Topological transformations for efficient structural analysis / / Ali Kaveh

• Autore: Kaveh Ali
• Pubblicazione: Cham, Switzerland : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (198 pages)
• Disciplina: 624.171
• Soggetto topico: Structural analysis (Engineering) - Mathematics; Topological transformation groups
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 The Main Objective of the Present Book -- References -- 2 Introduction to Graph Theory and Algebraic Graph Theory -- 2.1 Basic Concepts and Definitions of Graph Theory -- 2.1.1 Definition of a Graph -- 2.1.2 Adjacency and Incidence -- 2.1.3 Graph Operations -- 2.1.4 Walks, Trails and Paths -- 2.1.5 Cycles and Cutsets -- 2.1.6 Trees, Spanning Trees and Shortest Route Trees -- 2.2 Different Types of Graphs -- 2.3 Vector Spaces of a Graph -- 2.3.1 Cycle Space -- 2.3.2 Cutset Space -- 2.3.3 Cycle Bases Matrices -- 2.3.4 Cutset Bases Matrices -- 2.4 Planar Graphs -- Polyhedron Formula of Euler -- 2.4.1 Planar Graphs -- 2.5 Maximal Matching in Bipartite Graphs -- 2.5.1 Theorems on Matching -- 2.5.2 Maximum Matching -- 2.6 Historical Problem of Graph Theory -- 2.7 Definitions from Algebraic Graph Theory -- 2.7.1 The Adjacency Matrix -- 2.7.2 The Incidence Matrix -- 2.7.3 Incidence Matrix of an Oriented Graph -- 2.7.4 Some Properties of Symmetric Matrices -- 2.7.5 The Laplacian Matrix -- 2.8 Graphs Associated with Matrices -- References -- 3 Embedding Graphs on Lower Dimensional Spaces -- 3.1 Introduction -- 3.2 Graph Drawing for Calculating the DSI of Space Structures -- 3.3 Ordering for Constructing Well Structured Sparse Matrices: Graph Theory Methods -- 3.4 Bandwidth Optimization -- 3.4.1 Preliminaries -- 3.4.2 A Shortest Route Tree and Its Properties -- 3.4.3 Nodal Ordering for Bandwidth Reduction -- 3.5 Finite Element Nodal Ordering -- 3.5.1 Element Clique Graph Method -- 3.5.2 Skeleton Graph Method -- 3.5.3 Element Star Graph Method -- 3.5.4 Element Wheel Graph Method -- 3.5.5 Partially Triangulated Graph Method -- 3.5.6 Triangulated Graph Method -- 3.5.7 Natural Associate Graph Method (NAGM) -- 3.5.8 Incidence Graph Method (INGM) -- 3.5.9 Representative Graph Method (REGM). ; 3.5.10 Complete Representative Graph Method (REGM) -- 3.6 Graph Models for Meshless Discretization -- 3.6.1 Strongly Connected Associate Graph (SCAG) -- 3.6.2 Partially Connected Associate Graph (PCAG) -- 3.6.3 Weakly Connected Associate Graph (WCAG) -- 3.6.4 Associate Bipartite Graph (ABG) -- References -- 4 Embedding Graphs on Higher Dimensional Spaces -- 4.1 Introduction -- 4.2 Force Method of Structural Analysis -- 4.2.1 Equilibrium Equations -- 4.2.2 Compatibility Equations -- 4.3 Embeddings on Higher Dimensional Spaces -- 4.3.1 Definitions from Topology and Algebraic Topology -- 4.3.2 Orientable 2-Manifolds -- 4.3.3 Simplicial Complexes -- 4.3.4 CW-Complexes -- 4.3.5 Collapsible and Contractible Complexes -- 4.3.6 Homology Group -- 4.4 Cycle Bases Selection: Topological Methods -- 4.4.1 A 2-Dimensional Polyhedron Embedding -- 4.4.2 Admissible Embeddings -- 4.4.3 Modified Manifold Embedding -- 4.4.4 Embedding S on a Union of Disks -- 4.5 Graph-Theoretical Force Method -- References -- 5 Embedding Graphs on Spaces of Identical Dimensions -- 5.1 Introduction -- 5.2 Element Ordering for Frontwidth Reduction -- A Line Graph -- 5.3 Element and Nodal Ordering -- A K-Total Graph -- 5.3.1 Definitions -- 5.3.2 Algorithm for Bandwidth Reduction of Rectangular Matrices -- 5.3.3 Entire Graph -- 5.4 Generalized Cycle