Analytic Static Deflection Solutions of Beams Resting on Strong Nonlinear Elastic Foundations

樑在強非線性彈性基底上時之靜態撓曲的解析解

陳朝光(Chao-Kuang Chen) ； 周立國(Li-Kuo Chou) ； 李森墉(Sen-Yung Lee)

《中國機械工程學刊》 39卷1期 (2018/02) Pp. 99-104

摘要

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.

關鍵字

deflection of beams ； strong nonlinear elastic foundation ； Modified Adomian method ； perturbation method

並列摘要

本文利用Adomian方法來求取樑在強非線性彈性基底上時之靜態撓曲的解析解，如果外力之函數式可析函數(Analysis function)，則推導所得的樑之非線性撓曲可以馬克勞林級數表示之，同時亦推導出此馬克勞林級數之係數間的遞迴關係式。結果顯示，所提出的方法是精確有效的，有效的成功應用於強非線性問題，結果獲得與擾動法(Perturbation)做比較。發現擾動法解的誤差將隨之非線性係數之增加而增加，同時亦將隨著外力的增加而增加。