Understanding the dynamic response of trees to a strong wind is crucial to alleviating the damages and losses of tree forests caused by windstorms. Previous studies have elucidated small deformations of a broad range of tree species, yet mathematical models that can accurately pinpoint the location and severity of wind-induced damages are still lacking. To bridge this gap, the present work puts forward the first geometrically accurate, physics-based model to capture large deformation of trees induced by a strong wind. The proposed model incorporates a branched tree architecture to represent the topology of a realistic tree. The large, dynamic deformation of the trunk and branches of the tree is described by a system of nonlinear partial differential equations derived from structural theories rooted in classical mechanics. The aerodynamic loading is quantified based on the instantaneous relative velocity between the wind and the tree. The proposed model could successfully reproduce the effects of aerodynamic damping by capturing the nonlinear interplays between the wind and the tree, in contrast to prior analytical models that relied on empirical assumptions of the damping coefficients. The model further reveals a reduction in the drag force due to wind-induced shape reconfiguration, which is enhanced exponentially as a function of the wind speed. The proposed modeling framework could aid in the development of novel forest management strategies to mitigate wind-induced economic and environmental losses.

中文翻译：

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强风下树木变形大

了解树木对强风的动态响应对于减轻风暴对乔木林的破坏和损失至关重要。先前的研究已经阐明了多种树种的微小变形，但仍然缺乏能够准确确定风造成损害的位置和严重程度的数学模型。为了弥补这一差距，目前的工作提出了第一个几何精确的、基于物理的模型来捕捉强风引起的树木的大变形。所提出的模型采用分支树架构来表示现实树的拓扑。树干和树枝的大动态变形由非线性偏微分方程组来描述，该方程组源自经典力学的结构理论。空气动力载荷是根据风和树之间的瞬时相对速度来量化的。与依赖阻尼系数经验假设的先前分析模型相比，所提出的模型可以通过捕获风和树之间的非线性相互作用成功地再现空气动力阻尼的效果。该模型进一步揭示了由于风引起的形状重构而导致的阻力减小，该阻力随着风速的函数呈指数增强。拟议的建模框架可以帮助制定新颖的森林管理战略，以减轻风引起的经济和环境损失。