Transverse displacements of cracked beams on Pasternak soil

Abstract

AbstractThe response analysis of cracked beams resting on elastic foundations can be conveniently and satisfactorily addressed by applying the simplified crack model within the 1D finite element model. For the very commonly implemented Winkler's soil model, the exact transverse displacements’ interpolation functions, the stiffness matrix, as well as the corresponding load‐vector for the linearly distributed continuous transverse load were recently presented in closed symbolic forms. This paper upgrades the existing 1D finite element solution to the more realistic Pasternak soil model. The derivation implements the exact Winkler soil model transverse displacements’ functions as interpolation functions of the Pasternak soil model. In this way, a complementary stiffness matrix is obtained which upgrades the existing Winkler solution into an approximate Pasternak soil model solution. Also this matrix is derived in closed symbolic form and it can be easily added to the existing finite element solutions. The implementation and the quality of the results are being presented through a comparative case study to support the discussed approach.