Applications of Hill Functions (Applied Mathematic's Finite Element) to Applied Mechanics Problems,

Abstract

Almost any success in the application of the Ritz method depends on the proper choice of coordinate functions. In the paper hill functions, which are constructed in different orders on the basis of the Legendre polynomials, are used as coordinate functions. For boundary conditions other than free ones, artificial spring parameters are introduced of necessity at boundary and hill functions are used without stipulating prescribed boundary conditions in advance. It is noted that the technique described herein is referred to as the finite element method by applied mathematicians. Two one-dimensional applied mechanics problems with various end conditions are employed to illustrate the method. Results obtained here compare very nicely with exact solutions in the literature. It is, in general, found that even with lower order hill functions and coarse mesh the method still yields satisfactory results. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD0738966

Entities

People

  • Robert Kao

Organizations

  • The Catholic University of America

Tags

DTIC Thesaurus Topics

  • Applied Mechanics
  • Boundaries
  • Finite Element Analysis
  • Literature
  • Mathematics
  • Mechanics
  • Polynomials

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)