Vertex-to-face contact searching algorithm for three-dimensional frictionless contact problems

Abstract

SUMMARYThis article presents a new vertex-to-face contact searching algorithm for the three-dimensional (3-D) discontinuous deformation analysis (DDA). In this algorithm, topology is applied to the contact rule when any two polyhedrons are close to each other. Attempt is made to expand the original contact searching algorithm from two-dimensional (2-D) to 3-D DDA. Examples are provided to demonstrate the new contact rule for vertex-to-face contacts between two polyhedrons with planar boundaries.

Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm

“…Wu et al [9] developed a theory of 3-D DDA and then applied it to a slope toppling at Amatoribashi-nishi in Japan, but they did not present contact theory for the six types of block contacts. Wu et al [10] developed a new contact searching algorithm for frictionless vertex-to-face contact problems, and presented the 3-D DDA formulation for normal contact force. Yeung et al [11] and Wu [12] presented algorithms for edge-to-edge contacts.…”

Condensed form of complementarity formulation for discontinuous deformation analysis

“…[13][14][15][16][17][18], among which is the 3-dimensional contact theory by Shi [19]. With this theory, the singular contact such as vertex-to-vertex contact will become easy to treat.…”

A fast direct search algorithm for contact detection of convex polygonal or polyhedral particles

“…Another genre is referred to as the direct search or improved direct search algorithms [8][9][10]. Other methods include the approaching face method [5], an improved approaching face algorithm [6], vertex-to-face searching algorithm [7] and multi-shell cover method [11]. Boon et al [1] generalize contact between convex polyhedral particles as a convex optimization problem and used a linear program method to solve it.…”