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Abstract

This research is a review on previous work on linear elastic behavior of beams resting on uniform and non-uniform Winkler foundation. Several methods were used previously by other researchers starting from analytical and numerical such as series, finite difference and finite element formulations which are developed to solve various problems. The finite element method is formulated previously by using beam, plate and solid 3D elements to model beams and spring elements to model Winkler foundation in the past. Also, the finite difference coded in MATLAB and Fortran was used to formulate the problems to deal with various variables using Gauss Jordan and Gauss elimination to solve them and to compare with the results. Also, the Fourier series coded in various computer program to obtain the results and used to check and compare with the results obtained from other methods. In both methods, Fourier series and finite-difference, the formulations are based on the basic differential equations. The results obtained from previous studies using different methods are given and discussed together to compare and check the accuracy of the solutions. Good agreement is found in these methods, which indicate the efficiency of these methods which was used by previous studies.