The plasma optical boundary reconstruction technique based on Hommen's theory is promising for future tokamaks with high parameters. In this work, we conduct detailed analysis and simulation verification to estima...The plasma optical boundary reconstruction technique based on Hommen's theory is promising for future tokamaks with high parameters. In this work, we conduct detailed analysis and simulation verification to estimate the ‘logic loophole' of this technique. The finite-width effect and unpredictable errors reduce the technique's reliability, which leads to this loophole. Based on imaging theory, the photos of a virtual camera are simulated by integrating the assumed luminous intensity of plasma. Based on Hommen's theory, the plasma optical boundary is reconstructed from the photos. Comparing the reconstructed boundary with the one assumed, the logic loophole and its two effects are quantitatively estimated. The finite-width effect is related to the equivalent thickness of the luminous layer, which is generally about 2-4 cm but sometimes larger. The level of unpredictable errors is around 0.65 cm. The technique based on Hommen's theory is generally reliable, but finite-width effect and unpredictable errors have to be taken into consideration in some scenarios. The parameters of HL-2M are applied in this work.展开更多
Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and...Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empiricai method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli＇s photo-elastic experiment and Isida＇s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.展开更多
The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By usin...The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.展开更多
基金supported by the Tsinghua University 2021 Doctoral Summer Projectsupported by the National Key R&D Program of China (No. 2018YFE0301102)National Natural Science Foundation of China (Nos. 11875020 and 11875023)。
文摘The plasma optical boundary reconstruction technique based on Hommen's theory is promising for future tokamaks with high parameters. In this work, we conduct detailed analysis and simulation verification to estimate the ‘logic loophole' of this technique. The finite-width effect and unpredictable errors reduce the technique's reliability, which leads to this loophole. Based on imaging theory, the photos of a virtual camera are simulated by integrating the assumed luminous intensity of plasma. Based on Hommen's theory, the plasma optical boundary is reconstructed from the photos. Comparing the reconstructed boundary with the one assumed, the logic loophole and its two effects are quantitatively estimated. The finite-width effect is related to the equivalent thickness of the luminous layer, which is generally about 2-4 cm but sometimes larger. The level of unpredictable errors is around 0.65 cm. The technique based on Hommen's theory is generally reliable, but finite-width effect and unpredictable errors have to be taken into consideration in some scenarios. The parameters of HL-2M are applied in this work.
基金supported by the National Natural Science Foundation of China (No. 51179115)
文摘Two explicit expressions of the stress concentration factor for a tension finite-width strip with a central elliptical hole and an eccentric elliptical hole, respectively, are formulated by using a semi-analytical and semi-empiricai method. Accuracy of the results obtained from these expressions is better, and application scope is wider, than the results of Durelli＇s photo-elastic experiment and Isida＇s formula. When eccentricity of the elliptical hole is within a certain range, the error is less than 8%. Based on the relation between the stress concentration factor and the stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack is derived with the obtained stress concentration factor expressions. Compared with the existing formulae and the finite element analysis, this stress intensity factor expression also has sufficient accuracy.
基金Project supported by the National Natural Science Foundation of China (No.90305023)
文摘The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.
