Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

Abstract This paper presents a new numerical model that can add a finite element mesh into each block of the three-dimensional discontinuous deformation analysis (3-D DDA), originally developed by Gen-hua Shi. The main objectives of this research are to enhance DDA block’s deformability. Formulations of stiffness and force matrices in 3-D DDA with conventional Trilinear (8-node) and Serendipity (20-node) hexahedral isoparametric finite elements meshed block system due to elastic stress, initial stress, point load, body force, displacement constraints, inertia force, normal and shear contact forces are derived in detail for program coding. The program code for the Trilinear and Serendipity hexahedron elements have been developed, and it has been applied to some examples to show the advantages achieved when finite element is associated with 3-D DDA to handle problems under large displacements and deformations. Results calculated for the same models by use of the original 3-D DDA are far from the theoretical solutions while the results of new numerical model are quite good in agreement with theoretical solutions; however, for the Trilinear elements, more number of elements are needed.

[1]  C. H. Juang,et al.  Vertex‐to‐face contact searching algorithm for three‐dimensional frictionless contact problems , 2005 .

[2]  Q. H. Jiang,et al.  A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis , 2004 .

[3]  Ming C. Lin,et al.  Efficient collision detection for animation and robotics , 1993 .

[4]  Brian Mirtich,et al.  Impulse-based dynamic simulation of rigid body systems , 1996 .

[5]  Bernard Amadei,et al.  Extensions of discontinuous deformation analysis for jointed rock masses , 1996 .

[6]  Kianoosh Hatami,et al.  Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm , 2008 .

[7]  Gen-hua Shi.  Block system modeling by discontinuous deformation analysis , 1993 .

[8]  Ali Mortazavi,et al.  Discontinuous deformation analysis with second-order finite element meshed block , 2006 .

[9]  Shi Genhua.  Theory and examples of three dimensional discontinuous deformation analyses , 2020, Frontiers of Rock Mechanics and Sustainable Development in the 21st Century.

[10]  Lanru Jing,et al.  A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering , 2003 .

[11]  Eric Perkins,et al.  A fast contact detection algorithm insensitive to object sizes , 2001 .

[12]  S. M. Hsiung.  Discontinuous Deformation Analysis (DDA) With nth Order Polynomial Displacement Functions , 2001 .

[13]  S. Amir Reza Beyabanaki,et al.  High-order three-dimensional discontinuous deformation analysis (3-D DDA) , 2010 .

[14]  Vinod K. Garga,et al.  A numerical method for modelling large displacements of jointed rocks. I. Fundamentals , 1993 .

[15]  Dawei Zhao,et al.  A fast contact detection algorithm for 3-D discrete element method , 2004 .

[16]  Hui Rong Bao,et al.  Nodal-based discontinuous deformation analysis , 2010 .

[17]  P. A. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART I. A SCHEME TO DETECT AND REPRESENT CONTACTS IN A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .

[18]  Youssef M A Hashash,et al.  Shortest link method for contact detection in discrete element method , 2006 .

[19]  Qinghui Jiang,et al.  Validation of block theory and three-dimensional discontinuous deformation analysis as wedge stability analysis methods , 2003 .

[20]  Yung-ming Cheng,et al.  Rigid body rotation and block internal discretization in DDA analysis , 2000 .

[21]  Lin Gao,et al.  Formulations of the three-dimensional discontinuous deformation analysis method , 2004 .

[22]  A. Munjiza.  The Combined Finite-Discrete Element Method , 2004 .

[23]  J. Williams,et al.  Discrete element simulation and the contact problem , 1999 .

[24]  David M. Doolin,et al.  Review of validation of the discontinuous deformation analysis (DDA) method , 2006 .

[25]  M. R. Yeung,et al.  A model of edge-to-edge contact for three-dimensional discontinuous deformation analysis , 2007 .

[26]  Elmer G. Gilbert,et al.  The Gilbert-Johnson-Keerthi distance algorithm: a fast version for incremental motions , 1997, Proceedings of International Conference on Robotics and Automation.

[27]  Yuzo Ohnishi,et al.  Theory of three-dimensional discontinuous deformation analysis and its application to a slope toppling at Amatoribashi, Japan , 2005 .

[28]  Jian-Hong Wu.  New edge-to-edge contact calculating algorithm in three-dimensional discrete numerical analysis , 2008, Adv. Eng. Softw..