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A simple method for determining large deflection states of arbitrarily curved planar elastica

机译:一种确定任意弯曲平面弹性体大挠度状态的简便方法

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摘要

The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler–Bernoulli and large displacement theory. The problem is solved numerically using Runge–Kutta–Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms.
机译:本文讨论了一种用于确定任意弯曲的平面弹性的大挠度状态的相对简单的方法,该方法由一组有限的初始笔直柔性段建模。基本方程是使用Euler–Bernoulli和大位移理论建立的。使用Runge–Kutta–Fehlberg积分方法和Newton方法以数值方式解决了非线性方程组的问题。此解决方案技术已在几个数值示例上进行了测试。从所获得的结果与文献中的结果进行比较,可以得出结论,所开发的方法是有效的并且给出了准确的结果。显示的解决方案可以用作测试通过更复杂算法获得的结果的参考工具。

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