Symbolic Solution of Short Beam on Elastic Foundation Using the Computer Algebra System

Abstract

In this paper, the aim is to utilize Computer Algebra Systems to derive a closed-form solution for foundation-structure response. Typically, the subgrade reactive pressure beneath a loaded foundation region is modelled using a series of independent linear spring systems, but this approach has limitations and is not practical due to the lack of continuity between the springs and the unloaded foundation medium. To address this issue, a short beam structure has been introduced on an elastic foundation, which can restrict the vertical displacement on both the loaded and unloaded regions of the foundation. To obtain a closed-form solution for displacement and the bending moment of the foundation based on the imaginary beam inclusion, a MAPLE code has been developed to symbolically solve the governing differential equation using Computer Algebra Systems. Additionally, a comparison between the present solution and the analytical solution is provided for two prominent practical problems in the civil engineering applications.