Muutke küpsiste eelistusi

E-raamat: Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory

,
  • Formaat: EPUB+DRM
  • Sari: Applied Mathematical Sciences 149
  • Ilmumisaeg: 25-Sep-2019
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030214739
Teised raamatud teemal:
  • Formaat - EPUB+DRM
  • Hind: 55,56 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation TheorySuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Applied Mathematical Sciences 149
  • Ilmumisaeg: 25-Sep-2019
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030214739
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This book provides a modern static imperfect bifurcation theory applicable to bifurcation phenomena of physical and engineering problems and fills the gap between the mathematical theory and engineering practice.

Systematic methods based on asymptotic, probabilistic, and group theoretic standpoints are used to examine experimental and computational data from numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its applications for practical problems, is illuminated by numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.

This third edition strengthens group representation and group-theoretic bifurcation theory. Several large scale applications have been included in association with the progress of computational powers. Problems and answers have been provided.

 Review of First Edition:

"The book is unique in considering the experimental identification of material-dependent bifurcations in structures such as sand, Kaolin (clay), soil and concrete shells. These are studied statistically. The book is an excellent source of practical applications for mathematicians working in this field. A short set of exercises at the end of each chapter makes the book more useful as a text. The book is well organized and quite readable for non-specialists."

 Henry W. Haslach, Jr., Mathematical Reviews, 2003
1 Overview of Book
1(34)
1.1 Introduction l
1.2 Fundamental Issues of a Static Problem
2(8)
1.2.1 Governing Equation with Imperfections
2(2)
1.2.2 Simple Examples of Bifurcation Behavior
4(6)
1.3 Overview of Theoretical Concepts
10(7)
1.3.1 Imperfection Sensitivity Law
10(2)
1.3.2 Worst Imperfection of Structural Systems
12(2)
1.3.3 Random Variation of Imperfections
14(1)
1.3.4 Experimentally Observed Bifurcation Diagrams
15(2)
1.4 Overview of Theoretical Tools
17(6)
1.4.1 Group-Theoretic Bifurcation Theory
17(3)
1.4.2 Block-Diagonalization in Bifurcation Analysis
20(3)
1.5 Overview of Bifurcation of Symmetric Systems
23(9)
1.5.1 Recursive Bifurcation and Mode Switching of Sands
23(2)
1.5.2 Recursive Bifurcation of Steel Specimens
25(2)
1.5.3 Echelon Modes on Uniform Materials
27(5)
1.5.4 Flower Patterns on a Honeycomb Structure
32(1)
Summary
32(3)
Part I Imperfect Behavior Around Simple Critical Points
2 Local Behavior Around Simple Critical Points
35(42)
2.1 Introduction
35(1)
2.2 General Mathematical Framework
36(5)
2.2.1 Governing Equation with Imperfections
36(1)
2.2.2 Critical Point
37(2)
2.2.3 Reciprocity
39(1)
2.2.4 Stability
40(1)
2.3 Illustrative Example of Bifurcation Analysis
41(5)
2.3.1 Governing Equation
41(2)
2.3.2 Exact Analysis
43(2)
2.3.3 Asymptotic Analysis
