ABSTRACT
All finite element formulations make use of element interpolation functions. In developing element interpolation functions using generalized coordinates, it is not always an easy task to satisfy spatial isotropy. This chapter discusses the development of interpolation functions for some "families" of C° elements, including higher-order ones. Higher-order elements maintain the interelement continuity of lower order elements, but employ a higher-order approximation. Elements comprising the so-called Lagrangian family are systematically derived with the aid of one-dimensional Lagrange polynomials. For a general one-dimensional Lagrangian element containing Nen nodes, the interpolation function associated with node i will be the Lagrange polynomial of degree (Nen – 1) that takes on the value of one at node i and the value of zero at the remaining nodes. In general, two-dimensional Lagrangian elements are quadrilateral in shape. The chapter considers the biquadratic member of the Lagrangian element family. The schematic relationship between the element and two quadratic one-dimensional elements used in determining its interpolation functions.
