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Introduction to Meshfree Methods and Their Programming 2005 ed. [Kõva köide]

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  • Formaat: Hardback, 480 pages, kõrgus x laius: 232x156 mm, kaal: 1930 g, XX, 480 p., 1 Hardback
  • Ilmumisaeg: 08-Jun-2005
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1402032285
  • ISBN-13: 9781402032288
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Introduction to Meshfree Methods and Their Programming 2005 ed.Suurem pilt
  • Formaat: Hardback, 480 pages, kõrgus x laius: 232x156 mm, kaal: 1930 g, XX, 480 p., 1 Hardback
  • Ilmumisaeg: 08-Jun-2005
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1402032285
  • ISBN-13: 9781402032288
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781402032288.html
Märksõnad:
The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.
Preface xiii
Authors xix
1 Fundamentals 1(36)
1.1 Numerical simulation
1(2)
1.2 Basics of mechanics for solids
3(11)
1.2.1 Equations for three-dimensional solids
4(5)
1.2.1.1 Stress components
4(1)
1.2.1.2 Strain-displacement equations
5(1)
1.2.1.3 Constitutive equations
6(1)
1.2.1.4 Equilibrium equations
7(1)
1.2.1.5 Boundary conditions and initial conditions
8(1)
1.2.2 Equations for two-dimensional solids
9(4)
1.2.2.1 Stress components
9(1)
1.2.2.2 Strain-displacement equation
10(1)
1.2.2.3 Constitutive equations
11(1)
1.2.2.4 Equilibrium equations
12(1)
1.2.2.5 Boundary conditions and initial conditions
12(1)
1.3 Strong-forms and weak-forms
13(1)
1.4 Weighted residual method
14(13)
1.4.1 Collocation method
17(1)
1.4.2 Subdomain method
18(1)
1.4.3 Least squares method
19(1)
1.4.4 Moment method
20(1)
1.4.5 Galerkin method
20(1)
1.4.6 Examples
21(23)
1.4.6.1 Use of the collocation method
23(1)
1.4.6.2 Use of the subdomain method
23(1)
1.4.6.3 Use of the least squares method
24(1)
1.4.6.4 Use of the moment method
24(1)
1.4.6.5 Use of the Galerkin method
25(1)
1.4.6.6 Use of more terms in the approximate solution
26(1)
1.5 Global weak-form for solids
27(7)
1.6 Local weak-form for solids
34(2)
1.7 Discussions and remarks
36(1)
2 Overview of meshfree methods 37(17)
2.1 Why Meshfree methods
37(2)
2.2 Definition of Meshfree methods
39(1)
2.3 Solution procedure of MFree methods
40(4)
2.4 Categories of Meshfree methods
44(7)
2.4.1 Classification according to the formulation procedures
45(2)
2.4.1.1 Meshfree methods based on weak-forms
45(1)
2.4.1.2 Meshfree methods based on collocation techniques
46(1)
2.4.1.3 Meshfree methods based on the combination of weak-form and collocation techniques
47(1)
2.4.2 Classification according to the function approximation schemes
47(2)
2.4.2.1 Meshfree methods based on the moving least squares approximation
48(1)
2.4.2.2 Meshfree methods based on the integral representation method for the function approximation
48(1)
2.4.2.3 Meshfree methods based on the point interpolation method
49(1)
2.4.2.4 Meshfree methods based on the other meshfree interpolation schemes
49(1)
2.4.3 Classification according to the domain representation
49(5)
2.4.3.1 Domain-type meshfree methods.
50(1)
