The contact between blocks is treated by the open-close iteration in the conventional discontinuous deformation analysis (DDA),which needs to introduce spurious springs between two blocks in contact and to assume the ...The contact between blocks is treated by the open-close iteration in the conventional discontinuous deformation analysis (DDA),which needs to introduce spurious springs between two blocks in contact and to assume the normal stiffness and the tangential stiffness (the penalty factors). Unreasonable values of stiffness would result in numerical problems. To avoid the penalty factors and the open-close iteration,we reformulate the DDA as a mixed complementary problem (MiCP) and then choose the path Newton method (PNM) to solve the problem. Some examples including those originally designed by Shi are reanalyzed,which proves feasibility of the proposed procedure.展开更多
Dynamic airspace management plans and assigns airspace resources to airspace users on demand to increase airspace capacity. Although many studies of air traffic flow management （ATFM） have sought to optimally alloca...Dynamic airspace management plans and assigns airspace resources to airspace users on demand to increase airspace capacity. Although many studies of air traffic flow management （ATFM） have sought to optimally allocate air traffic to get the best use of given airspace resources, few studies have focused on how to build an efficient air traffic network or how to adjust the current network in real time. This paper presents an integer program model named the dynamic air route open-close problem （DROP）. DROP has a cost-based objective function which takes into account constraints such as the shortest occupancy time of routes, which are not considered in ATFM models. The aim of DROP is to determine which routes will be opened to a certain user during a given time period. Simulation results show that DROP can facilitate utilization of air routes. DROP, a simplified version of an air traffic network constructing problem, is the first step towards realizing dynamic airspace management. The combination of ATFM and DROP can facilitate decisions toward more reasonable, efficient use of limited airspace resources.展开更多
Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） m...Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） method to deal with contact prob- lem, its computational efficiency is relatively low. However, spherical element based discontinuous deformation analysis （SDDA）, which uses very simple contact type like point-to-point contact, has higher calculation speed. In the framework of SDDA, this paper presents a very simple contact calculation approach by removing the OCI scheme and by adopting the maximal displacement increment （MDI）. Through some verification examples, it is proved that the proposed method is correct and effective, and a higher computational efficiency is obtained.展开更多
This paper presents a modified method of discontinuous deformation analysis(DDA). In the presented method, open-close iteration may not be needed, small penetration is permitted among blocks, and springs are added bet...This paper presents a modified method of discontinuous deformation analysis(DDA). In the presented method, open-close iteration may not be needed, small penetration is permitted among blocks, and springs are added between contacting block pairs only when a penetration takes place. The three contact patterns(i.e. sliding, locking and opening) in original DDA method are not involved, and the recognition of these contact patterns and treatment of transformation among patterns are not required either,signi fi cantly saving the computing time. In a convex to concave contact, there are two candidate entrance edges which may cause uncertainty. In this case, we propose the angle bisector criterion to determine the entrance edge. The spring stiffness is much larger than Young's modulus in the original DDA, however we fi nd that the correct results can still be obtained when it is much smaller than Young's modulus. Finally,the penetrations by using penalty method and augmented Lagrangian method are compared. Penetration of the latter is 1/4 of the former. The range of spring stiffness for the latter is wider than the former,being 0.01-1 of the former. Both methods can lead to correct contact forces.展开更多
While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. ...While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem(MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible.展开更多
Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibr...Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibration, and attenuation of angular velocity, were observed in the original NMM. The first two kind errors are owing to the small deformation assumption and the last one is due to the numerical damping. A large deformation NMM is proposed based on large deformation theory. In this method, the governing equation is derived using Green strain, the large deformation iteration and the open-close iteration are combined, and an updating strategy is proposed. The proposed method is used to analyze block rotation, beam bending, and rock falling problems and the results prove that all three kinds of errors are eliminated in this method.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 90715028)Research Project for Protection of High Cut Slopes in Three Gorges’ Reservoir (Grant No. 2008SXG01-2)
文摘The contact between blocks is treated by the open-close iteration in the conventional discontinuous deformation analysis (DDA),which needs to introduce spurious springs between two blocks in contact and to assume the normal stiffness and the tangential stiffness (the penalty factors). Unreasonable values of stiffness would result in numerical problems. To avoid the penalty factors and the open-close iteration,we reformulate the DDA as a mixed complementary problem (MiCP) and then choose the path Newton method (PNM) to solve the problem. Some examples including those originally designed by Shi are reanalyzed,which proves feasibility of the proposed procedure.
