Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading.
Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading.
复制标题
树干和树枝的结构分析：复杂荷载下承受大挠度的锥形悬臂梁。
作者：
J. Morgan;M. Cannell
利用悬臂梁的结构理论，可以推导出树干和树枝的尺寸、挠度和支撑成本。然而，只要挠度很小，基本理论就适用，并且需要复杂的解析解来解释复杂的锥度和加载模式。本文描述了一种处理大挠度、任何锥度模式以及任何分布加载模式、点加载模式或外部施加弯矩的方法。一根梁被认为是由一系列短段组成的，这样每一段只有很小的挠度，每一段都可以有规定的尺寸、杨氏模量和载荷。采用结构分析中的输运矩阵法确定了各节段和整梁的端部状态。通过比较预测的挠度与挠度(a)由bishop和Drucker（1945）使用解析解计算的挠度，(b)由Leiser和Kemper（1968）计算和测量的幼树树干挠度，以及(c)在锥形和非锥形塑料棒上测量的挠度，验证了该方法。
The dimensions, deflections and support costs of tree trunks and branches can be deduced using the structural theory for cantilever beams. However, elementary theory applies only as long as deflections are small, and complex analytical solutions are required to account for complex taper and patterns of loading. This paper describes a method that copes with large deflections, any patterns of taper, and any patterns of distributed loading, point loading or externally applied bending moments. A beam is considered to be composed of a series of short segments, such that each has only a small deflection, and each can have specified dimensions, Young's modulus and loading. The transport matrix method of structural analysis is used to determine the end conditions of each segment and of the whole beam. The method is verified by comparing predicted deflections with deflections (a) calculated using an analytical solution by Bisshopp and Drucker (1945), (b) calculated and measured for sapling tree trunks by Leiser and Kemper (1968), and (c) measured on tapered and untapered plastic rods.