Ebook: Optimal Analysis of Structures by Concepts of Symmetry and Regularity

Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models.
Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented.
The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms.
The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.

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Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models.
Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented.
The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms.
The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.

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Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models.
Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented.
The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms.
The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.

Content:
Front Matter....Pages i-xvi
Introduction to Symmetry and Regularity....Pages 1-14
Introduction to Graph Theory and Algebraic Graph Theory....Pages 15-35
Graph Products and Configuration Processing....Pages 37-67
Canonical Forms, Basic Definitions and Properties....Pages 69-113
Canonical Forms for Combinatorial Optimisation, Nodal Ordering and Graph Partitioning....Pages 115-129
Graph Products for Ordering and Domain Decomposition....Pages 131-152
Canonical Forms Applied to Structural Mechanics....Pages 153-263
Graph Products Applied to the Analysis of Regular Structures....Pages 265-313
Graph Products Applied to the Locally Modified Regular Structures Using Direct Methods....Pages 315-339
Graph Products Applied to the Regular and Locally Modified Regular Structures Using Iterative Methods....Pages 341-399
Group Theory and Applications in Structural Mechanics....Pages 401-432
Graph–Group Method for the Analysis of Symmetric-Regular Structures....Pages 433-458
Back Matter....Pages 459-463

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Optimal analysis is defined as an analysis that creates and uses sparse, well-structured and well-conditioned matrices. The focus is on efficient methods for eigensolution of matrices involved in static, dynamic and stability analyses of symmetric and regular structures, or those general structures containing such components. Powerful tools are also developed for configuration processing, which is an important issue in the analysis and design of space structures and finite element models.
Different mathematical concepts are combined to make the optimal analysis of structures feasible. Canonical forms from matrix algebra, product graphs from graph theory and symmetry groups from group theory are some of the concepts involved in the variety of efficient methods and algorithms presented.
The algorithms elucidated in this book enable analysts to handle large-scale structural systems by lowering their computational cost, thus fulfilling the requirement for faster analysis and design of future complex systems. The value of the presented methods becomes all the more evident in cases where the analysis needs to be repeated hundreds or even thousands of times, as for the optimal design of structures by different metaheuristic algorithms.
The book is of interest to anyone engaged in computer-aided analysis and design and software developers in this field. Though the methods are demonstrated mainly through skeletal structures, continuum models have also been added to show the generality of the methods. The concepts presented are not only applicable to different types of structures but can also be used for the analysis of other systems such as hydraulic and electrical networks.

Content:
Front Matter....Pages i-xvi
Introduction to Symmetry and Regularity....Pages 1-14
Introduction to Graph Theory and Algebraic Graph Theory....Pages 15-35
Graph Products and Configuration Processing....Pages 37-67
Canonical Forms, Basic Definitions and Properties....Pages 69-113
Canonical Forms for Combinatorial Optimisation, Nodal Ordering and Graph Partitioning....Pages 115-129
Graph Products for Ordering and Domain Decomposition....Pages 131-152
Canonical Forms Applied to Structural Mechanics....Pages 153-263
Graph Products Applied to the Analysis of Regular Structures....Pages 265-313
Graph Products Applied to the Locally Modified Regular Structures Using Direct Methods....Pages 315-339
Graph Products Applied to the Regular and Locally Modified Regular Structures Using Iterative Methods....Pages 341-399
Group Theory and Applications in Structural Mechanics....Pages 401-432
Graph–Group Method for the Analysis of Symmetric-Regular Structures....Pages 433-458
Back Matter....Pages 459-463
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