In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equi...In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equivalent condition of a point outside the convex set is given and proved rigorously.Then,the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables,and its geometric meaning is explained.Finally,the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary variables.The effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model(unmanned aerial vehicle)and complex nonlinear dynamic model(hypersonic glide vehicle).Comparison indicates the computational time of ELP method is only 1%-20%of that of the traditional Mixed-Integer Programming(MIP)method.展开更多
Mega-city region is the mainstream of global urban development and also the dominant model of the neo urbanization process in China. The Beijing-Tianjin-Hebei area, Yangtze River Delta area and Pearl River Delta area ...Mega-city region is the mainstream of global urban development and also the dominant model of the neo urbanization process in China. The Beijing-Tianjin-Hebei area, Yangtze River Delta area and Pearl River Delta area are China's three largest and most mature mega-city regions, the status of which represents the general level of the urban and regional development in China. Based on entire-array-polygon method, this paper makes a comprehensive evolution assessment of the three mega-city regions in terms of urban population index, urban economy index, urban life index, urban culture index and urban primacy index. In terms of general developing level, the three mega-city regions have progressed to optimize the structure. With their respective advantages and disadvantages, the three mega-city regions initially realize a "diversified" regional layout. The diference and gap among the three mega-city regions are obviously decreasing, which contributes to the regional balance of China metropolitan development. The rankings of the three mega-city regions will be in a continuous adjustment. The Beijing-Tianjin-Hebei area is possible to catch up and take the lead.展开更多
This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that ...This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.展开更多
A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid m...A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.展开更多
In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relat...In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.展开更多
为了克服开放街道地图数据的空间异质性特征对其在数据匹配、更新等方面应用所造成的影响,提出一种基于指标相关性的指标权重确定算法(Criteria Importan ce Through Inter-criteria Correlation,简称CRITIC)的开放街道地图面实体匹配...为了克服开放街道地图数据的空间异质性特征对其在数据匹配、更新等方面应用所造成的影响,提出一种基于指标相关性的指标权重确定算法(Criteria Importan ce Through Inter-criteria Correlation,简称CRITIC)的开放街道地图面实体匹配方法。该方法充分考虑开放街道地图数据的空间异质性,在开放街道地图中面实体与其他数据进行匹配时,引入CRITIC算法计算开放街道地图数据中每个面要素几何相似因子的权重,避免了对匹配数据集中的所有面实体采用相同的相似因子权重,减少了人为定权方法所带来的主观性及局限性,提高了开放街道地图面实体与其他数据集的匹配精度。实验结果表明,该方法有效地克服了开放街道地图数据的空间异质性特点对匹配精度的影响,提升了开放街道地图中面实体与其他面实体数据的匹配精度,匹配的准确率、召回率和F1分数分别达到97.56%、98.04%和97.80%,均优于对比方法。展开更多
National and international research on regional development has matured from the use of single elements and indicators to the application of comprehensive multi-element and multi-indicator measures. We selected 12 ind...National and international research on regional development has matured from the use of single elements and indicators to the application of comprehensive multi-element and multi-indicator measures. We selected 12 indicators from six dimensions for analysis in this study, including income, consumption, education, population urbanization, traffic, and indoor living facilities. We then proposed the polyhedron method to comprehensively measure levels of regional multidimensional development. We also enhanced the polygon and vector sum methods to render them more suitable for studying the status of regional multidimensional development. Finally, we measured levels of regional multidimensional development at county, city, and provincial scales across China and analyzed spatial differences using the three methods above and the weighted sum method applied widely. The results of this study reveal the presence of remarkable regional differences at the county scale across China in terms of single and multidimensional levels of regional development. Analyses show that values of the regional multidimensional development index （RMDI） are high in eastern coastal areas, intermediate in the midlands and in northern border regions, and low in the southwest and in western border regions. Districts characterized by enhanced and the highest levels of this index are distributed in eastern coastal areas, including cities in central and western regions, as well as areas characterized by the development of energy and mineral resources. The regional distribution of reduced and the lowest levels of this index is consistent with concentrations of areas that have always been impoverished. Correlation analyses of the results generated by the four methods at provincial, city, and county scales show that all are equivalent in practical application and can be used to generate satisfactory measures for regional multidimensional development. Additiona~ correlation analyses between RMDI values calculated using the polyhedron method and per capita gross domestic product （GDP） demonstrate that the latter is not a meaningful proxy for the level of regional multidimensional development.展开更多