45(1)
2.4 Liapunov-Schmidt Reduction
46(10)
2.4.1 Reduction Procedure
46(3)
2.4.2 Criticality Condition
49(2)
2.4.3 Direction of the Bifurcating Path
51(2)
2.4.4 Stability
53(1)
2.4.5 Power Series Expansion of Bifurcation Equation
54(2)
2.5 Classification of Simple Critical Points
56(12)
2.5.1 Limit Point
59(1)
2.5.2 Transcritical Bifurcation Point
60(3)
2.5.3 Pitchfork Bifurcation Point
63(5)
2.6 Example of Pitchfork Bifurcation
68(4)
2.6.1 Exact Analysis
69(2)
2.6.2 Asymptotic Analysis
71(1)
2.7 Appendix: Numerical Bifurcation Analysis Procedure
72(4)
2.7.1 Path Tracing
72(2)
2.7.2 Singularity Detection
74(1)
2.7.3 Branch Switching Analysis
75(1)
2.8 Problems
76(1)
Summary
76(1)
3 Imperfection Sensitivity Laws
77(24)
3.1 Introduction
77(2)
3.2 Imperfection Sensitivity Laws
79(8)
3.2.1 Limit Point
80(1)
3.2.2 Transcritical Bifurcation Point
81(1)
3.2.3 Pitchfork Bifurcation Point
81(2)
3.2.4 Systematic Derivation
83(4)
3.3 Imperfection Sensitivity of Simple Structures
87(6)
3.3.1 Propped Cantilever
87(2)
3.3.2 Truss Arches
89(4)
3.4 Realistic Example: Elastic-Plastic Plate
93(4)
3.4.1 Ultimate Buckling Strength
95(1)
3.4.2 Imperfection Sensitivity Laws
95(2)
3.5 Appendix: Hilltop Bifurcation of Steel
97(2)
3.6 Problems
99(1)
Summary
99(2)
4 Worst Imperfection (I)
101(20)
4.1 Introduction
101(1)
4.2 Illustrative Example
102(5)
4.2.1 Governing Equation and Imperfection Sensitivity
102(2)
4.2.2 Worst Imperfection
104(3)
4.3 Theory of Worst Imperfection
107(4)
4.3.1 Formulation
107(2)
4.3.2 Derivation of Worst Imperfection
109(2)
4.4 Imperfection with Multiple Categories
111(2)
4.5 Worst Imperfection of Simple Structures
113(6)
4.5.1 Truss Arches
113(5)
4.5.2 Regular-Hexagonal Truss Dome
118(1)
4.6 Problems
119(1)
Summary
120(1)
5 Random Imperfection (I)
121(20)
5.1 Introduction
121(2)
5.2 Probability Density Functions of Critical Loads
123(5)
5.2.1 Imperfection Coefficient
123(2)
5.2.2 Normalized Critical Load
125(2)
5.2.3 Critical Load
127(1)
5.3 Evaluation of Probability Density Functions
128(2)
5.3.1 Theoretical Evaluation Procedure
129(1)
5.3.2 Semi-empirical Evaluation Procedure
129(1)
5.4 Distribution of Minimum Values
130(3)
5.5 Scatter of Critical Loads of Structures and Sands
133(7)
5.5.1 Simple Example
133(3)
5.5.2 Sand Specimens
136(1)
5.5.3 Truss Tower Structure
137(3)
5.6 Problems
140(1)
Summary
140(1)
6 Experimentally Observed Bifurcation Diagrams
141(26)
6.1 Introduction
141(3)
6.2 The Koiter Two-Thirds Power Law
144(1)
6.3 Extensions of the Koiter Law
145(7)
6.3.1 Crossing-Parabola Law
145(2)
6.3.2 Laws for Experimentally Observed Bifurcation Diagrams
147(5)
6.4 Recovering the Perfect System from Imperfect Systems
152(3)
6.4.1 Recovery from a Single Imperfect Path
152(2)
6.4.2 Recovery from a Series of Imperfect Paths
154(1)
6.5 Examples of Observed Bifurcation Diagrams
155(9)
6.5.1 Regular-Hexagonal Truss Dome
155(4)
6.5.2 Sand Specimens
159(5)
6.6 Problems
164(1)
Summary
164(3)
Part II Theory of Imperfect Bifurcation for Systems with Symmetry
7 Group and Group Representation
167(34)
7.1 Introduction
167(1)
7.2 Group
168(4)
7.2.1 Basic Concepts
168(2)
7.2.2 Conjugacy
170(1)
7.2.3 Direct Product and Semidirect Product
171(1)
7.3 Group Representation
172(12)
