When trying to understand a complex system, it is quite useful to have available some simple models – not as solutions per se but as organizational principles for seeing through the voluminous numbers produced by the FE codes. This chapter is concerned with the construction of simple analytical models; it gathers together many of the simple models used throughout the previous chapters and tries to illustrate the approach to constructing these. Although the models are approximate, by basing them on sound mechanics principles, they are more likely to capture the essential features of a problem and thus have a wider range of application. The models discussed are shown in Figure 7.1.

The term “model” is widely used in many different contexts, but here we mean a representation of a physical system that may be used to predict the behavior of the system in some desired respect. The actual physical system for which the predictions are to be made is called the prototype.

There are two broad classes of models: physical models and mathematical models. The physical model resembles the prototype in appearance but is usually of a different size, may involve different materials, and frequently operates under loads, temperatures, and so on, that differ from those of the prototype. The mathematical model consists of one or more equations (and, more likely nowadays, a numerical FE model) that describe the behavior of the system of interest.