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CSME 2018/02
Volume 39 No.1
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99-104
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Analytic Static Deflection Solutions of Beams Resting on Strong Nonlinear Elastic Foundations
Chao-Kuang Chena, Li-Kuo Choua and Sen-Yung Leea
aDepartment of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, R.O.C.
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Abstract:
The analytic static deflection solutions of beams resting on nonlinear elastic foundations are developed by the modified Adomian method. If the applied force function is an analytic function, then the deflection function can be derived and expressed in Maclaurin series. A recurrence relation for the coefficients of the Maclaurin series is derived. It is shown that the proposed solution method is accurate and efficient. The solution method can be successfully applied to the problem with strong nonlinearity. The results are also compared with those obtained by the perturbation method. It is found that the error of the perturbation solution will increase not only when the nonlinear parameter is increased but also when the applied load is increased.
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Keywords: deflection of beams, strong nonlinear elastic foundation, Modified Adomian method, perturbation method
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©
2018
CSME , ISSN 0257-9731
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