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Meshless Methods and Their Numerical Properties [Kõva köide]

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(Nanyang Technological University, Singapore),
  • Formaat: Hardback, 447 pages, kõrgus x laius: 234x156 mm, kaal: 771 g, 35 Tables, black and white; 187 Illustrations, black and white
  • Ilmumisaeg: 22-Feb-2013
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466517468
  • ISBN-13: 9781466517462
Teised raamatud teemal:
Meshless Methods and Their Numerical PropertiesSuurem pilt
  • Formaat: Hardback, 447 pages, kõrgus x laius: 234x156 mm, kaal: 771 g, 35 Tables, black and white; 187 Illustrations, black and white
  • Ilmumisaeg: 22-Feb-2013
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466517468
  • ISBN-13: 9781466517462
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781466517462.html
Märksõnad:
Meshless, or meshfree methods, which overcome many of the limitations of the finite element method, have achieved significant progress in numerical computations of a wide range of engineering problems. A comprehensive introduction to meshless methods, Meshless Methods and Their Numerical Properties gives complete mathematical formulations for the most important and classical methods, as well as several methods recently developed by the authors. This book also offers a rigorous mathematical treatment of their numerical propertiesincluding consistency, convergence, stability, and adaptivityto help you choose the method that is best suited for your needs.

Get Guidance for Developing and Testing Meshless Methods

Developing a broad framework to study the numerical computational characteristics of meshless methods, the book presents consistency, convergence, stability, and adaptive analyses to offer guidance for developing and testing a particular meshless method. The authors demonstrate the numerical properties by solving several differential equations, which offer a clearer understanding of the concepts. They also explain the difference between the finite element and meshless methods.

Explore Engineering Applications of Meshless Methods

The book examines how meshless methods can be used to solve complex engineering problems with lower computational cost, higher accuracy, easier construction of higher-order shape functions, and easier handling of large deformation and nonlinear problems. The numerical examples include engineering problems such as the CAD design of MEMS devices, nonlinear fluid-structure analysis of near-bed submarine pipelines, and two-dimensional multiphysics simulation of pH-sensitive hydrogels. Appendices supply useful template functions, flowcharts, and data structures to assist you in implementing meshless methods.

Choose the Best Method for a Particular Problem

Providing insight into the special features and intricacies of meshless methods, this is a valuable reference for anyone developing new high-performance numerical methods or working on the modelling and simulation of practical engineering problems. It guides you in comparing and verifying meshless methods so that you can more confidently select the best method to solve a particular problem.

Arvustused

"This monograph is a blast of extensive and detailed mathematical exposition of meshless methods. It would serve as a quick reference guide for any one studying advanced numerical methods. The content has a blend of both physics and computational mathematics."Dr. Dominic Chandar, University of Wyoming, Laramie

"This book contains a comprehensive description of meshless approaches and their numerical algorithms. The easy-to-understand text clarifies some of the most advanced techniques for providing detailed mathematical derivation and worked examples where appropriate."Qinghua Qin, Australian National University, Canberra

"The authors presented a thorough, balanced, and informative review of the meshless method, which has been one of the most exciting areas in computational mechanics in the past decade. Drawing on their longtime experience and excellent works on meshless method, the authors covered the different aspects of meshless method skillfully and addressed many of the essential and tough issues including stability head on. The book is an excellent reference for scientists and engineers interested in meshless method and, more generally, numerical methods for partial differential equations."Rui Qiao, Associate Professor, Department of Mechanical Engineering, Clemson University, USA

