TheVariational principlesApproximation methods behaviour of a solid is described by differential equations that depend on location and time. As an example, the linear elastic and anisotropic structural behaviour in the three-dimensional case is defined with the equation systems shown in Chapter 2 . The problem is fully described when all boundary conditions (support conditions, geometry, load) are taken into account. Nevertheless, only in the rarest of cases is it possible to determine a mathematically rigorous solution for a given engineering problem. By rigorous, we mean that a problem can be solved in such a way that all governing equations as well as all underlying boundary conditions are exactly fulfilled. For this reason, a whole range of solution methods have been developed that can be used to find at least approximate solutions for a large number of engineering problems.