| This thesis presents the results obtained for a comparison of structural analysis of a basic structural system using one-dimensional finite elements with hierarchic sine series shape functions relative to standard finite elements. Conventional polynomial shape functions are combined with sine series functions to obtain higher order elements over an extended grid. The method is demonstrated for the static deflection, strain, and beam curvature as well as vibration frequencies of non-uniform bars and beams of varying cross-sections. It is demonstrated that hierarchic elements with these shape functions have convergence that is as good as or better than comparable hierarchic elements with polynomial shape functions. |
