This article presents a new higher-order beam model. The present beam model is governed by differential equations that are similar to those present in some existing higher-order beam models; however, the present beam model makes use of a novel method of calculating the transverse shear stiffness, which facilitates the calculation of a shear-warping stiffness without the need for an assumed warping displacement field, and without introducing any additional kinematic variables. The present beam model also facilitates the recovery of the distributions of longitudinal normal stresses and transverse shear stresses. The authors postulate that the bending and shear terms in first-order shear deformation theory represent the first two terms in an infinite series that would constitute an ideal one-dimensional beam model, and it is suggested that the present beam model constitutes the first four terms in this hypothetical infinite series. The present beam model is solved for several example beams, and the results are compared with those of existing classical and higher-order beam models, as well as computational results from finite element analyses. It is shown that the present beam model is able to accurately represent deformed shapes and stress distributions pertaining to beams that exhibit non-trivial shear compliance as well as non-trivial shear-warping stiffness. In the case of laminated composite beams comprising a large number of laminae, the present beam model offers a level of analytical fidelity that is comparable to that of existing zigzag beam models; however, unlike zigzag beam models, the present beam model is equally well suited for the analyses of beams comprising any number of laminae.

本文提出了一种新的高阶光束模型。当前的光束模型由微分方程控制，该方程类似于某些现有的高阶光束模型中的方程。然而，目前的梁模型利用了一种计算横向剪切刚度的新颖方法，该方法便于计算剪切翘曲刚度，而无需假定的翘曲位移场，并且无需引入任何其他运动学变量。本梁模型还有助于恢复纵向法向应力和横向剪应力的分布。作者假设一阶剪切变形理论中的弯曲和剪切项代表了构成理想一维梁模型的无穷级数中的前两个项，并建议目前的光束模型构成该假设无限级数的前四个项。解决了现有的光束模型中的几个示例光束，并将结果与​​现有的经典光束模型和高阶光束模型进行了比较，以及有限元分析的计算结果。结果表明，本梁模型能够准确地表示变形梁的形状和应力分布，这些梁具有非平凡的剪切柔度和非平凡的剪切翘曲刚度。对于包含大量薄片的层状复合梁，本梁模型提供了与现有之字形梁模型相当的分析保真度；但是，与之字形梁模型不同，