ABSTRACT
This chapter describes briefly some of the strategies which may be used to apply Gauss' theorem to the approximate solution of the solid mechanics problem. The principle of virtual displacements leads naturally to the displacement formulation of the finite element method, but this is by no means the only viable approach. It is the intention to deal with the specific topics as they arise. However, individual examples are taken more or less at random to illustrate the principles involved. Evidently, the higher the order of derivative compatibility required, the more will be the difficulties which arise in the determination of the orthogonal interpolation functions. Hermitian polynomials are a good example of such function construction. The chapter shows that the compatible displacement models, while maintaining displacement compatibility across element boundaries, satisfy equilibrium only in the mean at discrete points.
