ABSTRACT
In this chapter, the authors introduce various kinds of elements along with pertinent definitions in anticipation of dealing with more complex finite element problems. They discuss requirements for convergence of the finite element process as the elements become smaller and more numerous, and consider interpolation functions. The authors examine some elements in which the nodes are at the vertices of the elements. They present certain requirements for the interpolation functions of an element. The authors discuss the ways of finding interpolation functions for one-dimensional elements and interpolation functions for triangular elements by polynomials. They consider rectangular elements, for which they use Lagrange polynomials and then Hermite polynomials. The authors describe certain three-dimensional elements. These elements can be constructed by procedures that are direct extensions of the two-dimensional elements. The authors argue that using natural coordinates often permits simple closed-form integration procedures when determining stiffness matrices.