Preface xiii
Author xvii
1 Introduction
1(4)
1.1 Background
1(2)
1.2 About This Monograph
3(2)
2 Formulation of classical meshless methods
5(48)
2.1 Introduction
5(1)
2.2 Fundamentals of Meshless Methods
6(1)
2.3 Common Steps of Meshless Method
7(3)
2.3.1 Geometry creation
8(1)
2.3.2 Approximation of field variable
8(1)
2.3.3 Discretisation of governing differential equation
9(1)
2.3.4 Assembly of system of equations
9(1)
2.3.5 Solving assembled system of equations
10(1)
2.4 Classical Meshless Methods
10(42)
2.4.1 Smooth particle hydrodynamics
11(2)
2.4.2 Diffuse element method
13(3)
2.4.3 Element-free Galerkin method
16(2)
2.4.4 Natural element method
18(2)
2.4.5 Reproducing kernel particle method
20(5)
2.4.6 Partition of unity finite element method
25(2)
2.4.7 Finite point method
27(3)
2.4.8 Meshless local Petrov-Galerkin method
30(5)
2.4.9 Local boundary integral equation method
35(3)
2.4.10 Point interpolation method
38(2)
2.4.11 Gradient smoothing method
40(2)
2.4.12 Radial point interpolation-based finite difference method
42(5)
2.4.13 Generalized meshfree (GMF) approximation
47(2)
2.4.14 Maximum entropy (ME) approximation method
49(3)
2.5 Summary
52(1)
3 Recent developments of meshless methods
53(92)
3.1 Introduction
53(1)
3.2 Hermite-Cloud Method
53(20)
3.2.1 Formulation of Hermite-cloud method
54(6)
3.2.2 Numerical implementation
60(2)
3.2.3 Examples for validation
62(10)
3.2.4 Remarks
72(1)
3.3 Point Weighted Least-Squares Method
73(20)
3.3.1 Formulation of PWLS method
73(7)
3.3.2 Numerical implementation of PWLS method
80(3)
3.3.3 Examples for validation
83(9)
3.3.4 Remarks
92(1)
3.4 Local Kriging (LoKriging) Method
93(22)
3.4.1 Formulation of Kriging interpolation
94(5)
3.4.2 Numerical implementation of LoKriging method
99(4)
3.4.3 Examples for validation
103(11)
3.4.4 Remarks
114(1)
3.5 Variation of Local Point Interpolation Method (vLPIM)
115(10)
3.5.1 Meshless point interpolation
115(2)
3.5.2 Numerical implementation of vLPIM
117(5)
3.5.3 Examples for validation
122(3)
3.5.4 Remarks
125(1)
3.6 Random Differential Quadrature (RDQ) Method
125(18)
3.6.1 Formulation of fixed reproducing kernel particle method
128(4)
3.6.2 Formulation of differential quadrature method
132(2)
3.6.3 Development of RDQ method
134(9)
3.6.4 Remarks
143(1)
3.7 Summary
143(2)
4 Convergence and consistency analyses
145(68)
4.1 Introduction to Convergence Analysis
145(1)
4.2 Development of Superconvergence Condition
146(2)
4.3 Convergence Analysis
148(25)
4.3.1 Computation of convergence rate for distribution of random field nodes
150(1)
4.3.2 Remarks about effects of random nodes on convergence rate
150(2)
4.3.3 One-dimensional test problems
152(4)
4.3.4 Two-dimensional test problems
156(6)
4.3.5 Elasticity problems
162(11)
4.4 Application of RDQ Method for Solving Fixed-Fixed and Cantilever Microswitches under Nonlinear Electrostatic Loading
173(7)
4.5 Introduction to Consistency Analysis of RDQ Method
180(1)
4.6 Consistency Analysis of Locally Applied DQ Method
181(14)
4.6.1 Consistency analysis of one-dimensional wave equation by uniform distribution of virtual nodes
182(7)
4.6.2 Consistency analysis of one-dimensional wave equation by cosine distribution of virtual nodes
189(3)
4.6.3 Consistency analysis of one-dimensional Laplace equation by uniform distribution of virtual nodes
192(3)
4.7 Effect of Uniform and Cosine Distributions of Virtual Nodes on Convergence of RDQ Method
195(14)
4.7.1 One-dimensional test problems
195(8)
4.7.2 Two-dimensional test problems
203(4)
4.7.3 Elasticity problems
207(2)
4.8 Summary
209(4)
5 Stability analyses
213(42)
5.1 Introduction
213(4)
5.2 Stability Analysis of First-Order Wave Equation by RDQ Method
217(18)
5.2.1 Stability analysis of first-order wave equation by different schemes for discretisation of domains
217(9)
5.2.2 Consistency analysis of stable schemes and verification by numerically implementing first-order wave equation by locally applied DQ method
