Screen LibraryImperfect bifurcation in structures and materials : engineering use of group-theoretic bifurcation theory /
"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"--Page 4 of cover.
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| Main Authors: | |
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| Group Author: | |
| Published: |
Springer,
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| Publisher Address: | Cham : |
| Publication Dates: | [2019] |
| Literature type: | Book |
| Language: | English |
| Edition: | Third edition. |
| Series: |
Applied mathematical sciences (Springer-Verlag New York Inc.) ; volume 149. 0066-5452 |
| Subjects: | |
| Summary: |
"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"--Page 4 of cover. |
| Carrier Form: | xxv, 590 pages : illustrations (some color), forms ; 25 cm. |
| Bibliography: | Includes bibliographical references (pages 573-581) and index. |
| ISBN: |
9783030214722 (hardcover) : 3030214729 (hardcover) |
| Index Number: | QA380 |
| CLC: | TB11 |
| Call Number: | TB11/I263/3rd ed. |
| Contents: |
Overview of Book -- Fundamental Issues of a Static Problem -- Governing Equation with Imperfections -- Simple Examples of Bifurcation Behavior -- Overview of Theoretical Concepts -- Imperfection Sensitivity Law -- Worst Imperfection of Structural Systems -- Random Variation of Imperfections -- Experimentally Observed Bifurcation Diagrams -- Overview of Theoretical Tools -- Group- Theoretic Bifurcation Theory -- Block-Diagonalization in Bifurcation Analysis -- Overview of Bifurcation of Symmetric Systems -- Recursive Bifurcation and Mode Switching of Sands -- Recursive Bifurcation of Steel Specimens -- Echelon Modes on Uniform Materials -- Flower Patterns on a Honeycomb Structure -- Imperfect Behavior Around Simple Critical Points -- Local Behavior Around Simple Critical Points -- General Mathematical Framework -- Critical Point -- Reciprocity -- Stability -- Illustrative Example of Bifurcation Analysis -- Governing Equation -- Exact Analysis -- Asymptotic Analysis -- Liapunov-Schmidt Reduction -- Reduction Procedure -- Criticality Condition -- Direction of the Bifurcating Path -- Power Series Expansion of Bifurcation Equation -- Classification of Simple Critical Points -- Limit Point -- Transcritical Bifurcation Point -- Pitchfork Bifurcation Point -- Example of Pitchfork Bifurcation -- Appendix : Numerical Bifurcation Analysis Procedure -- Path Tracing -- Singularity Detection -- Branch Switching Analysis -- Problems -- Imperfection Sensitivity Laws -- Systematic Derivation -- Imperfection Sensitivity of Simple Structures -- Propped Cantilever -- Truss Arches -- Realistic Example : Elastic-Plastic Plate -- Ultimate Buckling Strength -- Appendix : Hilltop Bifurcation of Steel -- Worst Imperfection (I) -- Illustrative Example -- Governing Equation and Imperfection Sensitivity -- Worst Imperfection -- Theory of Worst Imperfection -- Formulation -- Derivation of Worst Imperfection -- Imperfection with Multiple Categories -- Worst Imperfection of Simple Structures -- Regular-Hexagonal Truss Dome -- Random Imperfection (I) -- Probability Density Functions of Critical Loads -- Imperfection Coefficient -- Normalized Critical Load -- Critical Load -- Evaluation of Probability Density Functions -- Theoretical Evaluation Procedure -- Semi-empirical Evaluation Procedure -- Distribution of Minimum Values -- Scatter of Critical Loads of Structures and Sands -- Simple Example -- Sand Specimens -- Truss Tower Structure -- The Koiter Two-Thirds Power Law -- Extensions of the Koiter Law -- Crossing-Parabola Law -- Laws for Experimentally Observed Bifurcation Diagrams -- Recovering the Perfect System from Imperfect Systems -- Recovery from a Single Imperfect Path -- Recovery from a Series of Imperfect Paths -- Examples of Observed Bifurcation Diagrams -- Theory of Imperfect Bifurcation for Systems with Symmetry -- Group and Group Representation -- Group -- Basic Concepts -- Conjugacy -- Direct Product and Semidirect Product -- Group Representation -- Irreducible Representation -- Absolute Irreducibility -- Schurʼs Lemma -- Block-Diagonalization Under Group Symmetry -- An Illustrative Example -- Block-Diagonalization Method : Basic Form -- Block-Diagonalization Method : Extended Form -- Block-Diagonalization of Symmetric Plate Element -- Symmetry of Element Stiffness Matrix -- Irreducible Representations -- Block-Diagonalization -- Group-Theoretic Bifurcation Theory -- Bifurcation Due to Reflection Symmetry -- Symmetry of Equations Group Equivariance of Governing Equation -- Equivariance of Linear Parts -- Group-Theoretic Critical Point -- Inheritance of Symmetry and Reciprocity -- Group Equivariance in the Reduction Process -- Direction of Bifurcating Paths -- Symmetry of Solutions -- Ordinary Point -- Orbit -- Simple Critical Point Under Symmetry -- Equivariant Branching Lemma -- Block-Diagonalization of Jacobian and Imperfection Sensitivity Matrices -- Example of Symmetric System -- Symmetry Group and Equivariance -- Symmetry of Critical Eigenvectors -- Symmetry of Imperfection Sensitivity Matrix -- Bifurcation Behavior of Dn-Equivariant Systems -- Dihedral and Cyclic Groups -- Definition of Groups -- Direct Branches -- Recursive Bifurcation -- Bifurcation of Domes -- Bifurcation Equations for a Double Critical Point -- Bifurcation Equations in Complex Variables -- Equivariance -- Perfect Behavior Around a Double Critical Point -- Bifurcating Branches -- Summary of Perfect Behavior -- Imperfect Behavior Around a Double Critical Point -- Bifurcation Equations in Polar Coordinates -- Solution Curves -- Examples of Solution Curves -- Case n̂ ... 