| Within this thesis a new method for formulating finite element stiffness matrices is presented. The main objective behind this work is to become more familiar with the dual nature of Chebyshev polynomials, specifically that they can be represented by both standard, algebraic polynomials and trigonometric functions. This is accomplished by using Chebyshev Polynomials in a familiar arena, the finite element method. The stiffness matrices are constructed in an isoparametric fashion from interpolation polynomials where Chebyshev polynomials are the basis functions. As a result the amount of integration in calculating the stiffness matrix is reduced. This reduction is due to orthogonality. |
