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Extended Finite Element and Meshfree Methods [Pehme köide]

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(Professor of Modeling and Simulation and Chair of Computational Mechanics, Bauhaus Universitat Weimar, Germany), , , (Assistant Professor of Civil, Environmental, and Architectural Engineering and faculty member of Materials Science and En)
  • Formaat: Paperback / softback, 638 pages, kõrgus x laius: 229x152 mm, kaal: 930 g
  • Ilmumisaeg: 13-Nov-2019
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0128141069
  • ISBN-13: 9780128141069
Teised raamatud teemal:
Extended Finite Element and Meshfree MethodsSuurem pilt
  • Formaat: Paperback / softback, 638 pages, kõrgus x laius: 229x152 mm, kaal: 930 g
  • Ilmumisaeg: 13-Nov-2019
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0128141069
  • ISBN-13: 9780128141069
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780128141069.html
Märksõnad:

Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis.

This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications.

  • Explains all the important theory behind XFEM and meshfree methods
  • Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes
  • Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods
  • Introduces alternative modeling methods to help readers decide what is most appropriate for their work
Preface xiii
Nomenclature xix
1 Introduction
1(18)
1.1 Partition of unity methods
1(5)
1.2 Moving boundary problems
6(2)
1.3 Fracture mechanics
8(2)
1.4 Level set methods
10(5)
1.4.1 Implicit interface and signed distance functions
11(1)
1.4.2 Discretization of the level set
12(1)
1.4.3 Capturing motion interface
12(2)
1.4.4 Level sets for 3D fracture modeling
14(1)
References
15(4)
2 Weak forms and governing equations
19(10)
2.1 Strong form for pure mechanical problems
19(5)
2.1.1 One dimensional model problem
19(1)
2.1.2 Model problem in higher dimensions
20(1)
2.1.3 Total Lagrangian formulation
21(1)
2.1.4 Updated Lagrangian formulation
22(2)
2.2 From the strong form to the weak form
24(3)
2.2.1 Weak form for the one-dimensional model problem
24(2)
2.2.2 Weak form for the total Lagrangian formulation
26(1)
2.3 Variational formulation
27(2)
3 Extended finite element method
29(124)
3.1 Formulation and concepts
29(7)
3.1.1 Standard XFEM
29(5)
3.1.2 Hansbo-Hansbo XFEM
34(2)
3.2 Blending, integration and solvers
36(14)
3.2.1 Blending
36(4)
3.2.2 Isoparametric 2D quadrilateral XFEM element for linear elasticity
40(1)
3.2.3 Shape functions
41(1)
3.2.4 The B-operator
42(2)
3.2.5 The element stiffness matrix
44(2)
3.2.6 Integration
46(4)
3.3 XFEM for static/quasi-static fracture modeling in 2D and 3D
50(10)
3.3.1 XFEM approximation for cracks
50(4)
3.3.2 Discrete equations
54(3)
3.3.3 Crack branching and crack junction
57(2)
3.3.4 Crack opening and crack closure
59(1)
3.4 XFEM for dynamic fracture modeling in 2D and 3D
60(5)
3.4.1 Diagonalized mass matrix
60(4)
3.4.2 Limitations
64(1)
3.5 Smoothed extended finite element method
65(12)
3.5.1 Introduction to SFEM
67(3)
3.5.2 Enrichment in SXFEM and selection of enriched nodes
70(2)
3.5.3 Displacement-, strain field approximation and discrete equations
72(3)
3.5.4 Numerical integration
75(2)
3.6 XFEM for coupled problems
77(28)
3.6.1 Hydro-mechanical problems
77(12)
3.6.2 Thermo-mechanical problems
89(3)
3.6.3 Piezoelectric materials
92(8)
3.6.4 Flexoelectricity
100(5)
3.7 XFEM for inverse analysis and topology optimization
105(41)
3.7.1 Inverse problem