2.4.3.2 Boundary-type meshfree methods.
50(1)
2.5 Future development
51(3)
3 Meshfree shape function construction 54(91)
3.1 Introduction
54(6)
3.1.1 Meshfree interpolation/approximation techniques
55(3)
3.1.2 Support domain
58(1)
3.1.3 Determination of the average nodal spacing
58(2)
3.2 Point interpolation methods
60(37)
3.2.1 Polynomial PIM shape functions
61(13)
3.2.1.1 Conventional polynomial PIM
61(6)
3.2.1.2 Weighted least square (WLS) approximation
67(2)
3.2.1.3 Weighted least square approximation of Hermite-type
69(5)
3.2.2 Radial point interpolation shape functions
74(12)
3.2.2.1 Conventional RPIM
74(7)
3.2.2.2 Hermite-type RPIM
81(5)
3.2.3 Source code for the conventional RPIM shape functions
86(11)
3.2.3.1 Implementation issues
86(2)
3.2.3.2 Program and data structure
88(2)
3.2.3.3 Examples of RPIM shape functions
90(7)
3.3 Moving least squares shape functions
97(17)
3.3.1 Formulation of MLS shape functions
97(5)
3.3.2 Choice of the weight function
102(4)
3.3.3 Properties of MLS shape functions
106(2)
3.3.4 Source code for the MLS shape function
108(6)
3.3.4.1 Implementation issues
108(3)
3.3.4.2 Program and data structure
111(1)
3.3.4.3 Examples of MLS shape functions
111(3)
3.4 Interpolation error using Meshfree shape functions
114(8)
3.4.1 Fitting of a planar surface
118(1)
3.4.2 Fitting of a complicated surface
118(4)
3.5 Remarks
122(2)
Appendix
124(7)
Computer programs
131(14)
4 Meshfree methods based on global weak-forms 145(92)
4.1 Introduction
145(3)
4.2 Meshfree radial point interpolation method
148(13)
4.2.1 RPIM formulation
148(7)
4.2.2 Numerical implementation
155(6)
4.2.2.1 Numerical integration
155(2)
4.2.2.2 Properties of the stiffness matrix
157(1)
4.2.2.3 Enforcement of essential boundary conditions
158(2)
4.2.2.4 Conformability of RPIM
160(1)
4.3 Element Free Galerkin method
161(6)
4.3.1 EFG formulation
161(2)
4.3.2 Lagrange multiplier method for essential boundary conditions
163(4)
4.4 Source code
167(10)
4.4.1 Implementation issues
167(4)
4.4.1.1 Support domain and the influence domain
167(2)
4.4.1.2 Background cells
169(1)
4.4.1.3 Method to enforce essential boundary conditions
169(1)
4.4.1.4 Shape parameters used in RBFs
169(2)
4.4.2 Program description and data structures
171(6)
4.5 Example for two-dimensional solids – a cantilever beam
177(19)
4.5.1 Using MFree_Global.f90
179(7)
4.5.2 Effects of parameters
186(7)
4.5.2.1 Parameter effects on RPIM method
187(4)
4.5.2.2 Parameter effects on EFG method
191(2)
4.5.3 Comparison of convergence
193(1)
4.5.4 Comparison of efficiency
194(2)
4.6 Example for 3D solids
196(2)
4.7 Examples for geometrically nonlinear problems
198(3)
4.7.1 Simulation of upsetting of a billet
199(1)
4.7.2 Simulation of large deflection of a cantilever beam
200(1)
4.7.3 Simulation of large deflection of a fixed-fixed beam
201(1)
4.8 MFree2D©
201(3)
4.9 Remarks
204(1)
Appendix
205(14)
Computer programs
219(18)
5 Meshfree methods based on local weak-forms 237(73)
5.1 Introduction
237(2)
5.2 Local radial point interpolation method
239(11)
5.2.1 LRPIM formulation
239(7)
5.2.2 Numerical implementation
246(4)
5.2.2.1 Type of local domains
246(1)
5.2.2.2 Property of the stiffness matrix
247(1)
5.2.2.3 Test (weight) function
248(1)
5.2.2.4 Numerical integration
248(2)
5.3 Meshless Local Petrov-Galerkin method
250(4)
5.3.1 MLPG formulation
250(2)
5.3.2 Enforcement of essential boundary conditions
252(1)
5.3.3 Commons on the efficiency of MLPG and LRPIM
253(1)
5.3.3.1 Comparison with FEM
254(1)
5.3.3.2 Comparison with MFree global weak-form methods
254(1)
5.4 Source code
254(8)
5.4.1 Implementation issues
254(2)
5.4.2 Program description and data structures
256(6)
5.5 Examples for two dimensional solids – a cantilever beam
262(17)
