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An anisotropic beam theory based on the extension of Boley's method

机译：基于Boley方法延伸的各向异性光束理论

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摘要

The objective of this contribution is the computation of the Airy stress function for anisotropic beam-type structures. In the first part an iterative procedure is applied for the determination of the stress function by means of Boley's method. This method was successfully applied by Boley for two-dimensional (2D) isotropic plates under plane stress conditions in order to compute the displacement field and the stress distribution. In this contribution a higher order theory for anisotropic beams is derived with Boley's iterative procedure and an analytical formula for the Airy stress function is given. In the second part of the paper a beam with rectangular cross section is considered and the derived anisotropic beam model is compared to two-dimensional (2D) finite element results performed in ABAQUS. Two examples are studied: first a cantilever with constant distributed load is investigated, then an axially end-loaded redundant beam that is clamped at the one end and simply supported at the other end is studied. In both cases the analytical results are in perfect agreement with the ABAQUS outcome. Furthermore the effects of different kinematic restrictions for realizing clamped boundary conditions are investigated and compared. For the redundant axially loaded beam it is shown that the Bernoulli-Euler beam theory yields misleading results because it does not take into account shear coupling. This phenomenon is included in our presented solution for anisotropic beams.
机译：该贡献的目的是计算各向异性光束型结构的通气应力功能。在第一部分中，应用迭代过程来通过Boley的方法确定应力功能。在平面应力条件下，通过Boley成功地应用该方法，用于计算位移场和应力分布的平面应力条件下的二维（2D）各向同性板。在该贡献中，对各向异性光束的高阶理论衍生利用Boley的迭代过程，并给出了通气函数的分析公式。在纸张的第二部分中，考虑具有矩形横截面的梁，并将导出的各向异性光束模型与在ABAQU中进行的二维（2D）有限元结果进行比较。研究了两个示例：首先研究具有恒定分布式负载的悬臂，然后研究了在一端夹紧并且简单地支撑在另一端的轴向端载的冗余光束。在这两种情况下，分析结果与ABAQUS结果完全一致。此外，研究了不同运动限制对实现夹紧边界条件的影响。对于冗余的轴向加载光束，表明Bernoulli-euler光束理论产生误导性结果，因为它没有考虑剪切耦合。这种现象包括在我们所提出的各向异性梁的溶液中。

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