The geometry relation and the contact point-pairs detection between two three dimensional(3D) objects with arbitrary shapes are essential problems involved in discontinuous computation and computational geometry. This...The geometry relation and the contact point-pairs detection between two three dimensional(3D) objects with arbitrary shapes are essential problems involved in discontinuous computation and computational geometry. This paper reported a geometry relation judgment and contact searching algorithm based on Contact Theory. A contact cover search algorithm is proposed to find all the possible contact cover between two blocks. Two blocks can come to contact only on these covers. Each contact cover can define a possible contact point-pair between two blocks. Data structure and flow chart are provided, as well as some examples in details.Contact problems involving concave blocks or parallel planes are considered to be very difficult in past and are solved by this algorithm. The proposed algorithm is compacted and applicable to the discontinuous computation, such as robotic control, rock mass stability, dam stability etc. A 3D cutting and block searching algorithm is also proposed in this study and used to search the outer boundary of the 3D entrance block when 3D concave blocks are encountered. The 3D cutting and block searching algorithm can be also used to form the block system for jointed rock.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
Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discont...Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.展开更多
In this work,we propose a formulation based on the Polygonal Discontinuous Galerkin(PolyDG)method for contact mechanics that arises in fluid-structure interaction problems.In particular,we introduce a consistent penal...In this work,we propose a formulation based on the Polygonal Discontinuous Galerkin(PolyDG)method for contact mechanics that arises in fluid-structure interaction problems.In particular,we introduce a consistent penalization approach to treat the frictionless contact between immersed structures that undergo large displacements.The key feature of the method is that the contact condition can be naturally embedded in the PolyDG formulation,allowing to easily support polygonal/polyhedral meshes.The proposed approach introduced a fixed background mesh for the fluid problem overlapped by the structure grid that is able to move independently of the fluid one.To assess the validity of the proposed approach,we report the results of several numerical experiments obtained in the case of contact between flexible structures immersed in a fluid.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51479001, 41471052)the China Institute of Water Resources and Hydropower Research Research & Development Support Program(Grant Nos. GE0145B462017, GE0145B692017)
文摘The geometry relation and the contact point-pairs detection between two three dimensional(3D) objects with arbitrary shapes are essential problems involved in discontinuous computation and computational geometry. This paper reported a geometry relation judgment and contact searching algorithm based on Contact Theory. A contact cover search algorithm is proposed to find all the possible contact cover between two blocks. Two blocks can come to contact only on these covers. Each contact cover can define a possible contact point-pair between two blocks. Data structure and flow chart are provided, as well as some examples in details.Contact problems involving concave blocks or parallel planes are considered to be very difficult in past and are solved by this algorithm. The proposed algorithm is compacted and applicable to the discontinuous computation, such as robotic control, rock mass stability, dam stability etc. A 3D cutting and block searching algorithm is also proposed in this study and used to search the outer boundary of the 3D entrance block when 3D concave blocks are encountered. The 3D cutting and block searching algorithm can be also used to form the block system for jointed rock.
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.
文摘Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.
基金this work is partially funded by INDAM-GNCS.PFA and SZ have been partially funded by the Italian research project MIUR PRIN17,number 201744KLJLCV has been partially supported by the H2020-MSCA-ITN-2017,EU project 765374“ROMSOC-Reduced Order Modelling,Simulation and Optimization of Coupled systems”and by the Italian research project MIUR PRIN172017AXL54F“Modeling the heart across the scales:from cardiac cells to the whole organ”.
文摘In this work,we propose a formulation based on the Polygonal Discontinuous Galerkin(PolyDG)method for contact mechanics that arises in fluid-structure interaction problems.In particular,we introduce a consistent penalization approach to treat the frictionless contact between immersed structures that undergo large displacements.The key feature of the method is that the contact condition can be naturally embedded in the PolyDG formulation,allowing to easily support polygonal/polyhedral meshes.The proposed approach introduced a fixed background mesh for the fluid problem overlapped by the structure grid that is able to move independently of the fluid one.To assess the validity of the proposed approach,we report the results of several numerical experiments obtained in the case of contact between flexible structures immersed in a fluid.
