A combined dam structure using different concrete materials offers many practical benefits.There are several real-world cases where largevolume heterogeneous concrete materials have been used together.From the enginee...A combined dam structure using different concrete materials offers many practical benefits.There are several real-world cases where largevolume heterogeneous concrete materials have been used together.From the engineering design standpoint,it is crucial to understand the deformation coordination characteristics and mechanical properties of large-volume heterogeneous concrete,which affect dam safety and stability.In this study,a large dam facility was selected for a case study,and various design schemes of the combined dam structure were developed by changing the configurations of material zoning and material types for a given dam shape.Elastoplastic analysis of the damfoundation-reservoir system for six schemes was carried out under dynamic conditions,in which the concrete damaged plasticity(CDP)model,the Lagrangian finite element formulation,and a surface-to-surface contact model were utilized.To evaluate the mechanical properties of zoning interfaces and coordination characteristics,the vertical distribution of the first principal stress at the longitudinal joint was used as the critical index of deformation coordination control,and the overall deformation and damage characteristics of the dam were also investigated.Through a comparative study of the design schemes,an optimal scheme of the combined dam structure was identified:large-volume roller-compacted concrete(RCC)is recommended for the dam body upstream of the longitudinal joint,and high-volume fly ash conventional concrete(CC)for the dam body downstream of the longitudinal joint.This study provides engineers with a reference basis for combined dam structure design.展开更多
In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexi...In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.展开更多
Absolute nodal coordinate formulation for a rectangular plate with large deformation was improved. Based on nonlinear elastic theory, a precise strain expression is used to derive the equations of motion. Both shear s...Absolute nodal coordinate formulation for a rectangular plate with large deformation was improved. Based on nonlinear elastic theory, a precise strain expression is used to derive the equations of motion. Both shear strain and transverse normal strain are taken into account. Different from the previous absolute nodal coordinate formulation, the absolute nodal coordinates, which describe the displacement and slope of the element nodes, are separated into three parts: the absolute nodal coordinates in X, Y and Z directions, respectively, so that the dimension of the mass, stiffness and force matrices is reduced. Furthermore, by using constant matrices, which can be calculated and saved before simulation, the nonlinear stiffness matrices can be calculated by matrix multiplication for each time step, so that the computational efficiency can be improved. Finally, simulation example of a rectangular plate with large deformation was used to verify the accuracy and efficiency of the present formulation.展开更多
Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discont...Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis (DDA) method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method (FEM) proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.展开更多
A new approach based on stereo vision technology is introduced to analyzesheet metal deformation. By measuring the deformed circle grids that are printed on the sheetsurface before forming, the strain distribution of ...A new approach based on stereo vision technology is introduced to analyzesheet metal deformation. By measuring the deformed circle grids that are printed on the sheetsurface before forming, the strain distribution of the workpiece is obtained. The measurement andanalysis results can be used to verify numerical simulation results and guide production. To getgood accuracy, some new techniques are employed: camera calibration based on genetic algorithm,feature abstraction based on self-adaptive technology, image matching based on structure feature andcamera modeling pre-constrains, and parameter calculation based on curve and surface optimization.The experimental values show that the approach proposed is rational and practical, which can providebetter measurement accuracy with less time than the conventional method.展开更多
Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new model...Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.展开更多
The interaction between pile and soft soil of the passive pile group subjected to soil movement was analyzed with three-dimensional finite element model by using ANSYS software. The soil was assumed to be elastic-plas...The interaction between pile and soft soil of the passive pile group subjected to soil movement was analyzed with three-dimensional finite element model by using ANSYS software. The soil was assumed to be elastic-plastic complying with the Drucker-Prager yield criterion in the analysis. The large displacement of soil was considered and contact elements were used to evaluate the interaction between pile and soil. The influences of soil depth of layer and number of piles on the lateral pressure of the pile were investigated, and the lateral pressure distributions on the (2×1) pile group and on the (2×2) pile group were compared. The results show that the adjacent surcharge may result in significant lateral movement of the soft soil and considerable pressure on the pile. The pressure acting on the row near the surcharge is higher than that on the other row, due to the "barrier" and arching effects in pile groups. The passive load and its distribution should be taken into account in the design of the passive piles.展开更多
