A Beam Theory for Anisotropic Materials
A Beam Theory for Anisotropic Materials
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DOI：
10.1115/1.3169063
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发表时间：
1985-06
期刊：
影响因子：
--
通讯作者：
O. Bauchau
中科院分区：
文献类型：
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作者：
O. Bauchau
梁理论在结构分析中起着重要的作用。基本假设是初始平面截面在变形后保持平面，忽略面外翘曲。基于这些假设的预测对于由各向同性材料制成的细长、实心、横截面梁是准确的。本文根据变分原理推导出的梁理论是基于唯一的运动学假设，即每个截面在其自身平面内是无限刚性的，但可以自由翘曲出平面。在对光束理论的伯努利和圣维南方法进行了简短的回顾之后，导出了一组标准正交本征翘曲。通过展开轴向位移或轴向应力在一系列特征翘曲中的分布，并利用能量原理推导控制方程，可以得到改进的解。改进的Saint-Venant方法不仅收敛速度快，而且只考虑少数特征扭曲项就能得到准确的结果。
Beam theory plays an important role in structural analysis. The basic assumption is that initially plane sections remain plane after deformation, neglecting out-of-plane warpings. Predictions based on these assumptions are accurate for slender, solid, cross-sectional beams made out of isotropic materials. The beam theory derived in this paper from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane. After a short review of the Bernoulli and Saint-Venant approaches to beam theory, a set of orthonormal eigenwarpings is derived. Improved solutions can be obtained by expanding the axial displacements or axial stress distribution in series of eigenwarpings and using energy principles to derive the governing equations. The improved Saint-Venant approach leads to fast converging solutions and accurate results are obtained considering only a few eigenwarping terms.