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

Gulkan P., Alemdar B.

STRUCTURAL ENGINEERING AND MECHANICS, cilt.7, sa.3, ss.259-276, 1999 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 3
  • Basım Tarihi: 1999
  • Doi Numarası: 10.12989/sem.1999.7.3.259
  • Dergi Adı: STRUCTURAL ENGINEERING AND MECHANICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.259-276
  • Anahtar Kelimeler: two-parameter elastic foundation, Winkler model, Pasternak model, element stiffness matrix, work equivalent nodal force, consistent mass matrix, consistent geometrical stiffness matrix
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.