The geomorphic minimum energy dissipation principle is important in the development of gully evolutionary theory.The impact of debris flows on channels during movement also adheres to this theory.A minimum energy diss...The geomorphic minimum energy dissipation principle is important in the development of gully evolutionary theory.The impact of debris flows on channels during movement also adheres to this theory.A minimum energy dissipation model for debris flows has been obtained from previous studies,which is derived from the flow rules of runoff along a channel under rainfall or ice-snow meltwater conditions.However,the lack of consideration for erosion characteristics has hindered a comprehensive understanding of the movement characteristics of debris flow.In this paper,the phenomenon of volume increase resulting from the entrainment along debris flow movement is considered in order to derive a model for the mean velocity,reflecting the minimum energy dissipation principle.The entire expression of the mean velocity model is determined through 38 typical glacial and rainstorm debris flow cases.To evaluate the reliability of the proposed model,we employed 164 monitoring data from 1995 to 2000 in the Jiangjia gully,Yunnan,China.The results show that the velocity calculated by the proposed model are highly correlated with those obtained from the monitoring data.Additionally,a comparison is made between the mean velocities calculated by the proposed model and those obtained from previous studies,highlighting the exceptional applicability of the proposed model.This study will contribute to reveal the movement laws of debris flow along the channel.展开更多
To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum poten...To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum potential energy and variational method are used and series functions with unknown coefficients are taken as trial functions of functional to solve the large deflection and non linear bending problem of a thin plate and find relation curves between deflection of plate and loads. The proposed method can capture the buckling and post buckling behaviors of a thin plate in different geometrical and load boundary conditions. The analysis confirms that there occur snap and bifurcation behaviors in the post buckling stage of the plate. And these results show the validity of the variational method for solving buckling problems of thin plate.展开更多
Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R...Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.展开更多
The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic...The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic properties of this material, we introduced a softening and a hardening function for a new nonlinear the- ological model with time-varying parameters. Based on this, we presented the instability condition of this model by using the principle of minimum potential energy. Combined with engineering practice, we cal- culated the urlstable time period of backfill material. The results show that the time of instability of the backfill material relate to the initial parameters of the material, ＂the coefficients decided by temperature and the ratio of the plastic zone of the backfill material. Based on the results of our analysis from the point of view of energy, we can quickly obtain the time of instability of this model from our graphical analysis. The time of instability of the backfill material obtained from our investigation coincides with an actual project.展开更多
Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S)...Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.展开更多
A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high a...A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.展开更多
A new method is put forward for structural damage identification based on the homotopy continuation algorithm. A numerical example is presented to verify the method. The beams with different damage locations and diffe...A new method is put forward for structural damage identification based on the homotopy continuation algorithm. A numerical example is presented to verify the method. The beams with different damage locations and different damage extents are identified by this method. The numerical examples have proved that this new method is capable of easy convergence, which is not sensitive to the initial iterative values. It is effective for accurately identifying multiple damages. By incorporating the finite element method into the homotopy continuation algorithm, the damage identifying ability of the new method can be greatly enhanced.展开更多
The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the f...The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.展开更多
Projectile perforation of concrete slabs will produce numerous concrete fragments on the rear face of the concrete slabs. These concrete fragments will cause serious secondary damage to the indoor personnel and equipm...Projectile perforation of concrete slabs will produce numerous concrete fragments on the rear face of the concrete slabs. These concrete fragments will cause serious secondary damage to the indoor personnel and equipment of protective structures.Accurately evaluating the damage area of concrete slabs is an important problem. Therefore, a theoretical model of a rigid projectile perforation of concrete slabs is constructed using the energy method in this paper. In this model, a new shear failure method is proposed to calculate the energy consumption of the shear formation by combining with the von-Mises failure criterion and failure strain. Based on the energy conservation and principle of minimum potential energy, explicit equations for the perforation performance are formulated. The theoretical predictions agree well with the experimental results. Furthermore,experiments on a high-speed projectile normal perforation of concrete are carried out to verify the accuracy of the corresponding theoretical prediction.展开更多
The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Ca...The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.展开更多
The stress-dilatancy relation is important for understanding fault mechanics and brittle deformation of rocks,and hence the onset of frictional instability.The principle of minimum energy ratio was proposed by Rowe,an...The stress-dilatancy relation is important for understanding fault mechanics and brittle deformation of rocks,and hence the onset of frictional instability.The principle of minimum energy ratio was proposed by Rowe,and this Rowe’s theory has been applied to deformation of granular materials.Rowe suggested that the energy ratio,which is the ratio of the energy dissipation rate to energy supply rate,would be a minimum and constant value.The relation between the rate of dilatancy and the maximum stress ratio can be extended to the case of a random assembly of irregular particles whereby the rate of internal work absorbed in frictional heat is a minimum as the mass dilates.According to Rowe’s law.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41925030)the Nyingchi National Sustainable Development Experimental Zone Project(2023-SYQ-007)+1 种基金the Chinese Academy of Sciences Light of West China Programthe Science and Technology Research Program of Institute of Mountain Hazards and Environment,Chinese Academy of Sciences(Grant No.IMHE-ZDRW-02).
