Title Swift analysis of civil engineering structures using graph theory methods / Ali Kaveh, Hossein Rahami, Iman Shojaei

Published Cham : Springer, 2020

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Description 1 online resource (311 pages) Series Studies in Systems, Decision and Control Ser. ; v. 290 Studies in systems, decision and control ; v. 290. Contents Intro -- Preface -- Contents -- 1 Definitions from Graph Theory and Graph Products -- 1.1 Introduction -- 1.2 Basic Definitions -- 1.2.1 Definition of a Graph -- 1.2.2 Adjacency and Incidence -- 1.2.3 Isomorphic Graphs -- 1.2.4 Graph Operations -- 1.3 Different Types of Graphs -- 1.4 Matrix Representation of a Graph -- 1.5 Definitions of Graph Products -- 1.5.1 Cartesian Product -- 1.5.2 Direct Product -- 1.5.3 Strong Cartesian Product -- 1.5.4 Lexicographic Product -- References -- 2 Basic Concepts and Definitions of Symmetry and Regularity -- 2.1 Introduction 2.2 Kronecker Product and Different Matrix Patterns -- 2.3 Block Diagonalization of Compound Matrices -- 2.3.1 Inverse of a Block Matrix -- 2.4 Block Diagonalization of Adjacency and Laplacian Matrices -- 2.4.1 Nodal Numbering of Graphs Generated by Graph Products -- 2.4.2 Block Diagonalization of Adjacency Matrices -- 2.4.3 Block Diagonalization of Laplacian Matrices -- 2.5 Decomposition of the Block Matrices -- 2.5.1 Decomposition of the Matrices of the Form Fn (Am, Bm, Cm) -- 2.5.2 Conditions for Full Decomposability of Block Matrices -- 2.5.3 Decomposition of the Matrices of Other Forms 2.6 Circulant Block Matrices -- 2.7 Complementary Examples -- References -- 3 Static Analysis of Near-Regular Skeletal Structures: Additional Members -- 3.1 Introduction -- 3.2 Analysis of Near-Regular Structures with Additional Members Using Displacement Methods -- 3.2.1 A Comprehensive Example -- 3.2.2 Complementary Examples -- 3.3 Analysis of Near-Regular Structures with Additional Members Using Force Methods -- 3.3.1 Formulation of the Flexibility Matrix -- 3.3.2 Analysis of Regular Structures with Excessive Members -- 3.3.3 Analysis of Regular Structures with Some Missing Members 3.3.4 Complementary Examples -- 3.3.5 Appendix: Calculation of the Flexibility Matrix B Without the Formation of the Equilibrium Matrix A -- References -- 4 Static Analysis of Near-Regular Skeletal Structures: Additional Nodes -- 4.1 Introduction -- 4.2 Analysis of Near-Regular Structures with Additional Nodes Using Displacement Methods -- 4.2.1 Computational Complexity of the Method -- 4.2.2 Complementary Examples -- 4.3 Analysis of Near-Regular Structures with Additional Nodes Using Force Methods -- 4.4 Eigensolution of Near-Regular Structures 4.4.1 Decomposition of Partitioned Block Matrices -- 4.4.2 Computational Complexity of Eigensolution of Near-Regular Graphs via Solution of Characteristic Equation -- 4.4.3 A Simple Illustrative Example -- 4.4.4 Complementary Examples -- References -- 5 Static Analysis of Nearly Regular Continuous Domains -- 5.1 Introduction -- 5.2 Finite Element Solution of Regular and Near Regular Patterns -- 5.2.1 Efficient Finite Element Solution Regular Patterns -- 5.2.2 Efficient Finite Element Solution of Near-Regular Patterns -- 5.2.3 Examples Summary This book proposes and validates a number of methods and shortcuts for frugal engineers, which will allow them to significantly reduce the computational costs for analysis and reanalysis and, as a result, for structural design processes. The need for accuracy and speed in analyzing structural systems with ever-tighter design tolerances and larger numbers of elements has been relentlessly driving forward research into methods that are capable of analyzing structures at a reasonable computational cost. The methods presented are of particular value in situations where the analysis needs to be repeated hundreds or even thousands of times, as is the case with the optimal design of structures using different metaheuristic algorithms. Featuring methods that are not only applicable to skeletal structures, but by extension also to continuum models, this book will appeal to researchers and engineers involved in the computer-aided analysis and design of structures, and to software developers in this field. It also serves as a complement to previous books on the optimal analysis of large-scale structures utilizing concepts of symmetry and regularity. Further, its novel application of graph-theoretical methods is of interest to mathematicians Notes 5.3 Finite Element Solution of Problems with an Arbitrary Domain: A Hyper Pre-solved Element Bibliography Includes bibliographical references Notes Print version record Subject Structural analysis (Engineering) -- Mathematics Structural analysis (Engineering) -- Data processing Civil engineering, surveying & building. Maths for engineers. Technology & Engineering -- Civil -- General. Technology & Engineering -- Engineering (General) Structural analysis (Engineering) -- Data processing Structural analysis (Engineering) -- Mathematics Genre/Form Electronic books Form Electronic book Author Rahami, Hossein Shojaei, Iman ISBN 9783030455491 3030455491

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