Basic Definitions and Concepts of Structural Mechanics and Theory of Graphs

Abstract

This chapter consists of two parts. In the first part, basic definitions, concepts and theorems of structural mechanics are presented. These theorems are employed in the following chapters and are very important for their understanding. For determination of the distribution of internal forces and displacements, under prescribed external loading, a solution to the basic equations of the theory of structures should be obtained, satisfying the boundary conditions. In the matrix methods of structural analysis, one must also use these basic equations. In order to provide a ready reference for the development of the general theory of matrix structural analysis, the most important basic theorems are introduced in this chapter, and illustrated through simple examples.

In the second part, basic concepts and definitions of graph theory are presented. Since some of the readers may be unfamiliar with the theory of graphs, simple examples are included to make it easier to understand the presented concepts.