文摘The geomorphic minimum energy dissipation principle is important in the development of gully evolutionary theory.The impact of debris flows on channels during movement also adheres to this theory.A minimum energy dissipation model for debris flows has been obtained from previous studies,which is derived from the flow rules of runoff along a channel under rainfall or ice-snow meltwater conditions.However,the lack of consideration for erosion characteristics has hindered a comprehensive understanding of the movement characteristics of debris flow.In this paper,the phenomenon of volume increase resulting from the entrainment along debris flow movement is considered in order to derive a model for the mean velocity,reflecting the minimum energy dissipation principle.The entire expression of the mean velocity model is determined through 38 typical glacial and rainstorm debris flow cases.To evaluate the reliability of the proposed model,we employed 164 monitoring data from 1995 to 2000 in the Jiangjia gully,Yunnan,China.The results show that the velocity calculated by the proposed model are highly correlated with those obtained from the monitoring data.Additionally,a comparison is made between the mean velocities calculated by the proposed model and those obtained from previous studies,highlighting the exceptional applicability of the proposed model.This study will contribute to reveal the movement laws of debris flow along the channel.
文摘To investigate the buckling and post buckling behaviors of elastic thin plate under frictionless unilateral restraint, enduring the coupling action of lognitudinal and transverse loads, the principle of minimum potential energy and variational method are used and series functions with unknown coefficients are taken as trial functions of functional to solve the large deflection and non linear bending problem of a thin plate and find relation curves between deflection of plate and loads. The proposed method can capture the buckling and post buckling behaviors of a thin plate in different geometrical and load boundary conditions. The analysis confirms that there occur snap and bifurcation behaviors in the post buckling stage of the plate. And these results show the validity of the variational method for solving buckling problems of thin plate.
基金supported by the National Natural Science Foundation of China (Grant 11502286)
文摘Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.
基金Project (No. 50874089) is supported by the National Natural Science Foundation of ChinaProject (No. 20096121110002) by the College of Doctoral Foundation of the Ministry of Education the Scientific Research Program Funded by Shaanxi Provincial Education Commission (No. 2010JK692)
文摘The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic properties of this material, we introduced a softening and a hardening function for a new nonlinear the- ological model with time-varying parameters. Based on this, we presented the instability condition of this model by using the principle of minimum potential energy. Combined with engineering practice, we cal- culated the urlstable time period of backfill material. The results show that the time of instability of the backfill material relate to the initial parameters of the material, ＂the coefficients decided by temperature and the ratio of the plastic zone of the backfill material. Based on the results of our analysis from the point of view of energy, we can quickly obtain the time of instability of this model from our graphical analysis. The time of instability of the backfill material obtained from our investigation coincides with an actual project.
文摘Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.
文摘A new high-order multi-joint finite element for thin-walled bar was derived from the Hermite interpolation polynomial and minimum potential energy principle. This element's characteristics are that it is of high accuracy and can be used in finite method analysis of bridge, tall mega-structure building.
基金Project supported by the National Natural Science Foundation of China (No.50238040).
文摘A new method is put forward for structural damage identification based on the homotopy continuation algorithm. A numerical example is presented to verify the method. The beams with different damage locations and different damage extents are identified by this method. The numerical examples have proved that this new method is capable of easy convergence, which is not sensitive to the initial iterative values. It is effective for accurately identifying multiple damages. By incorporating the finite element method into the homotopy continuation algorithm, the damage identifying ability of the new method can be greatly enhanced.
文摘The stress field in granular soils heap(including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations.Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleighe Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy’s partial differential equations, generalized Hooke’s law and boundary equations. A function is built with the Rayleighe Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleighe Ritz method and numerical simulations, it is demonstrated that the Rayleighe Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.
基金supported by the National Natural Science Foundation of China(Grant Nos.11390362&11521062)
文摘Projectile perforation of concrete slabs will produce numerous concrete fragments on the rear face of the concrete slabs. These concrete fragments will cause serious secondary damage to the indoor personnel and equipment of protective structures.Accurately evaluating the damage area of concrete slabs is an important problem. Therefore, a theoretical model of a rigid projectile perforation of concrete slabs is constructed using the energy method in this paper. In this model, a new shear failure method is proposed to calculate the energy consumption of the shear formation by combining with the von-Mises failure criterion and failure strain. Based on the energy conservation and principle of minimum potential energy, explicit equations for the perforation performance are formulated. The theoretical predictions agree well with the experimental results. Furthermore,experiments on a high-speed projectile normal perforation of concrete are carried out to verify the accuracy of the corresponding theoretical prediction.
基金supported by the National Natural Science Foundation of China(Grant No.10872108,10876100)the Program for New Century Excellent Talents in University(Grant No. NCET-07-0477)+1 种基金the National Basic Research Program of China(Grant No. 2010CB832701)ASFC
文摘The sensitivity problem to mesh distortion and the low accuracy problem of the stress solutions are two inherent difficulties in the finite element method.By applying the fundamental analytical solutions (in global Cartesian coordinates) to the Airy stress function of the anisotropic materials,8-and 12-node plane quadrilateral hybrid stress-function (HS-F) elements are successfully developed based on the principle of the minimum complementary energy.Numerical results show that the present new elements exhibit much better and more robust performance in both displacement and stress solutions than those obtained from other models.They can still perform very well even when the element shapes degenerate into a triangle and a concave quadrangle.It is also demonstrated that the proposed construction procedure is an effective way for developing shape-free finite element models which can completely overcome the sensitivity problem to mesh distortion and can produce highly accurate stress solutions.
基金funded by a Grantin-Air for Scientific Research(24244077).
文摘The stress-dilatancy relation is important for understanding fault mechanics and brittle deformation of rocks,and hence the onset of frictional instability.The principle of minimum energy ratio was proposed by Rowe,and this Rowe’s theory has been applied to deformation of granular materials.Rowe suggested that the energy ratio,which is the ratio of the energy dissipation rate to energy supply rate,would be a minimum and constant value.The relation between the rate of dilatancy and the maximum stress ratio can be extended to the case of a random assembly of irregular particles whereby the rate of internal work absorbed in frictional heat is a minimum as the mass dilates.According to Rowe’s law.
