ELEMENT FOR BEAM ON WINKLER ELASTIC FOUNDATION BASED ON ANALYTICAL TRIAL FUNCTIONS

Based on Winkler elastic foundation beam theory, the general analytical solution of a deflection equation for an elastic foundation beam is deduced; the element matrixes and equivalent load arrays of Winkler elastic foundation Euler and Timoshenko beams based on analytical trial functions are established by applying the principle of minimum potential energy. The element stiffness matrixes of Winkler elastic foundation Euler and Timoshenko beams via Ritz method are also created. Through calculating, the results are obtained by two types of elements, and then are compared with results via general beam-foundation finite element model and analytical solutions. The comparisons show that there is a noticeable difference between the results by Ritz method and analytical solution due to that the polynomial shape function is unable to accurately simulate the actual deformation of an elastic foundation beam, but the difference becomes smaller with the increasing number of elements in the analysis of an elastic foundation beam; the results are identical with analytical solutions when applying analytical trial functions regardless of the number of elements, which means the displacement shape function based on an analytical trial function is much more accurate than a general polynomial shape function. It is proved that the Winkler elastic foundation beam element based on an analytical trial function can satisfy the accuracy and efficiency requirement. It would be applied in practice engineering.