Grain growth and shrinkage are essential to the thermal and mechanical stability of nanocrystalline metals,which are assumed to be governed by the coordinated deformation between neighboring grain boundaries(GBs)in th...Grain growth and shrinkage are essential to the thermal and mechanical stability of nanocrystalline metals,which are assumed to be governed by the coordinated deformation between neighboring grain boundaries(GBs)in the nanosized grains.However,the dynamics of such coordination has rarely been reported,especially in experiments.In this work,we systematically investigate the atomistic mechanism of coordinated GB deformation during grain shrinkage in an Au nanocrystal film through combined stateof-the-art in situ shear testing and atomistic simulations.We demonstrate that an embedded nanograin experiences shrinkage and eventually annihilation during a typical shear loading cycle.The continuous grain shrinkage is accommodated by the coordinated evolution of the surrounding GB network via dislocation-mediated migration,while the final grain annihilation proceeds through the sequential dislocation-annihilation-induced grain rotation and merging of opposite GBs.Both experiments and simulations show that stress distribution and GB structure play important roles in the coordinated deformation of different GBs and control the grain shrinkage/annihilation under shear loading.Our findings establish a mechanistic relation between coordinated GB deformation and grain shrinkage,which reveals a general deformation phenomenon in nanocrystalline metals and enriches our understanding on the atomistic origin of structural stability in nanocrystalline metals under mechanical loading.展开更多
Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation(ANCF). The int...Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation(ANCF). The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.展开更多
In the present study,the dynamics of the tendon system of a tension-leg platform(TLP)is investigated through the absolute nodal coordinate formulation(ANCF).Based on the energy conversion principle,the stiffness,gener...In the present study,the dynamics of the tendon system of a tension-leg platform(TLP)is investigated through the absolute nodal coordinate formulation(ANCF).Based on the energy conversion principle,the stiffness,generalized elastic force,external load and mass matrices of the element are deduced to perform the element assembling by using the finite element method.Then the motion equation of the tendon/riser is established.In this study,the TLP in the International Ship Structures Committee(ISSC)model under the first and second wave forces is considered as the case study.The simulation is performed in the MATLAB environment.Moreover,the accuracy and reliability of the programs are verified for cases of beam model with theoretical solutions.It is found that the motion response of tendons is affected by the TLP movement and environmental load,simultaneously.Then,the motion response is calculated using the SESAM software and exported as the boundary of ANCF tendons.Finally,the static and dynamic characteristics of the four tendons of ISSC TLP are analyzed systematically by the ANCF method.Performed analysis proves the effectiveness and feasibility of the ANCF method.It is concluded that the proposed method is a powerful scheme for calculating the dynamics of tendon/riser in the field of ocean engineering.展开更多
The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deforma...The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain- displacement relation, equations of motion for flexible multi-body system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation (ANCF) verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models.展开更多
A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the...A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.展开更多
It is imperative to understand the spatial and temporal coordination deformation mechanism and develop targeted deformation control technologies for high sidewall—bottom transfixion(HSBT)zones to guarantee the stabil...It is imperative to understand the spatial and temporal coordination deformation mechanism and develop targeted deformation control technologies for high sidewall—bottom transfixion(HSBT)zones to guarantee the stability of rock surrounding underground hydro-powerhouses under complex geological conditions.In this study,the spatial and temporal coordinated deformation control of HSBT zones was addressed from the aspects of the deformation mechanism,failure characteristics,and control requirements,and some coordinated deformation control technologies were proposed.On this basis,a case study was conducted on the deformation control of the HSBT zone of the underground powerhouse at the Wudongde hydropower station,China.The results showed that the relationship between excavation and support,and the mismatch of deformation and support of the surrounding rock mass in the HSBT zone of underground caverns with a large span and high in-situ stress can be appropriately handled.The solution requires proper excavation and construction procedures,fine blasting control,composite and timely support,and real-time monitoring and dynamic feedback.The technologies proposed in this study will ensure the safe,high-quality,and orderly construction of the Baihetan and Wudongde underground caverns,and can be applied to other similar projects.展开更多
In accordance with the geometric equations of elastic mechanics in the sphere coordinates, the displacement equation of blocks on asphere consisting of 6 deforming parameters is developed. The formula for distance bet...In accordance with the geometric equations of elastic mechanics in the sphere coordinates, the displacement equation of blocks on asphere consisting of 6 deforming parameters is developed. The formula for distance between blocks is derived under the supposition that all block boundaries are prime arcs. The kinematic constraint and the penalty function for reasonable contact between blocks are developed. The normal equations and their coefficient matrix, based on the Least Squares Principle, are derived. The problem of adjudging penetration between blocks is discussed, and a solution is proposed.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51879185)the Fund of the National Dam Safety Research Center(Grant No.CX2019B02).
