Exact analysis of beams on two-parameter elastic foundations

Efficient beams on two-parameter elastic foundation finite elements have recently been developed. The stiffness matrix and nodal loud vector of these elements have been derived on the basis of the exact displacement function obtained from the solution of the governing differential equation. Most of the existing elements are, however, either limited to certain combinations of beam and foundation parameters, or provide only the solution of the homogeneous form of the governing equation. In this paper a new finite element is derived which eliminates these limitations. The stiffness matrix, nodal load vector and shape function of the clement are derived using the differential equation of a beam on a two-parameter elastic foundation. The complete solution of the equation corresponding to the most common types of load is also presented. This permits the determination of the deflections and internal forces anywhere along a simple or continuous beam on two-parameter foundations.