Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on ...Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.展开更多
A four-bar linkage mechanism with links fabricated from symmetric laminates was studied. The mass matrix of the beam dement was obtained in light of the mass distribution characteristics of composite materials. The st...A four-bar linkage mechanism with links fabricated from symmetric laminates was studied. The mass matrix of the beam dement was obtained in light of the mass distribution characteristics of composite materials. The stiffness matrix of the beam element was derived from the constitutive equations of each layer and the relationship between the strain distribution and the node displacement of the beam element. The specific damping capacity of the beam element was analyzed according to the strain distribution of the beam element and the strain energy dissipation caused by vibration in each direction of each layer; and the damping coefficients were obtained according to the principle that the total energy dissipation of the beam element was equal to the work done by the equivalent damping force during a cycle of vibration, from which the damping matrix of the dynamic equations was obtained. Using the finite element method, the dynamic analytic model of the mechanism was obtained. The dynamic responses and natural frequency of the mechanism were obtained by simulation, respectively, and those of the simulation obtained by the proposed model were analyzed and compared with the results obtained by the conventional model. The work provides theoretical basis to a certain extent for the further research on nonlinear vibration characteristics and optimum design of this kind of mechanism.展开更多
In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto ...In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto the differential-difference equations.With the extended method,we study the well-known differential-difference KPequation,KZ equation and (2+1)-dimensional ANNV system,and both the Lie point symmetry groups and the non-Liesymmetry groups are obtained.展开更多
The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work...The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.展开更多
基金Project(51008188)supported by National Natural Science Foundation of ChinaProject(KLE-TJGE-B1302)supported by Key Laboratory Fund of Geotechnical and Underground Engineering of Ministry of Education,ChinaProject(SKLGDUEK1205)supported by Open Program of State Key Laboratory for Geomechanics and Deep Underground Engineering,China
文摘Long-term settlements for underground structures, such as tunnels and pipelines, are generally observed after the completion of construction in soft clay. The soil consolidation characteristic has great influences on the long-term deformation for underground structures. A three-dimensional consolidation analysis method under the asymmetric loads is developed for porous layered soil based on Biot's classical theory. Time-displacement effects can be fully considered in this work and the analytical solutions are obtained by the state space approach in the Cartesian coordinate. The Laplace and double Fourier integral transform are applied to the state variables in order to reduce the partial differential equations into algebraic differential equations and easily obtain the state space solution. Starting from the governing equations of saturated porous soil, the basic relationship of state space variables is established between the ground surface and the arbitrary depth in the integral transform domain. Based on the continuity conditions and boundary conditions of the multi-layered pore soil model, the multi-layered pore half-space solutions are obtained by means of the transfer matrix method and the inverse integral transforms. The accuracy of proposed method is demonstrated with existing classical solutions. The results indicate that the porous homogenous soils as well as the porous non-homogenous layered soils can be considered in this proposed method. When the consolidation time factor is 0.01, the value of immediate consolidation settlement coefficient calculated by the weighted homogenous solution is 27.4% bigger than the one calculated by the non-homogeneity solution. When the consolidation time factor is 0.05, the value of excess pore water pressure for the weighted homogenous solution is 27.2% bigger than the one for the non-homogeneity solution. It is shown that the material non-homogeneity has a great influence on the long-term settlements and the dissipation process of excess pore water pressure.
基金Projects(50175031, 50565001) supported by the National Natural Science Foundation of China project (2003203) supported by the New Century Ten Hundred and Thousand Talent Project Special Foundation of Guangxi+1 种基金 project(0542005) supported by Guangxi Science Foundation project(205119) supported by the Key Project of Chinese Ministry of Education
文摘A four-bar linkage mechanism with links fabricated from symmetric laminates was studied. The mass matrix of the beam dement was obtained in light of the mass distribution characteristics of composite materials. The stiffness matrix of the beam element was derived from the constitutive equations of each layer and the relationship between the strain distribution and the node displacement of the beam element. The specific damping capacity of the beam element was analyzed according to the strain distribution of the beam element and the strain energy dissipation caused by vibration in each direction of each layer; and the damping coefficients were obtained according to the principle that the total energy dissipation of the beam element was equal to the work done by the equivalent damping force during a cycle of vibration, from which the damping matrix of the dynamic equations was obtained. Using the finite element method, the dynamic analytic model of the mechanism was obtained. The dynamic responses and natural frequency of the mechanism were obtained by simulation, respectively, and those of the simulation obtained by the proposed model were analyzed and compared with the results obtained by the conventional model. The work provides theoretical basis to a certain extent for the further research on nonlinear vibration characteristics and optimum design of this kind of mechanism.
文摘In this paper,based on the symbolic computing system Maple,the direct method for Lie symmetry groupspresented by Sen-Yue Lou [J.Phys.A:Math.Gen.38 (2005) L129] is extended from the continuous differential equationsto the differential-difference equations.With the extended method,we study the well-known differential-difference KPequation,KZ equation and (2+1)-dimensional ANNV system,and both the Lie point symmetry groups and the non-Liesymmetry groups are obtained.
基金Supported by the Chinese Academy of Sciences Program "Frontier Topics in Mathematical Physics" (KJCX3-SYW-S03)Supported Partially by the National Natural Science Foundation of China under Grant No.11035008
文摘The present work is much motivated by finding an explicit way in the construction of the Jack symmetric function,which is the spectrum generating function for the Calogero-Sutherland (CS) model.To accomplish this work,the hidden Virasoro structure in the CS model is much explored.In particular,we found that the Virasoro singular vectors form a skew hierarchy in the CS model.Literally,skew is analogous to coset,but here specifically refer to the operation on the Young tableaux.In fact,based on the construction of the Virasoro singular vectors,this hierarchical structure can be used to give a complete construction of the CS states,i.e.the Jack symmetric functions,recursively.The construction is given both in operator formalism as well as in integral representation.This new integral representation for the Jack symmetric functions may shed some insights on the spectrum constructions for the other integrable systems.
