A method for representing boundaries in discrete element modelling - part I: Geometry and contact detection

The discrete element method for analysis of the dynamic behaviour of discon tinuous media is well established. However, its application to engineering problems is still limited to simplified representations of structural bound aries and their kinematics. In this paper a method is developed for represe nting three-dimensional boundaries of arbitrary geometry and for modelling the interaction between boundary objects and particles within the discrete element modelling framework. The approach, which we term the finite wall me thod, uses planar triangular elements to approximate the boundary surface t opology. Any number of wall elements can be used to model the shape of the structure. A contact detection scheme is presented for boundary surfaces an d spheres based on a series of vector projections to reduce the problem dim ensionally. The algorithm employs spatial sporting to obtain the set of pot ential contacts between spheres and wall elements prior to contact resoluti on. In a further stage, all possible contact conditions including contact w ith surfaces, edges and corners are explicitly determined. Part I of this t wo-part series of papers describes the finite wall method for representatio n of surface geometry and fully elaborates the method for detecting and res olving contact between boundary wall elements and spheres. In Part II the f inite wall method is extended to apply kinematics to linearly independent b oundary objects using combinations of translational and rotational motion. An approach is developed for coupling the DEM with the FEM for the purpose of optimising the design of structures which are dynamically interacting wi th particulate media. Copyright (C) 2001 John Wiley & Sons, Ltd.