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
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
The principle of stationary mutual potential energy, which was introduced by Shield and Prager, can be considered as an extension of the principle of minimum potential energy from one-loading system to two-loadlng sys...The principle of stationary mutual potential energy, which was introduced by Shield and Prager, can be considered as an extension of the principle of minimum potential energy from one-loading system to two-loadlng system. By this stationary principle, we can obtain the necessary and sufficient condition of optimality for structural design.展开更多
综合能源系统(integrated energy system,IES)作为能源转型中的重要环节已得到越来越多国家的广泛关注。构建一套匹配中国国情的综合能源系统评价体系和评价方法不仅能够为综合能源系统规划后评价打下基础,以此对规划方案进行优劣排序;...综合能源系统(integrated energy system,IES)作为能源转型中的重要环节已得到越来越多国家的广泛关注。构建一套匹配中国国情的综合能源系统评价体系和评价方法不仅能够为综合能源系统规划后评价打下基础,以此对规划方案进行优劣排序;还能够提高综合能源系统项目的管理水平,在制定统一、完整的综合能源系统综合评价标准时提供参考。为此,首先结合园区IES基本特征以及运行特性,构建包含经济性、可靠性、环保性以及智能友好性4个方面的综合评价指标体系;然后为解决IES在运行中的不确定性问题,对基于传统云物元模型的综合评价体系提出云熵优化,即考虑不同评价者对模糊性的可接受程度;为解决单一赋权方法可能导致的评价结果过于主观或过于客观的问题,选择基于最小鉴别信息原理将决策实验室法与熵权法相结合的综合赋权法,并采用变权法进一步完善综合评价指标;最后通过算例分析,验证所提综合评价体系的科学正确性。展开更多
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.
文摘The principle of stationary mutual potential energy, which was introduced by Shield and Prager, can be considered as an extension of the principle of minimum potential energy from one-loading system to two-loadlng system. By this stationary principle, we can obtain the necessary and sufficient condition of optimality for structural design.
文摘综合能源系统(integrated energy system,IES)作为能源转型中的重要环节已得到越来越多国家的广泛关注。构建一套匹配中国国情的综合能源系统评价体系和评价方法不仅能够为综合能源系统规划后评价打下基础,以此对规划方案进行优劣排序;还能够提高综合能源系统项目的管理水平,在制定统一、完整的综合能源系统综合评价标准时提供参考。为此,首先结合园区IES基本特征以及运行特性,构建包含经济性、可靠性、环保性以及智能友好性4个方面的综合评价指标体系;然后为解决IES在运行中的不确定性问题,对基于传统云物元模型的综合评价体系提出云熵优化,即考虑不同评价者对模糊性的可接受程度;为解决单一赋权方法可能导致的评价结果过于主观或过于客观的问题,选择基于最小鉴别信息原理将决策实验室法与熵权法相结合的综合赋权法,并采用变权法进一步完善综合评价指标;最后通过算例分析,验证所提综合评价体系的科学正确性。