5.5.1 The use of the MFree_local.f90
262(5)
5.5.2 Studies on the effects of parameters
267(9)
5.5.2.1 Parameters effects on LRPIM
268(6)
5.5.2.2 Parameter effects on MLPG
274(2)
5.5.3 Comparison of convergence
276(2)
5.5.4 Comparison of efficiency
278(1)
5.6 Remarks
279(2)
Appendix
281(11)
Computer programs
292(18)
6 Meshfree collocation methods 310(70)
6.1 Introduction
310(1)
6.2 Techniques for handling derivative boundary conditions
311(2)
6.3 Polynomial point collocation method for 1D problems
313(22)
6.3.1 Collocation equations for 1D system equations
313(10)
6.3.1.1 Problem description
313(1)
6.3.1.2 Function approximation using MFree shape functions
314(1)
6.3.1.3 System equation discretization
315(1)
6.3.1.4 Discretization of Dirichlet boundary condition
316(1)
6.3.1.5 Discretized system equation with only Dirichlet boundary conditions
316(1)
6.3.1.6 Discretized system equations with DBCs
317(6)
6.3.2 Numerical examples for 1D problems
323(12)
6.4 Stabilization in convection-diffusion problems using MFree methods
335(8)
6.4.1 Nodal refinement
338(1)
6.4.2 Enlargement of the local support domain
338(1)
6.4.3 Total upwind support domain
339(2)
6.4.4 Adaptive upwind support domain
341(1)
6.4.5 Biased support domain
342(1)
6.5 Polynomial point collocation method for 2D problems
343(9)
6.5.1 PPCM formulation for 2D problems
344(2)
6.5.2 Numerical examples
346(6)
6.6 Radial point collocation method for 2D problems
352(12)
6.6.1 RPCM formulation
352(1)
6.6.2 RPCM for 2D Poisson equations
352(2)
6.6.3 RPCM for 2D convection-diffusion problems
354(10)
6.6.3.1 Steady state convection-diffusion problem
354(5)
6.6.3.2 Linear dynamic convection-diffusion equations
359(5)
6.7 RPCM for 2D solids
364(14)
6.7.1 Hermite-type RPCM
364(7)
6.7.2 Use of regular grid (RG)
371(7)
6.8 Remarks
378(2)
7 Meshfree methods based on local weak form and collocation 380(74)
7.1 Introduction
380(1)
7.2 Meshfree collocation and local weak-form methods
381(3)
7.2.1 Meshfree collocation method
381(1)
7.2.2 Meshfree weak-form method
382(1)
7.2.3 Comparisons of meshfree collocation and weak-form methods
383(1)
7.3 Formulation for 2-D statics
384(7)
7.3.1 The idea
384(2)
7.3.2 Local weak-form
386(1)
7.3.3 Discretized system equations
387(3)
7.3.4 Numerical implementation
390(1)
7.3.4.1 Property of stiffness matrix
390(1)
7.3.4.2 Type of local domains
391(1)
7.3.4.3 Numerical integration
391(1)
7.4 Source code
391(2)
7.4.1 Implementation issues
392(1)
7.4.2 Program description
392(1)
7.5 Examples for testing the code
393(7)
7.6 Numerical examples for 2D elastostatics
400(10)
7.6.1 1D truss member with derivative boundary conditions
400(1)
7.6.2 Standard patch test
401(2)
7.6.3 Higher-order patch test
403(4)
7.6.4 Cantilever beam
407(3)
7.6.5 Hole in an infinite plate
410(1)
7.7 Dynamic analysis for 2-D solids
410(13)
7.7.1 Strong-form of dynamic analysis
412(1)
7.7.2 Local weak-form for the dynamic analysis
412(1)
7.7.3 Discretized formulations for dynamic analysis
413(3)
7.7.3.1 Free vibration analysis
414(1)
7.7.3.2 Direct analysis of forced vibration
415(1)
7.7.4 Numerical examples
416(7)
7.7.4.1 Free vibration analysis
417(1)
7.7.4.2 Forced vibration analysis
417(6)
7.8 Analysis for incompressible flow problems
423(20)
7.8.1 Simulation of natural convection in an enclosed domain
423(11)
7.8.1.1 Governing equations and boundary conditions
423(1)
7.8.1.2 Discretized system equations
424(3)
7.8.1.3 Numerical results for the problem of natural convection
427(7)
7.8.2 Simulation of the flow around a cylinder
434(9)
7.8.2.1 Governing equation and boundary condition
434(3)
7.8.2.2 Computation procedure
437(1)
7.8.2.3 Results and discussion
437(6)
7.9 Remarks
443(2)
Appendix
445(5)
Computer programs
450(4)
Reference 454(19)
Index 473