文摘A combined dam structure using different concrete materials offers many practical benefits.There are several real-world cases where largevolume heterogeneous concrete materials have been used together.From the engineering design standpoint,it is crucial to understand the deformation coordination characteristics and mechanical properties of large-volume heterogeneous concrete,which affect dam safety and stability.In this study,a large dam facility was selected for a case study,and various design schemes of the combined dam structure were developed by changing the configurations of material zoning and material types for a given dam shape.Elastoplastic analysis of the damfoundation-reservoir system for six schemes was carried out under dynamic conditions,in which the concrete damaged plasticity(CDP)model,the Lagrangian finite element formulation,and a surface-to-surface contact model were utilized.To evaluate the mechanical properties of zoning interfaces and coordination characteristics,the vertical distribution of the first principal stress at the longitudinal joint was used as the critical index of deformation coordination control,and the overall deformation and damage characteristics of the dam were also investigated.Through a comparative study of the design schemes,an optimal scheme of the combined dam structure was identified:large-volume roller-compacted concrete(RCC)is recommended for the dam body upstream of the longitudinal joint,and high-volume fly ash conventional concrete(CC)for the dam body downstream of the longitudinal joint.This study provides engineers with a reference basis for combined dam structure design.
基金The project supported by the National Natural Science Foundation of China(10472066,10372057)The English text was polished by Yunming Chen.
文摘In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.
基金The National Natural Science Foundation of China (No10472066,No50475021)
文摘Absolute nodal coordinate formulation for a rectangular plate with large deformation was improved. Based on nonlinear elastic theory, a precise strain expression is used to derive the equations of motion. Both shear strain and transverse normal strain are taken into account. Different from the previous absolute nodal coordinate formulation, the absolute nodal coordinates, which describe the displacement and slope of the element nodes, are separated into three parts: the absolute nodal coordinates in X, Y and Z directions, respectively, so that the dimension of the mass, stiffness and force matrices is reduced. Furthermore, by using constant matrices, which can be calculated and saved before simulation, the nonlinear stiffness matrices can be calculated by matrix multiplication for each time step, so that the computational efficiency can be improved. Finally, simulation example of a rectangular plate with large deformation was used to verify the accuracy and efficiency of the present formulation.
文摘Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis (DDA) method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method (FEM) proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.
文摘A new approach based on stereo vision technology is introduced to analyzesheet metal deformation. By measuring the deformed circle grids that are printed on the sheetsurface before forming, the strain distribution of the workpiece is obtained. The measurement andanalysis results can be used to verify numerical simulation results and guide production. To getgood accuracy, some new techniques are employed: camera calibration based on genetic algorithm,feature abstraction based on self-adaptive technology, image matching based on structure feature andcamera modeling pre-constrains, and parameter calculation based on curve and surface optimization.The experimental values show that the approach proposed is rational and practical, which can providebetter measurement accuracy with less time than the conventional method.
基金The project is supported by the National Natural Science Foundation of China(10502028)the Special Foundation for the Authors of the Nationwide(China)Excellent Doctoral Dissertation(200242)the Science Research Foundation of China Agricultural University(2004016).
文摘Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate (QAC) method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF (5-DOF per node) quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.
基金Project(50378036) supported by the National Natural Science Foundation of China
文摘The interaction between pile and soft soil of the passive pile group subjected to soil movement was analyzed with three-dimensional finite element model by using ANSYS software. The soil was assumed to be elastic-plastic complying with the Drucker-Prager yield criterion in the analysis. The large displacement of soil was considered and contact elements were used to evaluate the interaction between pile and soil. The influences of soil depth of layer and number of piles on the lateral pressure of the pile were investigated, and the lateral pressure distributions on the (2×1) pile group and on the (2×2) pile group were compared. The results show that the adjacent surcharge may result in significant lateral movement of the soft soil and considerable pressure on the pile. The pressure acting on the row near the surcharge is higher than that on the other row, due to the "barrier" and arching effects in pile groups. The passive load and its distribution should be taken into account in the design of the passive piles.
