Mesh free methods : moving beyond the finite element method

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Başlık:

Yazar:

Liu, G. R. (Gui-Rong)

ISBN:

9780849312380

Ek Yazar:

Liu, G. R. (Gui-Rong)

Yayım Bilgisi:

Boca Raton: CRC Press, c2003.

Fiziksel Tanım:

692 p. : ill. ; 27 cm.

Konu Terimleri:

Mühendislik matematiği.

Sayısal analiz.

Engineering mathematics.

Numerical analysis.

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Materyal Türü

Kitap

Barkod

0055427

Yer Numarası

TA335L58 2003

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As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now, however, the limitations of FEM are becoming increasingly evident, and a new and more powerful class of techniques is emerging.

For the first time in book form, Mesh Free Methods: Moving Beyond the Finite Element Method provides full, step-by-step details of techniques that can handle very effectively a variety of mechanics problems. The author systematically explores and establishes the theories, principles, and procedures that lead to mesh free methods. He shows that meshless methods not only accommodate complex problems in the mechanics of solids, structures, and fluids, but they do so with a significant reduction in pre-processing time.

While they are not yet fully mature, mesh free methods promise to revolutionize engineering analysis. Filled with the new and unpublished results of the author's award-winning research team, this book is your key to unlocking the potential of these techniques, implementing them to solve real-world problems, and contributing to further advancements.

Author Notes

G. R. Liu is Director of the Centre for Advanced Computations in Engineering Science at the National University of Singapore.

