Galerkin method for bending analysis of beams on non-homogeneous foundation

Musa, Abubakr E. S.

doi:10.17512/jamcm.2017.3.06

Cited by 9 publications

(1 citation statement)

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“…The concepts of beams resting on elastic foundations have been extensively applied by geotechnical, road pavement and railway engineers in the analysis and design of railroads, road pavements and foundations. It is also used in the analysis and design of buried gas pipeline systems [1][2][3][4]. The application entailed the formulation of theories of beams as well as theories for the elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

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

Ike¹

2019

International Journal of Darshan Institute on Engineering Research and Emerging Technologies

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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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Section: Introductionmentioning

confidence: 99%