An exact finite element for a beam on a two-parameter elastic foundation: a revisit

Gulkan P., Alemdar B.

STRUCTURAL ENGINEERING AND MECHANICS, vol.7, no.3, pp.259-276, 1999 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 3
  • Publication Date: 1999
  • Doi Number: 10.12989/sem.1999.7.3.259
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.259-276
  • Keywords: two-parameter elastic foundation, Winkler model, Pasternak model, element stiffness matrix, work equivalent nodal force, consistent mass matrix, consistent geometrical stiffness matrix


An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.