General analysis of stressed beams on elastic foundation subjected to discontinuous loads

Abstract

Analytical solutions describing the static and dynamic behaviour of axially loaded beams with elastic end restrains resting on two parameter foundation subjected to multiple discontinuous lateral loads have been obtained using the Adomian decomposition method (ADM). Fourier expansion (FE) is used to transform discontinuous loads to continuous loading functions. The effects of the truncation index of both the ADM and FE on the accuracy of the obtained solutions are studied to assess the validity of the given solutions. The influences of end restraints, foundation stiffness, loading type, axial stressing and excitation frequency on the beam deflection and straining actions are investigated. It has been concluded that as the foundation stiffness increases relative to the beam stiffness, the effects of the end conditions on the beam behaviour decrease.

KEYWORDS:

• Discontinuous loads
• beam on elastic foundation
• Adomian decomposition method

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No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

MH Taha

MH Taha is an associate professor in the Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza, Egypt. He received his M.Sc. and Ph.D. in Engineering Mechanics in 1989 and 1995 respectively, and had been an academic staff member since his graduation in 1982. Also, as a certified consultant engineer, he has been managing his own engineering consultancy firm, ALFACONSULT, founded in 1996. His fields of interest include solid mechanics, structure dynamics, soil mechanics, analytical and numerical methods for solution of differential equations governing solid mechanics problems.