1 Introduction	p. 1
1.1 Defining Mesh Free Methods	p. 1
1.2 Need for MFree Methods	p. 3
1.3 The Idea of MFree Methods	p. 4
1.4 Outline of the Book	p. 4
2 Mesh Free Methods for Engineering Problems	p. 9
2.1 Physical Phenomena in Engineering	p. 9
2.2 Solution Procedure	p. 9
2.3 Modeling the Geometry	p. 10
2.4 Node Generation	p. 13
2.5 Shape Function Creation	p. 15
2.6 Property of Material or Media	p. 15
2.7 Boundary, Initial, and Loading Conditions	p. 15
2.8 Simulation	p. 16
2.9 Visualization	p. 18
2.10 MFree Method Procedure	p. 18
2.11 Remarks	p. 25
3 Mechanics of Solids and Structures	p. 27
3.1 Basics	p. 27
3.2 Equations for Three-Dimensional Solids	p. 28
3.3 Equations for Two-Dimensional Solids	p. 34
3.4 Equations for Truss Members	p. 37
3.5 Equations for Beams	p. 38
3.6 Equations for Plates	p. 43
3.7 Remarks	p. 51
4 Principles for Weak Forms	p. 53
4.1 Strong Forms vs. Weak Forms	p. 53
4.2 Hamilton's Principle	p. 54
4.3 Constrained Hamilton's Principle	p. 55
4.4 Galerkin Weak Form	p. 58
4.5 Constrained Galerkin Weak Form	p. 61
4.6 Minimum Total Potential Energy Principle	p. 62
4.7 Weighted Residual Method	p. 63
4.8 Weighted Residual Method with Constraints	p. 64
4.9 Points to Note	p. 65
4.10 Remarks	p. 65
5 MFree Shape Function Construction	p. 67
5.1 Overview	p. 67
5.2 Smoothed Particle Hydrodynamics Approach	p. 70
5.3 Reproducing Kernel Particle Method	p. 77
5.4 Moving Least Squares Approximation	p. 79
5.5 Point Interpolation Method	p. 87
5.6 Radial PIM	p. 96
5.7 Radial PIM with Polynomial Reproduction	p. 101
5.8 Polynomial PIM with Coordinate Transformation	p. 107
5.9 Matrix Triangularization Algorithm	p. 110
5.10 Comparison Study via Examples	p. 116
5.11 Compatibility of MFree Function Approximation	p. 138
5.12 On the Concept of Reproduction	p. 143
5.13 Other Methods	p. 144
5.14 Remarks	p. 144
6 Element Free Galerkin Method	p. 147
6.1 EFG Formulation with Lagrange Multipliers	p. 147
6.2 EFG with Penalty Method	p. 169
6.3 Constrained Moving Least Square Method for EFG	p. 181
6.4 EFG for Nonlinear Elastic Problems	p. 198
6.5 Summary	p. 210
7 Meshless Local Petrov-Galerkin Method	p. 211
7.1 MLPG Formulation	p. 212
7.2 MLPG for Dynamic Problems	p. 229
7.3 Remarks	p. 246
8 Point Interpolation Methods	p. 249
8.1 Polynomial Point Interpolation Method	p. 250
8.2 Application of PIM to Foundation Consolidation Problem	p. 266
8.3 Radial Point Interpolation Method	p. 276
8.4 Local Point Interpolation Method (LPIM)	p. 300
8.5 Local Radial Point Interpolation Method	p. 314
8.6 Application of LRPIM to Diffusion Equations	p. 335
8.7 Comparison Study	p. 339
8.8 Summary	p. 341
9 Mesh Free Methods for Fluid Dynamics Problems	p. 345
9.1 Introduction	p. 345
9.2 Smoothed Particle Hydrodynamics Method	p. 346
9.3 Local Petrov-Galerkin Method	p. 369
9.4 Local Radial Point Interpolation Method	p. 382
10 Mesh Free Methods for Beams	p. 391
10.1 PIM Shape Function for Thin Beams	p. 392
10.2 Elastostatic Analysis of Thin Beams	p. 396
10.3 Buckling Analysis of Thin Beams (Eigenvalue Problem)	p. 403
10.4 Free-Vibration Analysis of Thin Beams (Eigenvalue Problem)	p. 405
10.5 Forced Vibration Analysis of Thin Beams (Time-Dependent Problem)	p. 408
10.6 Timoshenko Beams	p. 413
10.7 Remarks	p. 419
11 Mesh Free Methods for Plates	p. 421
11.1 EFG Method for Thin Plates	p. 421
11.2 EFG Method for Thin Composite Laminates	p. 439
11.3 EFG Method for Thick Plates	p. 457
11.4 RPIM for Thick Plates	p. 475
11.5 MLPG for Thin Plates	p. 486
11.6 Remarks	p. 499
12 Mesh Free Methods for Shells	p. 501
12.1 EFG Method for Spatial Thin Shells	p. 502
12.2 EFG Method for Thick Shells	p. 523
12.3 RPIM for Thick Shells	p. 534
12.4 Summary	p. 544
13 Boundary Mesh Free Methods	p. 545
13.1 BPIM Using Polynomial Basis	p. 546
13.2 BPIM Using Radial Function Basis	p. 557
13.3 Remarks	p. 565
14 Mesh Free Methods Coupled with Other Methods	p. 567
14.1 Coupled EFG/BEM	p. 567
14.2 Coupled EFG and Hybrid BEM	p. 580
14.3 Coupled MLPG/FE/BE Methods	p. 589
14.4 Remarks	p. 599
15 Implementation Issues	p. 601
15.1 Definition of the Support Domain or Influence Domain	p. 601
15.2 Triangular Mesh and Size of the Influence Domain	p. 602
15.3 Node Numbering and Bandwidth of the Stiffness Matrix	p. 603
15.4 Bucket Algorithm for Node Searching	p. 604
15.5 Relay Model for Domains with Irregular Boundaries	p. 605
15.6 Adaptive Procedure Based on Background Cells	p. 625
15.7 Strategy for Local Adaptive Refinement	p. 634
15.8 Remarks	p. 644
16 MFree2D[copyright]	p. 645
16.1 Overview	p. 645
16.2 Techniques Used in MFree2D	p. 646
16.3 Preprocessing in MFree2D	p. 646
16.4 Postprocessing in MFree2D	p. 661
References	p. 675
Index	p. 685

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