7.3.1 Basic Concepts
172(5)
7.3.2 Irreducible Representation
177(4)
7.3.3 Absolute Irreducibility
181(1)
7.3.4 Schur's Lemma
182(2)
7.4 Block-Diagonalization Under Group Symmetry
184(12)
7.4.1 An Illustrative Example
184(2)
7.4.2 Block-Diagonalization Method: Basic Form
186(8)
7.4.3 Block-Diagonalization Method: Extended Form
194(2)
7.5 Block-Diagonalization of Symmetric Plate Element
196(4)
7.5.1 Symmetry of Element Stiffness Matrix
197(1)
7.5.2 Irreducible Representations
198(1)
7.5.3 Block-Diagonalization
199(1)
7.6 Problems
200(1)
Summary
200(1)
8 Group-Theoretic Bifurcation Theory
201(36)
8.1 Introduction
201(1)
8.2 Bifurcation Due to Reflection Symmetry
202(2)
8.3 Symmetry of Equations
204(4)
8.3.1 Group Equivariance of Governing Equation
204(2)
8.3.2 Equivariance of Linear Parts
206(1)
8.3.3 Group-Theoretic Critical Point
207(1)
8.4 Liapunov-Schmidt Reduction
208(9)
8.4.1 Inheritance of Symmetry and Reciprocity
208(1)
8.4.2 Reduction Procedure
209(3)
8.4.3 Group Equivariance in the Reduction Process
212(2)
8.4.4 Criticality Condition
214(1)
8.4.5 Direction of Bifurcating Paths
215(2)
8.5 Symmetry of Solutions
217(4)
8.5.1 Ordinary Point
218(1)
8.5.2 Critical Point
219(2)
8.5.3 Orbit
221(1)
8.6 Simple Critical Point Under Symmetry
221(2)
8.6.1 Limit Point
222(1)
8.6.2 Pitchfork Bifurcation Point
222(1)
8.7 Equivariant Branching Lemma
223(4)
8.8 Block-Diagonalization of Jacobian and Imperfection Sensitivity Matrices
227(1)
8.9 Example of Symmetric System
228(6)
8.9.1 Symmetry Group and Equivariance
229(2)
8.9.2 Irreducible Representations
231(1)
8.9.3 Symmetry of Critical Eigenvectors
232(1)
8.9.4 Symmetry of Imperfection Sensitivity Matrix
233(1)
8.10 Problems
234(1)
Summary
235(2)
9 Bifurcation Behavior of D.-Equivariant Systems
237(60)
9.1 Introduction
237(1)
9.2 Dihedral and Cyclic Groups
238(6)
9.2.1 Definition of Groups
238(3)
9.2.2 Irreducible Representations
241(3)
9.3 Symmetry of Solutions
244(11)
9.3.1 Direct Branches
244(4)
9.3.2 Recursive Bifurcation
248(1)
9.3.3 Bifurcation of Domes
249(6)
9.4 Bifurcation Equations for a Double Critical Point
255(5)
9.4.1 Bifurcation Equations in Complex Variables
255(3)
9.4.2 Equivariance
258(2)
9.4.3 Reciprocity
260(1)
9.5 Perfect Behavior Around a Double Critical Point
260(9)
9.5.1 Bifurcating Branches
261(3)
9.5.2 Stability
264(3)
9.5.3 Summary of Perfect Behavior
267(2)
9.6 Imperfect Behavior Around a Double Critical Point
269(6)
9.6.1 Bifurcation Equations in Polar Coordinates
269(1)
9.6.2 Solution Curves
270(2)
9.6.3 Examples of Solution Curves
272(3)
9.7 Imperfection Sensitivity Laws
275(8)
9.7.1 Case n > or = to 5
278(1)
9.7.2 Case n = 3
279(3)
9.7.3 Case n = 4
282(1)
9.8 Experimentally Observed Bifurcation Diagrams
283(9)
9.8.1 Crossing-Line Law
283(2)
9.8.2 Simple Bifurcation Point
285(1)
9.8.3 Double Bifurcation Point
286(2)
9.8.4 Numerical Example: Regular-Pentagonal Truss Dome
288(3)
9.8.5 Experimental Example: Cylindrical Sand Specimens
291(1)
9.9 Appendix: Double Bifurcation Point on Ca-Symmetric Path
292(2)
9.10 Problems
294(1)
Summary
295(2)
10 Worst Imperfection (II)
297(20)
10.1 Introduction
297(2)
10.2 Formulation of Worst Imperfection
299(3)
10.2.1 Group Equivariance
299(1)
10.2.2 Imperfection Sensitivity Law
