Natural Element Method for the Simulation of Structures and Processes [Hardcover]

Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a third way besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics. It is now considered to be a sub-discipline within computational science.

This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material forming processes involving solids and Newtonian and non-Newtonian fluids.

Foreword ix

Acknowledgements xi

Chapter 1. Introduction 1

1.1. SPH method 3

1.2. RKPM method 5

1.3. MLS based approximations 10

1.4. Final note 11

Chapter 2. Basics of the Natural Element Method 13

2.1. Introduction 13

2.2. Natural neighbor Galerkin methods 14

2.3. Exact imposition of the essential boundary conditions 22

2.4. Mixed approximations of natural neighbor type 27

2.5. High order natural neighbor interpolants 40

Chapter 3. Numerical Aspects 49

3.1. Searching for natural neighbors 49

3.2. Calculation of NEM shape functions of the Sibson type 52

3.3. Numerical integration 71

3.4. NEM on an octree structure 80

Chapter 4. Applications in the Mechanics of Structures and Processes 93

4.1. Two- and three-dimensional elasticity 93&ll"