富含孔隙/裂隙岩体的非线性变形对于工程的安全评价具有重要意义。在多物理场耦合分析求解器TOUGH-FLAC3D中实现双应变胡克模型(two-part Hooke s model,简称TPHM)的数值解法,并界定TPHM的适用条件。TPHM假设:对于岩体中可承受较大变形...富含孔隙/裂隙岩体的非线性变形对于工程的安全评价具有重要意义。在多物理场耦合分析求解器TOUGH-FLAC3D中实现双应变胡克模型(two-part Hooke s model,简称TPHM)的数值解法,并界定TPHM的适用条件。TPHM假设:对于岩体中可承受较大变形的软体(如孔隙、裂隙等),用基于自然应变(或真应变,即岩体变形与当前应力状态下的岩体体积之比)的胡克定律来描述;而对于只承受较小变形的硬体部分用基于工程应变(岩体变形与原始应力状态下的岩体体积之比)的胡克定律来描述。通过对室内岩样的应力-应变特征计算分析,表明TPHM在本质上反映了加卸载过程中低应力阶段的非线性变形行为,该力学响应完全取决于孔隙/裂隙的自然应变(真应变);通过对瑞士Mont Terri岩石实验室的深部ED-B巷道围岩的变形场计算分析,显示出TPHM较为准确地反映了开挖卸载诱发的围岩变形特征。因为TPHM本质上是考虑了低应力状态下孔隙/裂隙对岩石力学性质的影响,因此,在具有卸荷扰动特征的岩石工程中应用TPHM模型进行设计分析更符合实际。展开更多
The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments;and the theory takes into account non...The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments;and the theory takes into account nonlinear law of displacements distribution in cross section of the plate. The methods for constructing bimoment theory are based on Hooke’s Law, three-dimensional equations of the theory of dynamic elasticity and the method of displacements expansion into Maclaurin series. The article gives the expressions to determine the forces, moments and bimoments. Bimoment theory of plates is described by two unrelated two-dimensional systems with nine equations in each. On each edge of the plate, depending on the type of fastening, nine boundary conditions are given. As an example, the solution of the problem of dynamic bending of thick isotropic and orthotropic plate under the influence of transverse dynamic loads in the form of the Heaviside function is given. The equations of motion of the plate are solved by numerical method of finite differences. The numerical results are obtained for isotropic and orthotropic plate. The graphs of changes of displacements and stresses of faces surfaces of the plate are presented. Maximum values of these displacements are found and analyzed. It is shown that by Timoshenko theory numerical values of stresses are much smaller compared to the ones obtained by bimoment theory of plates. Maximum numerical values of generalized displacements, forces, moments, and bimoments are obtained and presented in tabular form. The analysis of numerical results is done and the conclusions are drawn.展开更多
In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings fo...In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.展开更多
A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical me...A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical mechanical stress （σ^M） originates from lat- tice strain （e）, following Hooke＇s law： σ^M=Cε, where C is elastic constant matrix. Recently, a new concept of quantum electronic stress （o-QE） is introduced to elucidate the extrinsic electronic effects on the stress state of solids and thin films, which follows a quantum analog of classical Hooke＇s law： ~QE=E（An）, where E is the deformation potential of electronic states and An is the variation of electron density. Here, we present mathematical derivation of both the classical and quantum Hooke＇s law from density functional theory. We further discuss the physical origin of quantum electronic stress, arising purely from electronic excitation and perturbation in the absence of lattice strain （g=0）, and its relation to the degeneracy pressure of electrons in solid and their interaction with the lattice.展开更多
Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering,such as tunnels and mines.The existing theoretical models describing the stress-strain relationship of a combined body ...Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering,such as tunnels and mines.The existing theoretical models describing the stress-strain relationship of a combined body lack a binary feature.Based on effective medium theory,this paper presents the governing equation of the“elastic modulus”for combined and single bodies under triaxial compressive tests.A binary effective medium model is then established.Based on the compressive experiment of concretegranite combined bodies,the feasibility of determining the stress threshold based on crack axial strain is discussed,and the model is verified.The model is further extended to coal-rock combined bodies of more diverse types,and the variation laws of the compressive mechanical parameters are then discussed.The results show that the fitting accuracy of the model with the experimental curves of the concretegranite combined bodies and various types of coal-rock combined bodies are over 95%.The crack axial strain method can replace the crack volumetric strain method,which clarifies the physical meanings of the model parameters.The variation laws of matrix parameters and crack parameters are discussed in depth and are expected to be more widely used in geotechnical engineering.展开更多
This work deals with the generation of MATLAB script files that assists the user in the design of a composite laminate to operate within safe conditions. The inputs of the program are the material properties, material...This work deals with the generation of MATLAB script files that assists the user in the design of a composite laminate to operate within safe conditions. The inputs of the program are the material properties, material limits and loading conditions. Equations based on Hooke’s Law for two-dimensional composites were used to determine the global and local stresses and strains on each layer. Failure analysis of the structure was performed via the Tsai-Wu failure theory. The output of the program is the optimal number of fibre layers required for the composite laminate, as well as the orientation of each layer.展开更多
We consider a continuum model for the evolution of an epitaxially-strained dislocation-free anisotropic thin solid film on isotropic deformable substrate in the absence of vapor deposition. By using a thin film approx...We consider a continuum model for the evolution of an epitaxially-strained dislocation-free anisotropic thin solid film on isotropic deformable substrate in the absence of vapor deposition. By using a thin film approximation we derived a nonlinear evolution equation. We examined the nonlinear evolution equation and found that there is a critical film thickness below which every film thickness is stable and a critical wave number above which every film thickness is stable.展开更多