300(1)
10.2.3 Optimization Problems for Worst Imperfection
301(1)
10.3 Simple Critical Points
302(2)
10.3.1 Worst Imperfection
302(1)
10.3.2 Resonance of Symmetry
303(1)
10.4 Double Critical Points
304(6)
10.4.1 Block-Diagonalization
304(4)
10.4.2 Worst Imperfection
308(1)
10.4.3 Resonance of Symmetry
309(1)
10.5 Examples of Worst Imperfection
310(5)
10.5.1 Truss Tents
310(3)
10.5.2 Regular-Hexagonal Truss Dome
313(2)
10.6 Problems
315(1)
Summary
316(1)
11 Random Imperfection (II)
317(18)
11.1 Introduction
317(1)
11.2 Probability Density Function of Critical Loads
318(8)
11.2.1 Formulation
318(2)
11.2.2 Derivation of Probability Density Functions
320(5)
11.2.3 Semi-empirical Evaluation
325(1)
11.3 Distribution of Minimum Values
326(1)
11.4 Examples of Scatter of Critical Loads
327(6)
11.4.1 Regular-Polygonal Truss Tents and Domes
327(2)
11.4.2 Pentagonal Truss Dome
329(2)
11.4.3 Cylindrical Specimens of Sand and Concrete
331(2)
11.5 Problems
333(1)
Summary
334(1)
12 Numerical Analysis of Symmetric Systems
335(26)
12.1 Introduction
335(1)
12.2 Numerical Bifurcation Analysis of Symmetric Systems
336(3)
12.2.1 Analysis Procedure
336(1)
12.2.2 Examples of Numerical Bifurcation Analysis
337(2)
12.3 Revised Scaled-Corrector Method
339(9)
12.3.1 Original Scaled-Corrector Method
340(2)
12.3.2 Revised Scaled-Corrector Method
342(2)
12.3.3 Regular-Hexagonal Truss Dome
344(4)
12.4 Use of Block-Diagonalization in Bifurcation Analysis
348(11)
12.4.1 Eigenanalysis Versus Block-Diagonalization
348(6)
12.4.2 Block-Diagonal Form for Dn-Symmetric System
354(1)
12.4.3 Block-Diagonal Form for Cn-Symmetric System
355(4)
12.5 Problems
359(1)
Summary
360(1)
13 Efficient Transformation for Block-Diagonalization
361(44)
13.1 Introduction
361(2)
13.2 Construction of Transformation Matrix: Illustration
363(7)
13.2.1 Regular-Triangular Truss
363(1)
13.2.2 Representation Matrix
364(2)
13.2.3 Local Transformation Matrix
366(2)
13.2.4 Assemblage of Local Transformations
368(2)
13.3 Construction of Transformation Matrix: General Procedure
370(13)
13.3.1 Representation Matrix
370(5)
13.3.2 Local Transformation Matrix
375(4)
13.3.3 Assemblage of Local Transformations
379(4)
13.4 Formulas for Local Transformation Matrices
383(7)
13.5 Appendix: Derivation of Local Transformation Matrices
390(11)
13.5.1 Case ξ = Oz
391(1)
13.5.2 Case ξ = Oxy
391(1)
13.5.3 Case ξ = 1Mz
391(2)
13.5.4 Case ξ = 1Mxy
393(2)
13.5.5 Case ξ = 2z
395(2)
13.5.6 Case ξ = 2xy
397(4)
13.6 Problems
401(1)
Summary
402(3)
Part III Modeling of Bifurcation Phenomena
14 Bifurcation Behaviors of Cylindrical Soils
405(30)
14.1 Introduction
405(4)
14.2 Groups for Spatial Symmetry
409(5)
14.2.1 Symmetry of Cylindrical Domain
409(2)
14.2.2 Subgroups of pooh
411(3)
14.2.3 Example of Description of Cylindrical Sand Deformation
414(1)
14.3 Experiments on Cylindrical Sand Specimens
414(10)
14.3.1 Recursive Bifurcation Behavior
417(1)
14.3.2 Mode Switching Behavior
418(4)
14.3.3 Recovery of Perfect System
422(1)
14.3.4 Application of Crossing-Line Law
423(1)
14.4 Appendix: Derivation of Bifurcation Rules
424(9)
14.4.1 Bifurcation of Dnh-Equivariant System
425(6)
14.4.2 Bifurcation of Dnd-Equivariant System
431(2)
14.5 Problems
433(1)
