ABSTRACT
This chapter considers triangular elements to help illustrate the methodology of finite elements in a fairly general manner. It describes certain elements in terms of general shape and considers certain requirements on interpolation functions for convergence, and turns to ways of finding interpolation functions. The chapter also considers the beam problem and it starts by expressing the field variable w(x) in terms of a third-order, parameter-laden polynomial. To get the interpolation functions for triangular elements of the kind, it transforms the Lagrangian interpolation formula from Cartesian to natural coordinates: where the interpolation functions are then given as the product of the three so-called Lagrange polynomials. The chapter point outs that the bicubic polynomial discussed is formed from the Pascal triangle in a symmetric manner.
