| Description |
1 online resource (210 p.) |
| Contents |
Cover -- Endorsements -- Half Title -- Title Page -- Copyright Page -- Contents -- Foreword -- Preface -- Symbols -- Acknowledgment -- I. This is Fundamental Part -- 1. Introduction -- 1.1. A Review of Science and Engineering Approaches for Symmetry -- 1.2. Symmetric Structures -- 1.3. Origami and Symmetry -- 1.3.1. Relationship between Kresling Folds and Symmetry -- 1.4. Bamboo Knitting Patterns and Symmetry -- 1.4.1. Basic Patterns of Bamboo Weaving and Their Symmetry -- 1.4.2. Bamboo Weaving and Observations on Symmetry -- 1.4.3. Bamboo Braids Optimizing Symmetry and Strength |
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1.5. Equilibrium and Symmetry using Balancing Toys, Yajirobee -- 2. Symmetry and Its Representation -- 2.1. Basic Concept of a Group -- 2.1.1. Group Definition -- 2.1.2. Symmetry Operation -- 2.1.3. Systematic Classification for Symmetric Structures -- 2.2. Representation of Group -- 2.3. Simplification of Expression -- 2.4. Supplementary Information on Group Tables -- 2.5. Subgroups and Conjugate Elements -- 2.5.1. Isomorphism and Quasi-isomorphism -- 2.5.2. Conjugate Elements and Types -- 2.5.3. Subgroups and Immutable Subgroups -- 2.5.4. Translation Group and Rotation Group |
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2.6. Group Representation -- 2.6.1. Representation Matrix of Group G -- 2.6.2. Representation Theory in General -- 2.6.3. Reducible and Irreducible Representations -- 2.6.4. Indicators and Their Properties -- 2.6.5. Orthogonal Irreducible Representation Matrix -- 2.6.6. Linear Transformation Group -- 3. Group Theory and Structural Mechanics -- 3.1. Group Theory and Dynamics -- 3.2. Dynamic Problem -- 3.3. Group Theory and Statics -- 3.4. Orbital Concept -- 3.4.1. Orbital Concept and Matrix Coordinate Transforms -- 4. Basics of the Finite Element Method |
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4.1. Finite Element Method as a Structural Analysis for a Discrete Model -- 4.2. Fundamentals of Continuum Mechanics -- 4.2.1. Solid Members -- 4.2.2. Plate and Shell elements -- 4.2.3. Mindlin's Plate Theory -- 4.2.4. Kirchhoff-Love's Plate Theory -- 4.3. Rigid Frame Members -- 4.3.1. Timoshenko Beam Theory -- 4.3.2. Bernoulli-Euler Beam Theory -- 4.4. Fundamentals of the Finite Element Method -- 4.4.1. Finite Element -- 4.4.2. Displacement Function and Shape Function -- 4.4.3. Formulation of Stiffness Equation -- 4.5. Formulation of Finite Elements -- 4.5.1. Plane Element |
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4.5.2. 4-Node Rectangular Element -- 4.5.3. 4-Node Isoparametric Quadrilateral Element -- 4.5.4. 3D Solid Element -- 4.5.5. Plate and Shell Element -- 4.5.6. Rigid Frame Element -- 4.6. Finite Element Method Techniques -- 4.6.1. Numerical Integration Method -- 4.6.2. Mesh Dependency of Solution -- 4.7. Programming the Finite Element Method -- 4.7.1. Assembly of Overall Stiffness Matrix -- 4.7.2. Coordinate Transformation -- 4.7.3. Introduction Method of Support Conditions -- 4.7.4. Solving Simultaneous Equations -- II. This is the Application of Group Theory to Symmetric Structures |
| Summary |
Ario and Zawidzki show readers how to handle symmetric structures in engineering using group-theoretic bifurcation theory as a mathematical tool for the finite element analysis of symmetric structures |
| Notes |
Description based upon print version of record |
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5. Block Diagonalization Theory for Dihedral Groups |
| Genre/Form |
Electronic books
|
| Form |
Electronic book
|
| Author |
Zawidzki, Machi
|
| ISBN |
9781040004371 |
|
1040004377 |
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