Summary
433(2)
15 Bifurcation of Steel Specimens
435(14)
15.1 Introduction
435(1)
15.2 Symmetry of a Rectangular Parallelepiped Domain
436(2)
15.3 Recursive Bifurcation Rule
438(1)
15.4 Experimental Study
439(8)
15.4.1 Effect of Cross-Sectional Shape
441(3)
15.4.2 Recursive Bifurcation
444(3)
15.5 Computational Study
447(1)
15.6 Problems
448(1)
Summary
448(1)
16 Echelon-Mode Formation
449(54)
16.1 Introduction
449(5)
16.2 Symmetry Group of Cylindrical Domain
454(3)
16.2.1 Geometrical Symmetry
454(1)
16.2.2 Underlying Translational Symmetry
455(2)
16.3 Subgroups for Patterns with High Spatial Frequencies
457(5)
16.3.1 Diamond Pattern
457(1)
16.3.2 Oblique Stripe Pattern
458(1)
16.3.3 Echelon Mode
459(3)
16.4 Recursive Bifurcation Leading to Echelon Modes
462(2)
16.4.1 Direct Bifurcation
462(1)
16.4.2 Recursive Bifurcation via Oblique Stripe Pattern
462(1)
16.4.3 Physical Scenario for Echelon Mode Formation
463(1)
16.5 Experiment on a Soil Specimen
464(3)
16.5.1 Deformation Patterns: Phenomenological Observation
464(2)
16.5.2 Deformation Patterns: Symmetry
466(1)
16.6 Image Simulations for Stripes on Kaolin
467(9)
16.6.1 Image Simulation Procedure
467(3)
16.6.2 Image Simulation for Kaolin
470(6)
16.7 Patterns on Sand Specimens
476(7)
16.7.1 Experiment and Visualization of Strain Fields
476(1)
16.7.2 Image Simulation
477(3)
16.7.3 Numerical Simulation
480(1)
16.7.4 Three-Dimensional Patterns
481(2)
16.8 Appendix: Derivation of Bifurcation Rules
483(18)
16.8.1 Bifurcation of O(2) x O(2)-Equivariant System
483(8)
16.8.2 Bifurcation of OB±nn-Equivariant System
491(8)
16.8.3 Bifurcation of Dinfinityinfinity-Equivariant System
499(2)
16.9 Problems
501(1)
Summary
501(2)
17 Flower Patterns on Honeycomb Structures
503(44)
17.1 Introduction
503(2)
17.2 Symmetry of Representative Volume Element
505(2)
17.3 Bifurcation Rule for Representative Volume Element
507(5)
17.3.1 Irreducible Representations for 2 x 2 Cells
507(1)
17.3.2 Simple Critical Points
508(2)
17.3.3 Double Critical Points
510(1)
17.3.4 Triple Critical Points
510(2)
17.4 Derivation of Bifurcation Equation
512(3)
17.5 Solving of Bifurcation Equation
515(10)
17.5.1 The Representative Case: µ = (3, 3)
515(6)
17.5.2 Another Case: µ = (3, 1)
521(2)
17.5.3 Other Cases: µ = (3, 2) and µ = (3, 4)
523(1)
17.5.4 Stability of Bifurcating Branches
523(1)
17.5.5 Analysis by Equivariant Branching Lemma
524(1)
17.6 Numerical Analysis of Honeycomb Cellular Solids
525(3)
17.7 Irreducible Representations for n x n Cells
528(2)
17.7.1 Four-Dimensional Irreducible Representations
528(1)
17.7.2 Six-Dimensional Irreducible Representations
529(1)
17.7.3 Twelve-Dimensional Irreducible Representations
530(1)
17.8 Solving of Bifurcation Equation for n x n Cells
530(16)
17.8.1 Bifurcation Point of Multiplicity 6
531(6)
17.8.2 Bifurcation Point of Multiplicity 12
537(9)
17.9 Problems
546(1)
Summary
546(1)
A Answers to Problems 547(26)
References 573(10)
Index 583
Kiyohiro Ikeda is a Professor in the Department of Civil Engineering, Graduate School of Engineering at Tohoku University. Kazuo Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology at University of Tokyo.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97830302147396e.html
Märksõnad: