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Deflection of Non-Uniform Beams Resting on a Non-Linear Elastic Foundation Using (GDQM)

Ramzy M. Abumandour 1, Islam M. Eldesoky 1, Mohamed A. Safan 2, R. M. Rizk-Allah 1, and Fathi A. Abdelmgeed 1
1. Basic Engineering Sciences Department, Faculty of Engineering, Menofia University, Egypt
2. Department of Civil Engineering, Faculty of Engineering, Menoufia University, Egypt

Abstract—In this study, a method of a new technique of GDQM is presented for determining the deflection of a non-uniform beam resting on a non-linear elastic foundation, subjected to axial and transverse distributed force. The nonlinear subgrade model which describes the foundation includes the linear and nonlinear Winkler (normal) parameters and the linear Pasternak (shear) foundation parameter. The nonlinear 4th order differential equation of beam is solved using a new technique. In construction of numerical scheme a GDQM is used to transform the differential equation into a set of nonlinear algebraic equations. Then, these nonlinear algebraic equations solved by Newton’s method. Comparison the present results with the previous solutions proves the accuracy of this combination. 
Index Terms—nonlinear elastic foundation, deflection, GDQM and newton’s method

Cite: Ramzy M. Abumandour, Islam M. Eldesoky, Mohamed A. Safan, R. M. Rizk-Allah, and Fathi A. Abdelmgeed, "Deflection of Non-Uniform Beams Resting on a Non-Linear Elastic Foundation Using (GDQM)," International Journal of Structural and Civil Engineering Research, Vol. 6, No. 1, pp. 52-56, February 2017. doi: 10.18178/ijscer.6.1.52-56