Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing pr...Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.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
文摘Two dimensional irregular polygons packing problem is very difficult to be solved in traditional optimal way.Simulated annealing(SA)algorithm is a stochastic optimization technique that can be used to solve packing problems.The whole process of SA is introduced firstly in this paper. An extended neighborhood searching method in SA is mainly analyzed. A general module of SA algorithm is given and used to lay out the irregular polygons. The judgment of intersection and other constrains of irregular polygons are analyzed. Then an example that was used in the paper of Stefan Jakobs is listed.Results show that this SA algorithm shortens the computation time and improves the solution.
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.