Columnar jointed rock mass with unique geometric and geological properties is one spectacular example of geometrical order in nature.Columnar joints are generally accepted to be formed by spatially uniform volume cont...Columnar jointed rock mass with unique geometric and geological properties is one spectacular example of geometrical order in nature.Columnar joints are generally accepted to be formed by spatially uniform volume contraction during cooling.In this paper,substantial field work was performed to study the geological characteristics of irregular columnar jointed basalt on the left bank dam foundation in the Baihetan Hydropower Station,where the columnar jointed rock mass is extensively exposed due to excavation.The quantitative measurements of the sizing of polygonal crack pattern of columnar joints and assessment of their degree of irregularity were summarized.Considering the irregularity of polygonal crack pattern,a modified Voronoi polygon(MVP)method was developed to model the special polygonal crack pattern of columnar joints.The new polygonal pattern obtained by the MVP method consists of a large number of irregular polygons,of which the degree of irregularity is consistent with the field measurement results.This method can reproduce the rapid evolution from an initial ideal regular hexagonal pattern to a final actual irregular polygonal pattern as the degree of irregularity increases.The compression tests of columnar jointed rock mass with different irregularity show that the geometric irregularity has a great influence on its mechanical properties.This numerical construction method provides a reliable way to reconstruct columnar joint structure with specific polygonal crack pattern,which is consistent with onsite columnar jointed basalt.展开更多
基金supported by the National Natural Science Foundation of China(No.52232014)the National Natural Science Foundation of China Joint Fund(No.U2241215)。
文摘In this article,an Enlarged Polygon/Polyhedron(ELP)method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance(CPOA)constraints in trajectory optimization.First,the equivalent condition of a point outside the convex set is given and proved rigorously.Then,the ELP condition describing the CPOA constraints equivalently is given without introducing binary variables,and its geometric meaning is explained.Finally,the ELP method is used to transform the CPOA trajectory optimization problem into an optimal control problem without binary variables.The effectiveness and validity of ELP method are demonstrated through simulations with both simple linear dynamic model(unmanned aerial vehicle)and complex nonlinear dynamic model(hypersonic glide vehicle).Comparison indicates the computational time of ELP method is only 1%-20%of that of the traditional Mixed-Integer Programming(MIP)method.
文摘Mega-city region is the mainstream of global urban development and also the dominant model of the neo urbanization process in China. The Beijing-Tianjin-Hebei area, Yangtze River Delta area and Pearl River Delta area are China's three largest and most mature mega-city regions, the status of which represents the general level of the urban and regional development in China. Based on entire-array-polygon method, this paper makes a comprehensive evolution assessment of the three mega-city regions in terms of urban population index, urban economy index, urban life index, urban culture index and urban primacy index. In terms of general developing level, the three mega-city regions have progressed to optimize the structure. With their respective advantages and disadvantages, the three mega-city regions initially realize a "diversified" regional layout. The diference and gap among the three mega-city regions are obviously decreasing, which contributes to the regional balance of China metropolitan development. The rankings of the three mega-city regions will be in a continuous adjustment. The Beijing-Tianjin-Hebei area is possible to catch up and take the lead.
基金The authors would like to present our gratitude to the Flemish Government financially supporting for the VLIR-OUS TEAM Project,VN2017TEA454A103‘An innovative solution to protect Vietnamese coastal riverbanks from floods and erosion’.
文摘This paper presents an adapted stabilisation method for the equal-order mixed scheme of finite elements on convex polygonal meshes to analyse the high velocity and pressure gradient of incompressible fluid flows that are governed by Stokes equations system.This technique is constructed by a local pressure projection which is extremely simple,yet effective,to eliminate the poor or even non-convergence as well as the instability of equal-order mixed polygonal technique.In this research,some numerical examples of incompressible Stokes fluid flow that is coded and programmed by MATLAB will be presented to examine the effectiveness of the proposed stabilised method.
文摘A novel polygonal finite element method （PFEM） based on partition of unity is proposed, termed the virtual node method （VNM）. To test the performance of the present method, numerical examples are given for solid mechanics problems. With a polynomial form, the VNM achieves better results than those of traditional PFEMs, including the Wachspress method and the mean value method in standard patch tests. Compared with the standard triangular FEM, the VNM can achieve better accuracy. With the ability to construct shape functions on polygonal elements, the VNM provides greater flexibility in mesh generation. Therefore, several fracture problems are studied to demonstrate the potential implementation. With the advantage of the VNM, the convenient refinement and remeshing strategy are applied.
文摘In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.
文摘为了克服开放街道地图数据的空间异质性特征对其在数据匹配、更新等方面应用所造成的影响,提出一种基于指标相关性的指标权重确定算法(Criteria Importan ce Through Inter-criteria Correlation,简称CRITIC)的开放街道地图面实体匹配方法。该方法充分考虑开放街道地图数据的空间异质性,在开放街道地图中面实体与其他数据进行匹配时,引入CRITIC算法计算开放街道地图数据中每个面要素几何相似因子的权重,避免了对匹配数据集中的所有面实体采用相同的相似因子权重,减少了人为定权方法所带来的主观性及局限性,提高了开放街道地图面实体与其他数据集的匹配精度。实验结果表明,该方法有效地克服了开放街道地图数据的空间异质性特点对匹配精度的影响,提升了开放街道地图中面实体与其他面实体数据的匹配精度,匹配的准确率、召回率和F1分数分别达到97.56%、98.04%和97.80%,均优于对比方法。
基金National Natural Science Foundation of China,No.41171449Knowledge Innovation Project of the Chinese Academy of Sciences,No.KZZD-EW-06
文摘National and international research on regional development has matured from the use of single elements and indicators to the application of comprehensive multi-element and multi-indicator measures. We selected 12 indicators from six dimensions for analysis in this study, including income, consumption, education, population urbanization, traffic, and indoor living facilities. We then proposed the polyhedron method to comprehensively measure levels of regional multidimensional development. We also enhanced the polygon and vector sum methods to render them more suitable for studying the status of regional multidimensional development. Finally, we measured levels of regional multidimensional development at county, city, and provincial scales across China and analyzed spatial differences using the three methods above and the weighted sum method applied widely. The results of this study reveal the presence of remarkable regional differences at the county scale across China in terms of single and multidimensional levels of regional development. Analyses show that values of the regional multidimensional development index （RMDI） are high in eastern coastal areas, intermediate in the midlands and in northern border regions, and low in the southwest and in western border regions. Districts characterized by enhanced and the highest levels of this index are distributed in eastern coastal areas, including cities in central and western regions, as well as areas characterized by the development of energy and mineral resources. The regional distribution of reduced and the lowest levels of this index is consistent with concentrations of areas that have always been impoverished. Correlation analyses of the results generated by the four methods at provincial, city, and county scales show that all are equivalent in practical application and can be used to generate satisfactory measures for regional multidimensional development. Additiona~ correlation analyses between RMDI values calculated using the polyhedron method and per capita gross domestic product （GDP） demonstrate that the latter is not a meaningful proxy for the level of regional multidimensional development.
基金Projects(51621006,51779251)supported by the National Natural Science Foundation of China。
文摘Columnar jointed rock mass with unique geometric and geological properties is one spectacular example of geometrical order in nature.Columnar joints are generally accepted to be formed by spatially uniform volume contraction during cooling.In this paper,substantial field work was performed to study the geological characteristics of irregular columnar jointed basalt on the left bank dam foundation in the Baihetan Hydropower Station,where the columnar jointed rock mass is extensively exposed due to excavation.The quantitative measurements of the sizing of polygonal crack pattern of columnar joints and assessment of their degree of irregularity were summarized.Considering the irregularity of polygonal crack pattern,a modified Voronoi polygon(MVP)method was developed to model the special polygonal crack pattern of columnar joints.The new polygonal pattern obtained by the MVP method consists of a large number of irregular polygons,of which the degree of irregularity is consistent with the field measurement results.This method can reproduce the rapid evolution from an initial ideal regular hexagonal pattern to a final actual irregular polygonal pattern as the degree of irregularity increases.The compression tests of columnar jointed rock mass with different irregularity show that the geometric irregularity has a great influence on its mechanical properties.This numerical construction method provides a reliable way to reconstruct columnar joint structure with specific polygonal crack pattern,which is consistent with onsite columnar jointed basalt.
