Point Collocation Method for the Analysis of Euler-Bernoulli Beam on Winkler Foundation

Author (s):

  1. Charles Chinwuba Ike, Enugu State University of Science and Technology, Enugu State, Nigeria, ikecc2007@yahoo.com


In this study, the point collocation method was implemented to solve the boundary value problem (BVP) of simply supported Euler-Bernoulli beams resting on Winkler foundation for uniformly distributed load. Mathematically, the BVP solved was a fourth order non homogeneous ordinary differential equation with constant parameters for the case of prismatic cross-sections considered. A two term deflection function was used to determine the residual function. Dirac delta functions at the collocation points were used in a weighted residual statement of the problem to obtain the collocation equations which were solved to obtain the unknown parameters. The results obtained were reasonably in agreement with the solutions obtained in literature using 3 term Ritz solutions. The difference between the 2 term collocation and the 3 term Ritz solutions were insignificant at less than 5.02% considering the obvious simplicity offered by the point collocation method.

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