5 -- Case n̂ = 3 -- Case n̂ = 4 -- Crossing-Line Law -- Simple Bifurcation Point -- Double Bifurcation Point -- Numerical Example : Regular-Pentagonal Truss Dome -- Experimental Example : Cylindrical Sand Specimens -- Appendix : Double Bifurcation Point on Cn-Symmetric Path -- Worst Imperfection (II) -- Formulation of Worst Imperfection -- Group Equivariance -- Optimization Problems for Worst Imperfection -- Simple Critical Points -- Resonance of Symmetry -- Double Critical Points -- Examples of Worst Imperfection -- Truss Tents -- Random Imperfection (II) -- Probability Density Function of Critical Loads -- Derivation of Probability Density Functions -- Semi-empirical Evaluation -- Examples of Scatter of Critical Loads -- Regular-Polygonal Truss Tents and Domes -- Pentagonal Truss Dome -- Cylindrical Specimens of Sand and Concrete -- Numerical Analysis of Symmetric Systems -- Numerical Bifurcation Analysis of Symmetric Systems -- Analysis Procedure -- Examples of Numerical Bifurcation Analysis -- Revised Scaled-Corrector Method -- Original Scaled-Corrector Method -- Regular-Hexagonal Truss Dome Use of Block-Diagonalization in Bifurcation Analysis -- Eigenanalysis Versus Block-Diagonalization -- Block-Diagonal Form for Dn-Symmetric System -- Block-Diagonal Form for Cn-Symmetric System -- Efficient Transformation for Block-Diagonalization -- Construction of Transformation Matrix : Illustration -- Regular-Triangular Truss -- Representation Matrix -- Local Transformation Matrix -- Assemblage of Local Transformations -- Construction of Transformation Matrix : General Procedure -- Formulas for Local Transformation Matrices -- Appendix : Derivation of Local Transformation Matrices -- Case ... = 0z -- Case ... = 0xy -- Case ... = 1Mz -- Case ... = 1Mxy -- Case ... = 2z -- Case ... = 2xy -- Modeling of Bifurcation Phenomena -- Bifurcation Behaviors of Cylindrical Soils -- Groups for Spatial Symmetry -- Symmetry of Cylindrical Domain -- Subgroups of D ... h -- Example of Description of Cylindrical Sand Deformation -- Experiments on Cylindrical Sand Specimens -- Recursive Bifurcation Behavior -- Mode Switching Behavior -- Recovery of Perfect System -- Application of Crossing-Line Law -- Appendix : Derivation of Bifurcation Rules -- Bifurcation of Dnh-Equivariant System -- Bifurcation of Dnd-Equivariant System -- Bifurcation of Steel Specimens -- Symmetry of a Rectangular Parallelepiped Domain -- Recursive Bifurcation Rule -- Experimental Study -- Effect of Cross-Sectional Shape -- Computational Study -- Echelon-Mode Formation -- Symmetry Group of Cylindrical Domain -- Geometrical Symmetry -- Underlying Translational Symmetry -- Subgroups for Patterns with High Spatial Frequencies -- Diamond Pattern -- Oblique Stripe Pattern -- Echelon Mode -- Recursive Bifurcation Leading to Echelon Modes -- Direct Bifurcation -- Recursive Bifurcation via Oblique Stripe Pattern -- Physical Scenario for Echelon Mode Formation -- Experiment on a Soil Specimen -- Deformation Patterns : Phenomenological Observation -- Deformation Patterns : Symmetry -- Image Simulations for Stripes on Kaolin -- Image Simulation Procedure -- Image Simulation for Kaolin -- Patterns on Sand Specimens -- Experiment and Visualization of Strain Fields -- Image Simulation -- Numerical Simulation -- Three-Dimensional Patterns -- Bifurcation of O(2) x O(2)-Equivariant System -- Bifurcation of OB ...nñ-Equivariant System -- Bifurcation of D ...-Equivariant System -- Flower Patterns on Honeycomb Structures -- Symmetry of Representative Volume Element -- Bifurcation Rule for Representative Volume Element -- Irreducible Representations for 2 x 2 Cells -- Triple Critical Points -- Derivation of Bifurcation Equation -- Solving of Bifurcation Equation -- The Representative Case : ... = (3, 3) -- Another Case : = (3,1) -- Other Cases : ... = (3, 2) and ... = (3, 4) -- Stability of Bifurcating Branches -- Analysis by Equivariant Branching Lemma -- Numerical Analysis of Honeycomb Cellular Solids -- Irreducible Representations for n x n Cells -- Four-Dimensional Irreducible Representations -- Six-Dimensional Irreducible Representations -- Twelve-Dimensional Irreducible Representations -- Solving of Bifurcation Equation for n x n Cells -- Bifurcation Point of Multiplicity 6 -- Bifurcation Point of Multiplicity 12 -- Answers to Problems -- |