Page 10 - The Combined Finite-Discrete Element Method

Contents

Preface xi

Acknowledgements xiii

1 Introduction 1
1.1 General Formulation of Continuum Problems 1
1.2 General Formulation of Discontinuum Problems 2
1.3 A Typical Problem of Computational Mechanics
of Discontinua 4
1.4 Combined Continua-Discontinua Problems 27
1.5 Transition from Continua to Discontinua 28
1.6 The Combined Finite-Discrete Element Method 29
1.7 Algorithmic and Computational Challenge of the Combined Finite-Discrete
Element Method 32

2 Processing of Contact Interaction in the Combined Finite Discrete
Element Method 35
2.1 Introduction 35
2.2 The Penalty Function Method 40
2.3 Potential Contact Force in 2D 41
2.4 Discretisation of Contact Force in 2D 43
2.5 Implementation Details for Discretised Contact Force in 2D 43
2.6 Potential Contact Force in 3D 55
2.6.1 Evaluation of contact force 57
2.6.2 Computational aspects 58
2.6.3 Physical interpretation of the penalty parameter 62
2.6.4 Contact damping 63
2.7 Alternative Implementation of the Potential Contact Force 69

3 Contact Detection 73
3.1 Introduction 73
3.2 Direct Checking Contact Detection Algorithm 77
3.2.1 Circular bounding box 77
3.2.2 Square bounding object 78
3.2.3 Complex bounding box 79
3.3 Formulation of Contact Detection Problem for Bodies of Similar Size in 2D 80
3.4 Binary Tree Based Contact Detection Algorithm for Discrete Elements of
Similar Size 81