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首页> 外文期刊>American Journal of Engineering Research >Fifth Degree Hermittian Polynomial Shape Functions for the Finite Element Analysis of Clamped Simply Supported Euler – Bernoulli Beam
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Fifth Degree Hermittian Polynomial Shape Functions for the Finite Element Analysis of Clamped Simply Supported Euler – Bernoulli Beam

机译：五阶厄米特多项式形状函数用于夹紧简支欧拉-伯努利梁的有限元分析

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摘要

Fifth degree Hermittian polynomial shape functions were used in this work for the flexural analysis of Euler – Bernoulli beams with a prismatic cross-section. The analysis used the finite element stiffness method to generate the stiffness and load matrices for the problem. The beam of length l, considered was clamped at x = 0, and simply supported at x = l, and carried a linearly distributed transverse load on the longitudinal axis. The results showed that the fifth degree Hermittian polynomial shape function yielded exact solutions for the deflection, the bending moment and shear force distributions. The effectiveness of the use of fifth degree Hermittian polynomial shape functions in the finite element stiffness method to solve the flexural problem of a propped cantilever beam under linearly distributed transverse load was thus established.
机译：在这项工作中，使用五度Hermittian多项式形状函数对具有棱柱形截面的Euler – Bernoulli梁进行了挠曲分析。分析使用有限元刚度方法生成该问题的刚度和载荷矩阵。考虑长度为l的梁被夹紧在x = 0，并简单地以x = 1支撑，并在纵轴上承受线性分布的横向载荷。结果表明，五次埃尔米特多项式形状函数为挠度，弯矩和剪力分布提供了精确的解。因此，建立了在有限元刚度方法中使用五次Hermittian多项式形状函数来解决支撑悬臂梁在线性分布横向载荷下的挠曲问题的有效性。

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