Beam Elements on Two-Parameter Elastic Foundations

Two-parameter elastic foundations are more accurate than a one-parameter (Winkler) foundation and are simpler than semi-infinite elastic continuum foundation models. Two kinds of finite elements are formulated in this paper to analyze beams on one-or two-parameter foundations. Models include Winkler, Filonenko-Borodich, Pasternak, generalized, and Vlasov foundations. One of the two kinds of elements is based on the exact displacement function. The other is based on a cubic displacement function. The stiffness matrix and consistent load vector is derived for each. Numerical tests show that the element based on the exact displacement function can give exact numerical results even if the number of elements is very small. The element based on a cubic function may require a fine mesh to give acceptable results.