Based on the stress redistribution analysis of rock mass during the deep underground excavation, the unloading process of pre-flawed rock material was simulated by distinct element method (DEM). The effects of unloadi...Based on the stress redistribution analysis of rock mass during the deep underground excavation, the unloading process of pre-flawed rock material was simulated by distinct element method (DEM). The effects of unloading rate and flaw inclination angle on unloading strengths and cracking properties of pre-flawed rock specimens are numerically revealed. The results indicate that the unloading failure strength of pre-flawed specimen exhibits a power-function increase trend with the increase of unloading period. Moreover, combined with the stress state analysis on the flaws, it is found that the unloading failure strength increases with the increase of flaw inclination angle. The cracking distribution of pre-flawed specimens under the unloading condition closely depends on the flaw inclination angle, and three typical types of flaw coalescence are observed. Furthermore, at a faster unloading rate, the pre-flawed specimen experiences a sharper and quicker unloading failure process, resulting in more splitting cracks in the specimens.展开更多
From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this pa...From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J2 and J 22 of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.展开更多
基金Projects(41630642,11472311)supported by the National Natural Science Foundation of ChinaProject(2017zzts181)supported by the Cultivating Excellent Ph Ds of Central South University,ChinaProject(201806370062)supported by the China Scholarship Council
文摘Based on the stress redistribution analysis of rock mass during the deep underground excavation, the unloading process of pre-flawed rock material was simulated by distinct element method (DEM). The effects of unloading rate and flaw inclination angle on unloading strengths and cracking properties of pre-flawed rock specimens are numerically revealed. The results indicate that the unloading failure strength of pre-flawed specimen exhibits a power-function increase trend with the increase of unloading period. Moreover, combined with the stress state analysis on the flaws, it is found that the unloading failure strength increases with the increase of flaw inclination angle. The cracking distribution of pre-flawed specimens under the unloading condition closely depends on the flaw inclination angle, and three typical types of flaw coalescence are observed. Furthermore, at a faster unloading rate, the pre-flawed specimen experiences a sharper and quicker unloading failure process, resulting in more splitting cracks in the specimens.
基金supported by the National Natural Science Foundation of China (Grant nos. 11033009, 11125315 and 11103086)
文摘From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J2 and J 22 of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.
