortunate turn of events, Eqs. 52, 155, 156 and 157 contain errors. Please find below the correct version of the equations mentioned that should be regarded as the final version by the reader.
$$ \begin{aligned}&\int_{S}\int K_{31}^{0}(x_{1}-x_{10},x_{2}-x_{20})u_{10}(x_{10},x_{20})dx_{10}dx_{20} \\&\quad +\int_{S}\int K_{32}^{0}(x_{1}-x_{10},x_{2}-x_{20})u_{20}(x_{10},x_{20})dx_{10}dx_{20} \\&\quad +\int_{S}\int K_{33}^{0}(x_{1}-x_{10},x_{2}-x_{20})u_{30}(x_{10},x_{20})dx_{10}dx_{20}=\sigma_{33}, \end{aligned} $$
(52)
$$ \int_{-\infty }^{\infty }\int_{-\infty }^{\infty }\frac{\xi_{1}^{2}}{\left( \xi_{1}^{2}+\xi_{2}^{2}\right)^{3/2}}\exp \left( -\zeta x_{3}\right) \exp \left[ -i\left( x_{1}\xi_{1}+x_{2}\xi_{2}\right) \right] d\xi_{1}d\xi_{2}=\pi \left[ \frac{1}{R_{0}}+\frac{x_{2}^{2}-x_{1}^{2}}{R_{0}\left( R_{0}+z\right)^2 }\right], $$
(155)
$$ \int_{-\infty }^{\infty }\int_{-\infty }^{\infty }\frac{\xi_{2}^{2}}{\left( \xi_{1}^{2}+\xi_{2}^{2}\right)^{3/2}}\exp \left( -\zeta x_{3}\right) \exp \left[ -i\left( x_{1}\xi_{1}+x_{2}\xi_{2}\right) \right] d\xi_{1}d\xi_{2}=\pi \left[ \frac{1}{R_{0}}-\frac{x_{2}^{2}-x_{1}^{2}}{R_{0}\left( R_{0}+z\right)^2 }\right], $$
(156)
$$ \int_{-\infty }^{\infty }\int_{-\infty }^{\infty }\frac{\xi_{1}\xi_{2}}{\left( \xi_{1}^{2}+\xi_{2}^{2}\right)^{3/2}}\exp \left( -\zeta x_{3}\right) \exp \left[ -i\left( x_{1}\xi_{1}+x_{2}\xi_{2}\right) \right] d\xi_{1}d\xi_{2}=-\,\frac{2\pi x_{1}x_{2}}{R_{0}\left( R_{0}+z\right)^2 }. $$
(157)