Energy-Based Approximation Methods

The work and energy principles discussed so far offer the possibility to solve static problems in an exact way. In many practical applications, however, one will be confronted with the fact that a given problem can no longer be treated in the form of exact closed-analytical solutions or only with disproportionate computational effort. At this point, a number of energy-based approximate analysis methods have been established, a selection of which we will discuss in this chapter. In addition to classical methods such as the Ritz method and the Galerkin method which are the subject matter of the present chapter, we want to discuss in detail a modern and firmly established numerical method, namely the so-called Finite Element Method (short: FEM).