226(4)
5.2.3 Implementation of RDQ method for first-order wave equation by forward time and central space scheme
230(2)
5.2.4 Remarks on solution of first-order wave equation by RDQ method
232(3)
5.3 Stability Analysis of Transient Heat Conduction Equation
235(7)
5.3.1 Forward time-and forward space scheme
235(1)
5.3.2 Forward time and central space scheme
236(6)
5.4 Stability Analysis of Transverse Beam Deflection Equation
242(10)
5.4.1 Explicit approach to solve the transverse beam deflection equation by the RDQ method
242(6)
5.4.2 Implicit approach to solving transverse beam deflection equation by RDQ method
248(4)
5.5 Summary
252(3)
6 Adaptive analysis
255(40)
6.1 Introduction
255(4)
6.2 Error Recovery Technique in ARDQ Method
259(2)
6.3 Adaptive RDQ Method
261(6)
6.3.1 Computation of error in ARDQ method
262(1)
6.3.2 Adaptive refinement in ARDQ method
263(4)
6.4 Convergence Analysis in ARDQ Method
267(26)
6.4.1 One-dimensional test problems
268(8)
6.4.2 Two-dimensional test problems
276(9)
6.4.3 Semi-infinite plate with central hole
285(8)
6.5 Summary
293(2)
7 Engineering applications
295(72)
7.1 Introduction
295(1)
7.2 Application of Meshless Methods to Microelectromechanical System Problems
295(14)
7.2.1 Fixed-fixed microswitches
297(3)
7.2.2 Cantilever microswitches
300(4)
7.2.3 Microoptoelectromechanical systems devices
304(2)
7.2.4 Microtweezers
306(3)
7.3 Application of Meshless Method in Submarine Engineering
309(7)
7.3.1 Numerical implementation of Hermite-cloud method
309(2)
7.3.2 Numerical study of near-bed submarine pipeline under current
311(5)
7.4 Application of RDQ Method for two-dimensional Simulation of pH-Sensitive Hydrogel
316(47)
7.4.1 Model development of two-dimensional pH-sensitive hydrogel
320(17)
7.4.2 Two-dimensional simulation of pH-sensitive hydrogels by RDQ method
337(7)
7.4.3 Effects of solution pH and initial fixed-charge concentration on swelling of two-dimensional hydrogel
344(5)
7.4.4 Effects of Young's modulus and geometrical shape of hydrogel at dry state on swelling
349(14)
7.5 Summary
363(4)
Appendix A Derivation of characteristic polynomial φ(z) 367(2)
Appendix B Definition of reduced polynomial φl(z) 369(2)
Appendix C Derivation of discretisation equation by Taylor series 371(2)
Appendix D Derivation of ratio of successive amplitude reduction values for fixed-fixed beam using explicit and implicit approaches 373(4)
Appendix E Source code development 377(18)
References 395(14)
Index 409
Dr. Hua Li is currently an assistant professor at the School of Mechanical and Aerospace Engineering at Nanyang Technological University in Singapore. His research interests include the modeling and simulation of MEMS, focusing on the use of smart hydrogels in BioMEMS applications; the development of advanced numerical methodologies; and the dynamics of high-speed rotating shell structures. He has authored or co-authored several books and book chapters, as well as more than 110 articles published in top international peer-reviewed journals. His research has been extensively funded by agencies and industries and he acted as the principal investigator of a computational BioMEMS project awarded under A*STARs Strategic Research Programme in MEMS.

Dr. Shantanu S. Mulay currently works as a postdoctoral associate with Professor Rohan Abeyaratne of Massachusetts Institute of Technology as part of the SingaporeMIT Alliance for Research and Technology (SMART). Before joining Nanyang Technological University (NTU), Dr. Mulay worked in product enhancement of DMU (CATIA workbench) and the development of NISA (FEM product), where he gained exposure to a variety of areas such as the development of CAD translators, computational geometry, and handling user interfaces of FEM products. During his Ph.D. program at NTU, Dr. Mulay worked extensively in the field of computational mechanics and developed a meshless random differential quadrature (RDQ) method.