Abstract
Efficient hierarchical elements are presented for the p-version of the finite element method. The shape functions of the elements are expressed by simple polynomial series based on the p-approximation concept and the polynomials and those derivatives are given in the form of recurrence formulas, respectively. Furthermore, integral formulas for the stiffness matrices of regular elements are given in the explicit forms.
In this paper, quadrilateral, triangular and hexahedral elements are formulated for plane stress, plate bending and three dimensional stress analysis, and singular elements could be derived easily from those elements by the use of hierarchcal mapping technique and show superior convergence for concentrated loading.
