Full Description
The author has published many papers and books on topological transformations for optimal analysis of structures, where many methods and algorithms are developed. However, the framework of this book generalizes many concepts and makes the previously developed methods conceptually more attractive. The aim of the present work is two folds. On the one hand, it shows to mathematicians how the apparently pure mathematical concepts can be applied to the efficient solution of problems in structural mechanics. On the other hand, it illustrates to engineers the important role of mathematical concepts for the solution of engineering problems. The present framework provides efficient means for looking at problems and developing ideas by transforming the models (structures, networks, systems) to other spaces (higher dimension, lower dimension, or identical dimension) to simplify the problems.
This book is attractive for those who look at the deeper aspects of concepts and helps the readerto develop his/her own ideas. In general, it opens a new horizon for improving the existing methods in civil, mechanical, and electrical engineering.
Contents
The Main Objective of the Present Book.- Introduction to Graph Theory and Algebraic Graph Theory.- Embedding Graphs on Lower Dimensional Spaces.- Embedding Graphs on Higher Dimensional Spaces.- Embedding Graphs on spaces of Identical Dimensions.- Structural Configuration Generation.- Symmetry Using Linear Algebra and Graph Theory.- Complementary Space of Graphs.- Miscellaneous Applications Graph Problems Using Meta-heuristic Algorithms.
