Numerical Analysis of Curved Thin Beams on Winkler Foundation

Abstract

This research, deals with the linear elastic behavior of curved thin beams resting on Winkler foundation with both compressional and tangential resistances. Thin beam theory is extended to include the effect of curvature and externally distributed moments under static conditions. The computer program (CBFFD) coded in fortran_77 is developed to analyze curved thin beams on Winkler foundation by Fourier series and finite difference methods. The results from these methods are plotted with other solutions to compare and check the accuracy of the used methods. INTRODUCION The object of this research is to analyze curved thin beam using finite difference and Fourier series methods. The beam is resting on elastic foundation with Winkler frictional and compresional resistances, and loaded generally (both transverse distributed load and distributed moment). The linear elastic behavior of curved thin beams on elastic foundations is considered. The governing differential equation of curved thin beams (in terms of w only) is developed and converted into finite differences. A computer program in (Fortran language) is developed. This program assembles the finite difference equations to obtain a system of simultaneous algebraic equations and then the solution is obtained by using Gauss elimination method. The deflections and rotations for each node are obtained. The shear and moment are obtained by simple substitutions of the deflections into the finite difference equations of moment and shear. Also, this program used Fourier series method to solve the governing differential equation for simply supported beam and obtain the deflection, moment and shear. The obtained solutions compared with available results to check the accuracy of the used methods. Curved beams are one-dimensional structural elements that can sustain transverse loads by the development of bending, twisting and shearing resistances in the transverse sections of the beam. It's extensively used in engineering and other fields since such beams have many practical applications. The curved beam elements on elastic foundation would be helpful for the analysis of ring foundation of structures such as antennas, water towers structures, transmission towers and various other possible structures and superstructures. These are review of early studies on curved beam.