文摘富含孔隙/裂隙岩体的非线性变形对于工程的安全评价具有重要意义。在多物理场耦合分析求解器TOUGH-FLAC3D中实现双应变胡克模型(two-part Hooke s model,简称TPHM)的数值解法,并界定TPHM的适用条件。TPHM假设:对于岩体中可承受较大变形的软体(如孔隙、裂隙等),用基于自然应变(或真应变,即岩体变形与当前应力状态下的岩体体积之比)的胡克定律来描述;而对于只承受较小变形的硬体部分用基于工程应变(岩体变形与原始应力状态下的岩体体积之比)的胡克定律来描述。通过对室内岩样的应力-应变特征计算分析,表明TPHM在本质上反映了加卸载过程中低应力阶段的非线性变形行为,该力学响应完全取决于孔隙/裂隙的自然应变(真应变);通过对瑞士Mont Terri岩石实验室的深部ED-B巷道围岩的变形场计算分析,显示出TPHM较为准确地反映了开挖卸载诱发的围岩变形特征。因为TPHM本质上是考虑了低应力状态下孔隙/裂隙对岩石力学性质的影响,因此,在具有卸荷扰动特征的岩石工程中应用TPHM模型进行设计分析更符合实际。
文摘The paper is devoted to dynamic design of thick orthotropic cantilever plates by applying the bimoment theory of plates, which takes into account the forces, moments and bimoments;and the theory takes into account nonlinear law of displacements distribution in cross section of the plate. The methods for constructing bimoment theory are based on Hooke’s Law, three-dimensional equations of the theory of dynamic elasticity and the method of displacements expansion into Maclaurin series. The article gives the expressions to determine the forces, moments and bimoments. Bimoment theory of plates is described by two unrelated two-dimensional systems with nine equations in each. On each edge of the plate, depending on the type of fastening, nine boundary conditions are given. As an example, the solution of the problem of dynamic bending of thick isotropic and orthotropic plate under the influence of transverse dynamic loads in the form of the Heaviside function is given. The equations of motion of the plate are solved by numerical method of finite differences. The numerical results are obtained for isotropic and orthotropic plate. The graphs of changes of displacements and stresses of faces surfaces of the plate are presented. Maximum values of these displacements are found and analyzed. It is shown that by Timoshenko theory numerical values of stresses are much smaller compared to the ones obtained by bimoment theory of plates. Maximum numerical values of generalized displacements, forces, moments, and bimoments are obtained and presented in tabular form. The analysis of numerical results is done and the conclusions are drawn.
文摘In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.
基金supported by the DOE-BES program(Grant No.DE-04ER46148)NSF-MRSEC(Grant No.DMR-1121252)
文摘A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical mechanical stress （σ^M） originates from lat- tice strain （e）, following Hooke＇s law： σ^M=Cε, where C is elastic constant matrix. Recently, a new concept of quantum electronic stress （o-QE） is introduced to elucidate the extrinsic electronic effects on the stress state of solids and thin films, which follows a quantum analog of classical Hooke＇s law： ~QE=E（An）, where E is the deformation potential of electronic states and An is the variation of electron density. Here, we present mathematical derivation of both the classical and quantum Hooke＇s law from density functional theory. We further discuss the physical origin of quantum electronic stress, arising purely from electronic excitation and perturbation in the absence of lattice strain （g=0）, and its relation to the degeneracy pressure of electrons in solid and their interaction with the lattice.
基金the Major Program of National Natural Science Foundation of China(No.41941019)Shaanxi Province Innovative Talent Promotion Plan-Science and Technology Innovation Team(No.2021TD-55)Central University Natural Science Innovation Team(No.300102262402)。
文摘Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering,such as tunnels and mines.The existing theoretical models describing the stress-strain relationship of a combined body lack a binary feature.Based on effective medium theory,this paper presents the governing equation of the“elastic modulus”for combined and single bodies under triaxial compressive tests.A binary effective medium model is then established.Based on the compressive experiment of concretegranite combined bodies,the feasibility of determining the stress threshold based on crack axial strain is discussed,and the model is verified.The model is further extended to coal-rock combined bodies of more diverse types,and the variation laws of the compressive mechanical parameters are then discussed.The results show that the fitting accuracy of the model with the experimental curves of the concretegranite combined bodies and various types of coal-rock combined bodies are over 95%.The crack axial strain method can replace the crack volumetric strain method,which clarifies the physical meanings of the model parameters.The variation laws of matrix parameters and crack parameters are discussed in depth and are expected to be more widely used in geotechnical engineering.
文摘This work deals with the generation of MATLAB script files that assists the user in the design of a composite laminate to operate within safe conditions. The inputs of the program are the material properties, material limits and loading conditions. Equations based on Hooke’s Law for two-dimensional composites were used to determine the global and local stresses and strains on each layer. Failure analysis of the structure was performed via the Tsai-Wu failure theory. The output of the program is the optimal number of fibre layers required for the composite laminate, as well as the orientation of each layer.
文摘We consider a continuum model for the evolution of an epitaxially-strained dislocation-free anisotropic thin solid film on isotropic deformable substrate in the absence of vapor deposition. By using a thin film approximation we derived a nonlinear evolution equation. We examined the nonlinear evolution equation and found that there is a critical film thickness below which every film thickness is stable and a critical wave number above which every film thickness is stable.