105(10)
3.7.2 Optimization problems
115(1)
3.7.3 Mathematical form of a structural optimization problem
116(1)
3.7.4 Solid isotropic material with penalization (SIMP)
117(1)
3.7.5 Level set based optimization
118(1)
3.7.6 Nanoelasticity
118(12)
3.7.7 Nanopiezoelectricity
130(16)
3.8 Conditioning and solution of ill-conditioned systems
146(1)
References
147(6)
4 Phantom node method
153(8)
4.1 Formulation and concepts
153(1)
4.2 A crack tip element for the phantom node methods
154(4)
4.2.1 Three-node triangular element
154(3)
4.2.2 Four-node quadrilateral element
157(1)
4.3 Multiple crack modeling
158(1)
References
159(2)
5 Extended meshfree methods
161(154)
5.1 Introduction to meshfree methods
161(10)
5.1.1 Basic approximation
161(1)
5.1.2 Completeness and conservation
162(2)
5.1.3 Consistency, stability and convergence
164(1)
5.1.4 Continuity
165(1)
5.1.5 Partition of unity
165(2)
5.1.6 Kernel functions
167(4)
5.2 Some specific methods
171(19)
5.2.1 Approximation of the displacement field
171(6)
5.2.2 Spatial integration
177(8)
5.2.3 Essential boundary conditions
185(1)
5.2.4 Comparison of different methods
186(4)
5.3 Numerical instabilities
190(19)
5.3.1 Instability due to rank deficiency
192(1)
5.3.2 Tensile instability
193(1)
5.3.3 Attempts to remove instabilities
193(1)
5.3.4 Material instability in meshfree methods
194(15)
5.4 Fracture modeling in meshfree methods
209(8)
5.4.1 The visibility method
209(3)
5.4.2 The diffraction method
212(3)
5.4.3 The transparency method
215(2)
5.4.4 The "see through" and "continuous line" method
217(1)
5.5 The concept of enrichment
217(8)
5.5.1 Intrinsic enrichment
219(3)
5.5.2 Extrinsic enrichment
222(3)
5.6 (Extrinsically) enriched local PU meshfree methods
225(13)
5.6.1 Enriched methods with crack tip enrichment
226(4)
5.6.2 Enriched methods without crack tip enrichment
230(6)
5.6.3 Crack branching and crackjunction
236(2)
5.7 Extended local maximum entropy (XLME)
238(7)
5.7.1 Local Maximum Entropy (LME) approximants
239(4)
5.7.2 Numerical integration
243(2)
5.7.3 Condition number
245(1)
5.8 Cracking particle methods
245(8)
5.8.1 The enriched cracking particles method
246(4)
5.8.2 Applications to large deformations
250(1)
5.8.3 The cracking particles method without enrichment
250(1)
5.8.4 Cracking rules for cracking particle methods
251(2)
5.9 Comparison of different methods
253(10)
5.9.1 The mode I crack problem
253(7)
5.9.2 The mixed mode problem
260(3)
5.10 Extensions to mode II kinematics
263(2)
5.10.1 Enriching in the shear band plane
263(2)
5.10.2 Enforcing mode II-kinematics with the penalty method
265(1)
5.11 Discrete system of equations for pure mechanical problems
265(18)
5.11.1 Methods without enrichment
265(2)
5.11.2 Enriched methods
267(3)
5.11.3 Extension to dynamics
270(13)
5.12 Spatial integration
283(3)
5.13 Time integration
286(20)
5.13.1 Explicit-implicit time integration
286(1)
5.13.2 Explicit time integration, critical time step and mass lumping
287(17)
5.13.3 Crack propagation in time
304(2)
References
306(9)
6 Extended isogeometric analysis
315(44)
6.1 Formulation and concepts
315(5)
6.1.1 B-splines and NURBS
315(2)
6.1.2 Bezier extraction
317(3)
6.2 Hierarchical refinement with PHT-splines
320(4)
6.2.1 PHT-spline space
321(2)
6.2.2 Computing the control points
323(1)
6.3 Analysis using splines
324(5)
6.3.1 Galerkin method
325(2)
6.3.2 Linear elasticity
327(2)
6.4 Numerical examples
329(4)
6.4.1 Infinite plate with circular hole
329(1)
6.4.2 Open spanner
330(1)
6.4.3 Pinched cylinder
331(1)
