Abstract
The interpolation functions and models used in finite element analysis are presented in this chapter. Polynomial form of interpolation functions for one, two, and three dimensional problems are discussed. The simplex, complex, and multiplex elements are defined. The representation of interpolation polynomials in terms of nodal degrees of freedom, and considerations in selecting the order of the interpolation polynomials such as geometric isotropy or geometric invariance and convergence requirements are discussed. Interpolation polynomials in terms of global coordinates for simplex elements in one, two, and three dimensions are derived. Interpolation polynomials are presented for vector quantities. The linear interpolation polynomials in terms of local coordinates for one-dimensional element, two-dimensional triangle element, and three-dimensional tetrahedron element are derived. The closed-form integration formulas are presented in terms of natural coordinates for simplex elements in one, two, and three dimensions. The patch test for ensuring convergence of the results is outlined along with simple illustrative examples.
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