Based on the results of Hu and Lekhnitskii, the united solution of additional vertical stress coefficient for both transversely isotropic and isotropic half-space was obtained. Five typical load cases, namely, vertica...Based on the results of Hu and Lekhnitskii, the united solution of additional vertical stress coefficient for both transversely isotropic and isotropic half-space was obtained. Five typical load cases, namely, vertical circular uniform load, rectangular uniform load, linearly distributed rectangular load, uniform linear and strip loads are studied in detail. The final solutions are expressed in terms of elementary functions. Numerical results show that there are anisotropic effects on the variation of additional vertical stress coefficients.展开更多
Reducing the linear system of two first order equilibrium equations involving normal stress σ(ρ,θ) and shearing stress v(ρ,θ), by elimination, to two decoupled second order equations in σ and v, ...Reducing the linear system of two first order equilibrium equations involving normal stress σ(ρ,θ) and shearing stress v(ρ,θ), by elimination, to two decoupled second order equations in σ and v, we find that, for pressure only case, v(ρ,θ) vanishes in the half space. Consequently, the second order equation in σ can be simplified. In the language of linear system analysis, the medium(system) function, characterizing the mechanical behavior of a particulate medium in pressure only case, is obtained from the simplified second order equation ( 2 ρ+ 2 θ)σ(ρ,θ)=0 and can be inverted to give impulse reponse explicitly. Thus, response σ α(ρ,θ) may be computed directly from input, i.e., the surface pressure φ α(ρ) , by integration. Some explicit formulas for transmission problems, including response to input of strip linearly increasing pressure, are given in the paper.展开更多
[Objective] The paper was to understand the physiological response of space flight mutation new strains of Festuca arundinacea to high temperature stress. [Method] The influence of high temperature stress on eco-physi...[Objective] The paper was to understand the physiological response of space flight mutation new strains of Festuca arundinacea to high temperature stress. [Method] The influence of high temperature stress on eco-physiological characteristics of 11 F. arundinacea materials was studied in a pot experiment.Physiological and biochemical indexes,including soluble protein content,superoxide dismutase( SOD),peroxidase( POD) and catalase( CAT) activities,were measured and analyzed once every 4 d for a total of three times. Subordinate function and grey rational analysis were used to comprehensively evaluate the heat resistance of 11 materials. [Result] The soluble protein content decreased with the extension of heat resistance stress,while SOD,POD and CAT activities showed an upward trend. The high temperature resistance of 11 F. arundinacea materials was evaluated by subordinate function method. The resistance order was SP5-85> SP5-60 > SP5-71 > SP5-42 > SP5-94 > SP5-7 > SP5-88 > F. arundinacea cv Shuicheng > SP5-5 > SP5-89 = F. arundinacea cv Qiancao No. 1. The relational order of various heat resistance indexes and heat resistance obtained by grey rational analysis was SOD > CAT > POD > soluble protein content. [Conclusion]The result provides a theoretical basis for stress physiology and stress breeding of cold season grass in southwest region.展开更多
General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence ...General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence of two families of characteristic lines along which initial stresses and discontinuities in them are transmitted intact far down to infinity.This is against our intuition and not verifiable by experimental findings. For the fundamental case of infinite uniform pressure on the upper surface,a comparison between solutions from equilibrium equations in Cartesian coordinates and from those in polar coordinates is carried out in details.The semi infinite characteristic lines in the former are bent up to exponential spirals with both ends on the upper surface in the latter.Thus,the transmission pattern from solution in polar coordinates comes closer to actual situation.However,in polar reference frame,the solution for distribution of stresses in particulate half space under surface strip pressure or so can then only be obtained from boundary value problem of second order partial differential equation.展开更多
The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratica...The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect.展开更多
The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves a...The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson＇s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.展开更多
In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order f...In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).展开更多
文摘Based on the results of Hu and Lekhnitskii, the united solution of additional vertical stress coefficient for both transversely isotropic and isotropic half-space was obtained. Five typical load cases, namely, vertical circular uniform load, rectangular uniform load, linearly distributed rectangular load, uniform linear and strip loads are studied in detail. The final solutions are expressed in terms of elementary functions. Numerical results show that there are anisotropic effects on the variation of additional vertical stress coefficients.
文摘Reducing the linear system of two first order equilibrium equations involving normal stress σ(ρ,θ) and shearing stress v(ρ,θ), by elimination, to two decoupled second order equations in σ and v, we find that, for pressure only case, v(ρ,θ) vanishes in the half space. Consequently, the second order equation in σ can be simplified. In the language of linear system analysis, the medium(system) function, characterizing the mechanical behavior of a particulate medium in pressure only case, is obtained from the simplified second order equation ( 2 ρ+ 2 θ)σ(ρ,θ)=0 and can be inverted to give impulse reponse explicitly. Thus, response σ α(ρ,θ) may be computed directly from input, i.e., the surface pressure φ α(ρ) , by integration. Some explicit formulas for transmission problems, including response to input of strip linearly increasing pressure, are given in the paper.
基金Supported by United Fund of Guizhou Province(QKH J LKN[2013]24)Key Special Project of Guizhou Province(QKHZDZX[2014]6017)High-level Innovative Talents Training of Guizhou Province(QKHRC[2016]4024)
文摘[Objective] The paper was to understand the physiological response of space flight mutation new strains of Festuca arundinacea to high temperature stress. [Method] The influence of high temperature stress on eco-physiological characteristics of 11 F. arundinacea materials was studied in a pot experiment.Physiological and biochemical indexes,including soluble protein content,superoxide dismutase( SOD),peroxidase( POD) and catalase( CAT) activities,were measured and analyzed once every 4 d for a total of three times. Subordinate function and grey rational analysis were used to comprehensively evaluate the heat resistance of 11 materials. [Result] The soluble protein content decreased with the extension of heat resistance stress,while SOD,POD and CAT activities showed an upward trend. The high temperature resistance of 11 F. arundinacea materials was evaluated by subordinate function method. The resistance order was SP5-85> SP5-60 > SP5-71 > SP5-42 > SP5-94 > SP5-7 > SP5-88 > F. arundinacea cv Shuicheng > SP5-5 > SP5-89 = F. arundinacea cv Qiancao No. 1. The relational order of various heat resistance indexes and heat resistance obtained by grey rational analysis was SOD > CAT > POD > soluble protein content. [Conclusion]The result provides a theoretical basis for stress physiology and stress breeding of cold season grass in southwest region.
文摘General solution of stresses solved from the two dimensiona l system of equilibrium equations in Cartesian coordinates is characterized by the presence of two families of characteristic lines along which initial stresses and discontinuities in them are transmitted intact far down to infinity.This is against our intuition and not verifiable by experimental findings. For the fundamental case of infinite uniform pressure on the upper surface,a comparison between solutions from equilibrium equations in Cartesian coordinates and from those in polar coordinates is carried out in details.The semi infinite characteristic lines in the former are bent up to exponential spirals with both ends on the upper surface in the latter.Thus,the transmission pattern from solution in polar coordinates comes closer to actual situation.However,in polar reference frame,the solution for distribution of stresses in particulate half space under surface strip pressure or so can then only be obtained from boundary value problem of second order partial differential equation.
基金supported by the Research Fellow of Indian School of Mines in Dhanbad (No. 2010DR0016)
文摘The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect.
文摘The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson＇s half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity.
文摘In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of Liu et al. (2009).