6.4.4 Hollow sphere
332(1)
6.5 Adaptive analysis
333(8)
6.5.1 Determining the superconvergent point locations
333(4)
6.5.2 Superconvergent patch recovery
337(3)
6.5.3 Marking algorithm
340(1)
6.6 Multi-patch formulations for complex geometry
341(1)
6.7 XIGA for interface problems
341(14)
6.7.1 Governing and weak form equations
342(3)
6.7.2 Enriched basis functions selection
345(2)
6.7.3 Enrichment functions
347(1)
6.7.4 Greville Abscissae
348(1)
6.7.5 Repeating middle neighbor knots
349(1)
6.7.6 Inverse mapping
350(1)
6.7.7 Curve fitting
351(2)
6.7.8 Intersection points
353(1)
6.7.9 Triangular integration
354(1)
References
355(4)
7 Fracture in plates and shells
359(78)
7.1 Fractures in shell and plates using XFEM
359(11)
7.1.1 Weak form
359(2)
7.1.2 Implementation based on the Q4 element
361(1)
7.1.3 Shear locking
362(1)
7.1.4 Curvature strain smoothing
363(2)
7.1.5 Extended finite element method for shear deformable plates
365(2)
7.1.6 Smoothed extended finite element method
367(1)
7.1.7 Integration
368(2)
7.2 Fractures in shell and plates using the phantom node method
370(22)
7.2.1 Phantom node method for the Belytschko-Tsay shell element
370(8)
7.2.2 Phantom node method based on the three-node isotropic triangular MITC shell element
378(14)
7.3 Extended meshfree methods for fracture in shells
392(10)
7.3.1 Shell model
393(3)
7.3.2 Continuum constitutive models
396(1)
7.3.3 Crack model
397(5)
7.4 An immersed particle method for fluid-structure interaction
402(6)
7.5 XIGA models for plates and shells
408(24)
7.5.1 Kinematics of the shell
408(2)
7.5.2 Weak form
410(2)
7.5.3 Discretization of the displacement field and enrichment
412(7)
7.5.4 Discrete system of equations
419(3)
7.5.5 Edge cracked plates under tension or shear
422(6)
7.5.6 Pressurized cylinder with an axial crack
428(4)
References
432(5)
8 Fracture criteria and crack tracking procedures
437(34)
8.1 Fracture criteria
437(1)
8.2 Cracking criteria
437(8)
8.2.1 Criteria in LEFM
437(3)
8.2.2 Global energy criteria
440(1)
8.2.3 Rankine criterion
440(1)
8.2.4 Loss of material stability condition
441(2)
8.2.5 Rank-one-stability criterion
443(1)
8.2.6 Determining the crack orientation
444(1)
8.2.7 Computation of the crack length
444(1)
8.3 Crack surface representation and tracking the crack path
445(21)
8.3.1 The level set method to trace the crack path
447(4)
8.3.2 Tracking the crack path in 3D
451(11)
8.3.3 Adaptive crack propagation technique
462(2)
8.3.4 Comments
464(2)
References
466(5)
9 Multiscale methods for fracture
471(50)
9.1 Extended Bridging Domain Method
472(7)
9.1.1 Concurrent coupling of two models at different length scales
474(5)
9.1.2 Consistency of material properties
479(1)
9.2 Extended bridging scale method
479(12)
9.2.1 Consistency of material properties
481(2)
9.2.2 Upscaling and downscaling
483(8)
9.3 Multiscale aggregating discontinuity (MAD) method
491(12)
9.3.1 Overview of the method
491(3)
9.3.2 Coarse graining method
494(6)
9.3.3 Micro-macro linkage
500(3)
9.4 Crack opening in unit cells with the hourglass mode
503(1)
9.5 Stability of the macromaterial
504(3)
9.6 Implementation
507(1)
9.7 Numerical examples
508(8)
9.7.1 3D modeling of cracks in a nanocomposite
508(1)
9.7.2 Hierarchical multiscale example
508(2)
9.7.3 Semi-concurrent FE-FE coupling example
510(2)
9.7.4 Concurrent FE-XFEM coupling example
512(1)
9.7.5 MD-XFEM coupling example
513(3)
References
516(5)
10 A short overview of alternatives for fracture
521(60)
10.1 Numerical manifold method (finite cover method)