基金supports of the National Key Research and Development Program of China(No.2018YFB2000704)the National Natural Science Foundation of China(51771172 and 52071284)+2 种基金the Innovation Fund of the Zhejiang Kechuang New Materials Research Institute(ZKN-18-Z02)financial support from the National Natural Science Foundation of China(11902289)computational support from the Super Cloud Computing Center in Beijing。
文摘Grain growth and shrinkage are essential to the thermal and mechanical stability of nanocrystalline metals,which are assumed to be governed by the coordinated deformation between neighboring grain boundaries(GBs)in the nanosized grains.However,the dynamics of such coordination has rarely been reported,especially in experiments.In this work,we systematically investigate the atomistic mechanism of coordinated GB deformation during grain shrinkage in an Au nanocrystal film through combined stateof-the-art in situ shear testing and atomistic simulations.We demonstrate that an embedded nanograin experiences shrinkage and eventually annihilation during a typical shear loading cycle.The continuous grain shrinkage is accommodated by the coordinated evolution of the surrounding GB network via dislocation-mediated migration,while the final grain annihilation proceeds through the sequential dislocation-annihilation-induced grain rotation and merging of opposite GBs.Both experiments and simulations show that stress distribution and GB structure play important roles in the coordinated deformation of different GBs and control the grain shrinkage/annihilation under shear loading.Our findings establish a mechanistic relation between coordinated GB deformation and grain shrinkage,which reveals a general deformation phenomenon in nanocrystalline metals and enriches our understanding on the atomistic origin of structural stability in nanocrystalline metals under mechanical loading.
基金supported in part by the National Natural Science Foundation of China (Grants 11290151 and 11221202)supported in part by the Beijing Higher Education Young Elite Teacher Project (Grant YETP1201)
文摘Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation(ANCF). The internal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation.A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient contact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the proposed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51879047 and 51890915)the Engineering Development Program of Deepwater Semi-submersible Production Storage and Unloading Platform of China(Grant No.SSBQ-2020-HN-03-03)the Natural Science Foundation of Heilongjiang Province of China(Grant No.E2017029)。
文摘In the present study,the dynamics of the tendon system of a tension-leg platform(TLP)is investigated through the absolute nodal coordinate formulation(ANCF).Based on the energy conversion principle,the stiffness,generalized elastic force,external load and mass matrices of the element are deduced to perform the element assembling by using the finite element method.Then the motion equation of the tendon/riser is established.In this study,the TLP in the International Ship Structures Committee(ISSC)model under the first and second wave forces is considered as the case study.The simulation is performed in the MATLAB environment.Moreover,the accuracy and reliability of the programs are verified for cases of beam model with theoretical solutions.It is found that the motion response of tendons is affected by the TLP movement and environmental load,simultaneously.Then,the motion response is calculated using the SESAM software and exported as the boundary of ANCF tendons.Finally,the static and dynamic characteristics of the four tendons of ISSC TLP are analyzed systematically by the ANCF method.Performed analysis proves the effectiveness and feasibility of the ANCF method.It is concluded that the proposed method is a powerful scheme for calculating the dynamics of tendon/riser in the field of ocean engineering.
基金the National Natural Science Foundation of China(10472066,50475021).
文摘The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain- displacement relation, equations of motion for flexible multi-body system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation (ANCF) verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models.
基金The project supported by National Natural Science Foundation of China under Grant No. 90403019
文摘A new type of deformed XXZ model was constructed and diagonalized by the coordinate Bethe ansatz method. We obtained the energy and the Bethe ansatz equations of the model and also discussed some thermodynamics of the model.
基金This work is supported by the National Natural Science Foundation of China(Nos.51979146 and 12102230)the China Three Gorges Corporation Research Program(Nos.WDD/0490,WDD/0578,and BHT/0774)the China Postdoctoral Science Foundation(No.2022M711862).
文摘It is imperative to understand the spatial and temporal coordination deformation mechanism and develop targeted deformation control technologies for high sidewall—bottom transfixion(HSBT)zones to guarantee the stability of rock surrounding underground hydro-powerhouses under complex geological conditions.In this study,the spatial and temporal coordinated deformation control of HSBT zones was addressed from the aspects of the deformation mechanism,failure characteristics,and control requirements,and some coordinated deformation control technologies were proposed.On this basis,a case study was conducted on the deformation control of the HSBT zone of the underground powerhouse at the Wudongde hydropower station,China.The results showed that the relationship between excavation and support,and the mismatch of deformation and support of the surrounding rock mass in the HSBT zone of underground caverns with a large span and high in-situ stress can be appropriately handled.The solution requires proper excavation and construction procedures,fine blasting control,composite and timely support,and real-time monitoring and dynamic feedback.The technologies proposed in this study will ensure the safe,high-quality,and orderly construction of the Baihetan and Wudongde underground caverns,and can be applied to other similar projects.
文摘In accordance with the geometric equations of elastic mechanics in the sphere coordinates, the displacement equation of blocks on asphere consisting of 6 deforming parameters is developed. The formula for distance between blocks is derived under the supposition that all block boundaries are prime arcs. The kinematic constraint and the penalty function for reasonable contact between blocks are developed. The normal equations and their coefficient matrix, based on the Least Squares Principle, are derived. The problem of adjudging penetration between blocks is discussed, and a solution is proposed.