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Article
Publication date: 1 February 1992

GEN‐HUA SHI

A numerical model of deformable block systems that gives a unique solution for large displacement, large deformation and failure computations is presented. The forces acting on…

2198

Abstract

A numerical model of deformable block systems that gives a unique solution for large displacement, large deformation and failure computations is presented. The forces acting on each block, from external loading or contact with other blocks, satisfy the equilibrium equations. Equilibrium is also achieved between external forces and the block stresses. Furthermore, the analysis fulfills constraints of no tension between blocks and no penetration of one block into another. Also, Coloumb's law is fulfilled at all contact positions for both static and dynamic computations. The program ready algorithms with brief derivations are stated in this paper.

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Engineering Computations, vol. 9 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1992

PETER A. CUNDALL and ROGER D. HART

Discrete element methods are numerical procedures for simulating the complete behaviour of systems of discrete, interacting bodies. Three important aspects of discrete element…

2758

Abstract

Discrete element methods are numerical procedures for simulating the complete behaviour of systems of discrete, interacting bodies. Three important aspects of discrete element programs are examined: (1) the representation of contacts; (2) the representation of solid material; and (3) the scheme used to detect and revise the set of contacts. A proposal is made to define what constitutes a discrete element program, and four classes of such programs are described: the distinct element method, modal methods, discontinuous deformation analysis and the momentum‐exchange method. Several applications and examples are presented, and a list is given of suggestions for future developments.

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Engineering Computations, vol. 9 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1992

GRAHAM G.W. MUSTOE

A generalized weighted residual method is used to formulate the discrete element method (DEM) for rigid or deformable bodies. It is shown that this approach provides a unified…

573

Abstract

A generalized weighted residual method is used to formulate the discrete element method (DEM) for rigid or deformable bodies. It is shown that this approach provides a unified methodology for deriving many of the different discrete element techniques in current use today. This procedure is used to develop a number of different element formulations for use in problems in which the distinct bodies exhibit complex deformation behaviour such as beam or plate flexure, membrane action, and additional reinforcement of a jointed discontinuum. A covergence proof for the two‐dimensional beam element is given for mathematical validation. A number of examples are also presented which illustrate the usefulness of different discrete element types in engineering analyses of discontinuum problems.

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Engineering Computations, vol. 9 no. 2
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1995

J.R. Williams and R. O’Connor

We present an algorithm for contact resolution that is valid for a wide variety of polygonal two dimensional shapes and is of linear computational complexity. The algorithm is…

812

Abstract

We present an algorithm for contact resolution that is valid for a wide variety of polygonal two dimensional shapes and is of linear computational complexity. The algorithm is designed for use in discrete element analysis of granular and multibody systems exhibiting discontinuous behaviour. Contact detection usually consists of a spatial sorting phase and a contact resolution phase. The spatial sorting phase seeks to avoid an all‐to‐all body comparison by culling the number of objects which are potential contactors of a given object. The contact resolution phase resolves the details of the contact between two given objects. The algorithm presented here (called DFR) addresses the contact resolution phase and is applicable to convex geometries and to a restricted set of concave geometries. Examination of the algorithm establishes an upper bound linear computational complexity, of order O(N), with respect to the number of points (N) used to define the object boundary. The DFR algorithm is combined with a modified heapsort algorithm for spatial sorting of M bodies which has complexity O(M log M) and is applied to a baseline granular simulation problem to test its efficiency.

Details

Engineering Computations, vol. 12 no. 2
Type: Research Article
ISSN: 0264-4401

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