521(7)
10.1.1 The cover approximation
522(1)
10.1.2 The least square-based physical cover functions
523(1)
10.1.3 The imposition of boundary conditions
524(1)
10.1.4 Fracture modeling
524(3)
10.1.5 Geometric and material nonlinear analysis
527(1)
10.2 Peridynamics and dual-horizon peridynamics
528(34)
10.2.1 Dual-horizon peridynamics
531(8)
10.2.2 The dual property of dual-horizon
539(4)
10.2.3 Wave propagation in 1D homogeneous bar
543(1)
10.2.4 Numerical examples
544(18)
10.3 Phase field models
562(13)
10.3.1 Concepts
563(5)
10.3.2 Governing equations
568(1)
10.3.3 Discretization
569(3)
10.3.4 Solution schemes
572(1)
10.3.5 Implementations
573(2)
References
575(6)
11 Implementation details
581(20)
11.1 Computer implementation of enriched methods
581(9)
11.1.1 Pre-processing
582(3)
11.1.2 Processing
585(4)
11.1.3 Post-processing
589(1)
11.2 Numerical examples
590(7)
11.2.1 Crack propagation angle
591(1)
11.2.2 Hydro-mechanical model with center cracks
591(1)
11.2.3 Hydro-mechanical model with edge crack
592(5)
References
597(4)
Part 1 Appendices
A Derivation of shape derivative for the nanoelasticity problem
601(2)
B Derivation of the adjoint problem for the nanopiezoelectricity problem
603(4)
Index 607
Timon Rabczuk is Professor of Modeling and Simulation, and Chair of Computational Mechanics at the Bauhaus Universität Weimar, Germany. He has published more than 450 SCI papers, many of them on extended finite element and meshfree methods, multiscale methods and isogeometric analysis. He is editor-in-chief of CMC-Computers, Materials and Continua, associated editor of International Journal of Impact Engineering, assistant editor of Computational Mechanics, and executive editor of FSCE-Frontiers of Structural and Civil Engineering. He was listed as one of ISI Highly Cited Researchers in Computer Science and Engineering from 2014 up to now. Jeong-Hoon Song is Assistant Professor of Civil, Environmental, and Architectural Engineering and faculty member of Materials Science and Engineering Program at the University of Colorado, Boulder, USA. He received a Ph.D. in Theoretical and Applied Mechanics at Northwestern University in 2008 and has worked in the area of computational mechanics and physics of solids to develop new computational methods and algorithms for various multiscale/multiphysics phenomena. He has authored over 45 peer-reviewed journal publications and two book chapters and has presented over 70 research lectures at national and international conferences, seminars, and workshops. Xiaoying Zhuang is Associate Professor at the Institute of Continuum Mechanics at Leibniz Universität Hannover, Germany. She has been developing computational methods for two-dimensional and three-dimensional fracture problems using partition-of-unity methods, including meshfree methods, the extended finite element method (XFEM), the phantom node and finite cover method, and multiscale methods. She is on the editorial boards of international journals including Theoretical and Applied Fracture Mechanics, KSCE Journal of Civil Engineering, and Engineering Geology. Cosmin Anitescu is a researcher at the Institute for Structural Mechanics of the Bauhaus Universität Weimar, Germany. His research focuses on the theory and application of extended finite elements, meshfree methods, and isogeometric analysis to engineering problems. He is currently the main contributor and maintainer of IGAFEM, an educational software package written in Matlab for solving computational mechanics problems.