Contacts between two general blocks are the fundamental problem for discontinuous analysis. There are different contact points in different block positions, and there may have infinite contact point pairs in the same ...Contacts between two general blocks are the fundamental problem for discontinuous analysis. There are different contact points in different block positions, and there may have infinite contact point pairs in the same block position. In this paper, a new concept of an entrance block for solving the contacts between two general blocks is introduced. The boundary of an entrance block is a contact cover system. Contact covers may consist of contact vectors, edges, angles or polygons. Each contact cover defines a contact point and all closed-contact points define the movements, rotations and deformations of all blocks as in real cases. Given a reference point, the concept of entrance block simplifies the contact computation in the following ways.(1) The shortest distance between two blocks can be computed by the shortest distance between the reference point and the surface of the entrance block.(2) As the reference point outside the entrance block moves onto the surface of entrance block, the first entrance takes place. This first entrance point on the entrance block surface defines the contact points and related contact locations.(3) If the reference point is already inside the entrance block, it will exit the entrance block along the shortest path. The corresponding shortest exit point on the entrance block surface defines the contact points and related contact locations. All blocks and angles here are defined by inequality equations. Algebraic operations on blocks and angles are described here. Since the blocks and angles are point sets with infinite points, the geometric computations are difficult, and therefore the geometric computations are performed by related algebraic operations.展开更多
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2014CB047100)
文摘Contacts between two general blocks are the fundamental problem for discontinuous analysis. There are different contact points in different block positions, and there may have infinite contact point pairs in the same block position. In this paper, a new concept of an entrance block for solving the contacts between two general blocks is introduced. The boundary of an entrance block is a contact cover system. Contact covers may consist of contact vectors, edges, angles or polygons. Each contact cover defines a contact point and all closed-contact points define the movements, rotations and deformations of all blocks as in real cases. Given a reference point, the concept of entrance block simplifies the contact computation in the following ways.(1) The shortest distance between two blocks can be computed by the shortest distance between the reference point and the surface of the entrance block.(2) As the reference point outside the entrance block moves onto the surface of entrance block, the first entrance takes place. This first entrance point on the entrance block surface defines the contact points and related contact locations.(3) If the reference point is already inside the entrance block, it will exit the entrance block along the shortest path. The corresponding shortest exit point on the entrance block surface defines the contact points and related contact locations. All blocks and angles here are defined by inequality equations. Algebraic operations on blocks and angles are described here. Since the blocks and angles are point sets with infinite points, the geometric computations are difficult, and therefore the geometric computations are performed by related algebraic operations.
