引用本文: 赵则昂, 邓宗白, 宋安平. 悬臂梁大挠度变形的近似估计法[J]. 力学与实践, 2014, 36(3): 341-344,366.
ZHAO Ze'ang, DENG Zongbai, SONG Anping. AN APPROXIMATION METHOD FOR THE LARGE DEFLECTION OF CANTILEVER BEAMS[J]. MECHANICS IN ENGINEERING, 2014, 36(3): 341-344,366.
 Citation: ZHAO Ze'ang, DENG Zongbai, SONG Anping. AN APPROXIMATION METHOD FOR THE LARGE DEFLECTION OF CANTILEVER BEAMS[J]. MECHANICS IN ENGINEERING, 2014, 36(3): 341-344,366.

## AN APPROXIMATION METHOD FOR THE LARGE DEFLECTION OF CANTILEVER BEAMS

• 摘要: 研究了悬臂梁自由端受集中力作用时的大挠度变形问题，对大挠度的界定方法做出了一些讨论，并从计算数据分析和理论推导两方面归纳出一种不通过复杂计算就能对大挠度变形进行定量估计的方法. 分析表明，由挠曲线近似微分方程得出的自由端挠度值与梁长度之比值的平方，可以近似表示小挠度法计算挠度值偏离精确挠度值的误差，并由此得出大挠度变形的估计值. 该方法避免了复杂的微分方程求解和数值计算，有一定的工程实际意义.

Abstract: This paper studies the large deflection of cantilever beams. A simple method to obtain the deflection is developed through numerical and theoretical analyses. How to measure the extent of large deformation is discussed at the same time. The error between the accurate deflection and the approximate deflection, obtained by the approximate deformation equation, can be represented by the square of the ratio of the approximate deflection to the length of the beam. By using this relation, we can have an estimation of the accurate deflection value without complex calculation and numerical methods. This method can be used in practical applications.

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