Bases -- Interchange Graph -- 5.5 Cycle and Generalized Cycle Basis Ordering -- 5.6 The Rigidity of Planar Trusses -- 5.6.1 Simple, Compound and Complex Trusses -- 5.6.2 The Rigidity of Grid-Shaped Planar Trusses -- 5.6.3 Grids with Diagonal Rods -- 5.6.4 Grid with Diagonal Rods and/or Cables -- 5.6.5 Henneberg Sequence for Examining the Rigidity of Trusses -- 5.6.6 Complete Matching and Rigidity of Trusses -- 5.7 Duality of Cycle Bases and Cut Set Bases -- Dual Graph -- 5.7.1 A Planar Truss and Its Maxwell Diagram as Dual Graphs. ; 5.7.2 Flow Graph and Potential Graph, and Their Applications -- 5.7.3 Potential Graph and Its Application -- 5.8 Other Applications -- References -- 6 Structural Configuration Generation -- 6.1 Introduction -- 6.2 Algebraic Representation of a Graph in Integer Coordinate System -- 6.3 Representations of Operations on Graphs -- 6.3.1 Addition of Two Subgraphs -- 6.3.2 Subtraction of Two Subgraphs -- 6.4 Some Functions for Configuration Processing -- 6.4.1 Translation Functions -- 6.4.2 Rotation Functions -- 6.4.3 Reflection Functions -- 6.4.4 Projection Functions -- 6.5 Geometry of Structures -- References -- 7 Symmetry Using Linear Algebra and Graph Theory -- 7.1 Introduction -- 7.2 Basic Definitions -- 7.2.1 Basic Concepts from the Theory of Graphs -- 7.2.2 Basic Definitions from Linear Algebra -- 7.2.3 Definitions from Algebraic Graph Theory -- 7.3 Canonical Forms of a Matrix -- 7.3.1 Form I -- 7.3.2 Form II -- 7.3.3 Form III -- 7.3.4 Form IV -- 7.4 A Canonical Form Associated with Rotationally Repetitive Structures -- 7.5 Different Kinds of Symmetry -- 7.5.1 Form I Symmetry -- 7.5.2 Form II Symmetry -- 7.5.3 Form III Symmetry -- 7.6 The Form Associated with Rotationally Repetitive Structures -- 7.7 The Relations Between the Canonical Forms -- 7.7.1 The Relation Between the Form I and Form II -- 7.7.2 The Relation Between the Form II and Form III -- 7.7.3 The Relation Between the Form IV and Form III -- 7.8 The Relation Between the Canonical Form II and the Form Associated with Rotationally Repetitive Structures -- 7.9 Examples -- 7.10 Concluding Remarks -- References -- 8 Complementary Space of Graphs -- 8.1 Introduction -- 8.2 Theorems for Graph Partitioning -- 8.3 Largest Eigenvector of the Complementary Laplacian Matrix -- 8.4 Numerical Results -- 8.5 Concluding Remarks -- References. ; 9 Miscellaneous Applications Graph Problems Using Meta-Heuristic Algorithms -- 9.1 Introduction -- 9.2 Optimal Domain Decomposition Using Colliding Bodies Optimization and k-median Method -- 9.2.1 The Formulation of the CBO Algorithm -- 9.2.2 Mathematical Formulation of the k-median Problem -- 9.2.3 Numerical Examples -- 9.2.4 Results and Discussion on Examples -- 9.2.5 Concluding Remarks -- 9.3 Simulated Annealing Algorithm for Selecting Suboptimal Cycle Basis of a Graph -- 9.3.1 Definitions from Theory of Graphs -- 9.3.2 Simulated Annealing Algorithm -- 9.3.3 Simulated Annealing Algorithm for the Formation of a Suboptimal Cycle Basis -- 9.3.4 Generating the Initial Cycle Basis -- 9.3.5 Generating a Neighbor Solution -- 9.3.6 Reannealing (Restarting) -- 9.3.7 Algorithm Parameters -- 9.3.8 Examples -- 9.3.9 Conclusions -- 9.4 Further Miscellaneous Applications -- 9.4.1 Size Reduction Transformation -- References.
• Titolo autorizzato: Topological Transformations for Efficient Structural Analysis
• ISBN: 9783031123009; 9783031122996
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910620195603321
• Lo trovi qui: Univ. Federico II