Accession Number : AD0738966

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

Corporate Author : CATHOLIC UNIV OF AMERICA WASHINGTON D C DEPT OF CIVIL AND MECHANICAL ENGINEERING

Personal Author(s) : Kao,Robert

Report Date : JAN 1972

Pagination or Media Count : 36

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)

Descriptors :   (*CALCULUS OF VARIATIONS, NUMERICAL ANALYSIS), (*BOUNDARY VALUE PROBLEMS, *NUMERICAL ANALYSIS), (*BEAMS(STRUCTURAL), LOADS(FORCES)), CANTILEVER BEAMS, MECHANICAL CABLES, POLYNOMIALS, DEFLECTION

Subject Categories : Numerical Mathematics
      Structural Engineering and Building Technology
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE