OVERVIEW

This book is concerned with the development of analytical methods for solving problems in mechanics of materials that are generally considered beyond the scope of basic courses in the discipline. As such, the developments tend to evolve from fundamental principles such as equilibrium and conservation of energy.

In analyzing a particular physical problem, the analyst must develop a mathematical model that describes the problem. The mathematical model consists of equations that are solved to obtain formulas predicting the behavior of the mathematical model. It is imperative to keep in mind that what is being analyzed is a model of the physical problem rather than the physical problem itself. This is, perhaps, a subtle distinction, but it is of paramount importance. Thus, how well the results of the analysis predict the behavior of the physical problem depends on how well the mathematical model represents the physical problem at hand.

Any mathematical model is an idealization of the physical problem that the model represents. In developing the model, certain assumptions are made regarding the behavior of the physical problem in order to simplify the analysis. The goal of the analysis is to capture the essential behavior of the physical problem while ignoring behavior that is considered nonessential. For example, in developing the Bernoulli Euler beam theory studied in mechanics of materials courses, among other things it is assumed that straight lines perpendicular to the neutral axis before bending remain straight and perpendicular after bending. The resulting equations describe the deflection of the...