基金Supported by the Basic Research Foundation of Tsinghua Na-tional Laboratory for Information Science and Technology (TNList) the National High-Tech Research and Development (863) Program of China (No. 2006AA12A114)
文摘Dynamic airspace management plans and assigns airspace resources to airspace users on demand to increase airspace capacity. Although many studies of air traffic flow management （ATFM） have sought to optimally allocate air traffic to get the best use of given airspace resources, few studies have focused on how to build an efficient air traffic network or how to adjust the current network in real time. This paper presents an integer program model named the dynamic air route open-close problem （DROP）. DROP has a cost-based objective function which takes into account constraints such as the shortest occupancy time of routes, which are not considered in ATFM models. The aim of DROP is to determine which routes will be opened to a certain user during a given time period. Simulation results show that DROP can facilitate utilization of air routes. DROP, a simplified version of an air traffic network constructing problem, is the first step towards realizing dynamic airspace management. The combination of ATFM and DROP can facilitate decisions toward more reasonable, efficient use of limited airspace resources.
基金supported by the National Basic Research Program of China("973" Project)(Grant Nos.2014CB046904&2014CB047101)the National Natural Science Foundation of China(Grant Nos.51479191&51509242)
文摘Discontinuous deformation analysis （DDA） method is a newly developed discrete element method which employs the implicit time-integration scheme to solve the governing equations and the open-close iteration （OCI） method to deal with contact prob- lem, its computational efficiency is relatively low. However, spherical element based discontinuous deformation analysis （SDDA）, which uses very simple contact type like point-to-point contact, has higher calculation speed. In the framework of SDDA, this paper presents a very simple contact calculation approach by removing the OCI scheme and by adopting the maximal displacement increment （MDI）. Through some verification examples, it is proved that the proposed method is correct and effective, and a higher computational efficiency is obtained.
基金supported by CRSRI Open Research Program (No.CKWV2014206/KY)the National Basic Research Program of China (No.2011CB710603)
文摘This paper presents a modified method of discontinuous deformation analysis(DDA). In the presented method, open-close iteration may not be needed, small penetration is permitted among blocks, and springs are added between contacting block pairs only when a penetration takes place. The three contact patterns(i.e. sliding, locking and opening) in original DDA method are not involved, and the recognition of these contact patterns and treatment of transformation among patterns are not required either,signi fi cantly saving the computing time. In a convex to concave contact, there are two candidate entrance edges which may cause uncertainty. In this case, we propose the angle bisector criterion to determine the entrance edge. The spring stiffness is much larger than Young's modulus in the original DDA, however we fi nd that the correct results can still be obtained when it is much smaller than Young's modulus. Finally,the penetrations by using penalty method and augmented Lagrangian method are compared. Penetration of the latter is 1/4 of the former. The range of spring stiffness for the latter is wider than the former,being 0.01-1 of the former. Both methods can lead to correct contact forces.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2011CB013505&2014CB047100)the National Natural Science Foundation of China(Grant No.11172313)
文摘While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem(MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible.
基金This research was supported by the National Natural Science Foundation of China (Grant Nos. 51479001, 41471052)the IWHR Research & Development Support Program (GE0145B462017,GE0145B692017).
文摘Numerical manifold method (NMM) is an effective method for simulating block system, however, significant errors are found in its simulation of rotation problems. Three kinds of errors, as volume expansion, stress vibration, and attenuation of angular velocity, were observed in the original NMM. The first two kind errors are owing to the small deformation assumption and the last one is due to the numerical damping. A large deformation NMM is proposed based on large deformation theory. In this method, the governing equation is derived using Green strain, the large deformation iteration and the open-close iteration are combined, and an updating strategy is proposed. The proposed method is used to analyze block rotation, beam bending, and rock falling problems and the results prove that all three kinds of errors are eliminated in this method.
