Journal of Zhejiang University-SCIENCE A

, Volume 9, Issue 7, pp 907–915 | Cite as

Using FEM to predict tree motion in a wind field

  • Xiao-yi HuEmail author
  • Wei-ming Tao
  • Yi-mu Guo


In this paper we propose a finite element (FE) simulation method to predict tree motion in a wind field. Two FE tree models were investigated: One model was generated based on a realistic nature-looking geometric tree model, and the other was a symmetric model to investigate the influence of asymmetric material properties on tree motion. The vortex-induced vibration (VIV) theory is introduced to estimate the fluctuating wind force being exerted on tree stems and the fluid-structure interaction (FSI) analysis is also included in the simulation. The results indicate that asymmetric material properties result in the crosswind displacement of the investigated node and the main swaying direction deviation. The simulation reveals that under wind loading, a tree with leaves has much larger swaying amplitude along the wind direction and longer swaying period than a tree without leaves. However, the crosswind swaying amplitude is mainly due to branch interaction. The numerical simulation proved that the interaction of tree branches can prevent dangerous swaying motion developing.

Key words

Finite element method (FEM) Fluid-structure interaction (FSI) Vortex-induced vibration (VIV) Asymmetric Wind field 

CLC number

O39 O368 S7 


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  1. Ancelin, P., Courbaud, B., Thierry, F., 2004. Development of an individual tree-based mechanical model to predict wind damage within forest stands. Forest Ecology and Management, 203(1–3):101–121. [doi:10.1016/j.foreco.2004.07.067]CrossRefGoogle Scholar
  2. Baker, C.J., 1995. The development of a theoretical model for the windthrow of plants. Journal of Theoretical Biology, 175(3):355–372. [doi:10.1006/jtbi.1995.0147]CrossRefGoogle Scholar
  3. Baker, C.J., 1997. Measurements of the natural frequencies of trees. Journal of Experimental Botany, 48(5):1125–1132. [doi:10.1093/jxb/48.5.1125]CrossRefGoogle Scholar
  4. Gardiner, B.A., 1992. Mathematical Modeling of the Static and Dynamic Characteristics of Plantation Trees. In: Franke, J., Roeder, A. (Eds.), Mathematical Modeling of Forest Ecosystems. Sauerlander, Frankfurt/Main, p.40–61.Google Scholar
  5. Ken, J., 2003. Dynamic loading of trees. Journal of Arboriculture, 29(3):165–171.Google Scholar
  6. Ken, J., 2005. Dynamic Wind Loads on Trees. Tree Dynamics, Isaac,, downloaded in July, 2006.
  7. Moore, J.R, Maguire, D.A., 2004. Natural sway frequencies and damping ratios of trees: concepts, review and synthesis of previous studies. Trees, 18:195–203.CrossRefGoogle Scholar
  8. Niklas, K.J., 2000. Computing factors of safety against wind-induced tree stem damage. Journal of Experimental Botany, 51(345):797–806. [doi:10.1093/jexbot/51.345.797]CrossRefGoogle Scholar
  9. Nishimura, H., Taniike, Y., 2001. Aerodynamic characteristics of fluctuating forces on a circular cylinder. Journal of Wind Engineering and Industrial Aerodynamics, 89:713–723.CrossRefGoogle Scholar
  10. Saunderson, S.E.T., England, A.H., Baker, C.J., 1999. A dynamic model of the behaviour of sitka spruce in high winds. Journal of Theoretical Biology, 200(3):249–259. [doi:10.1006/jtbi.1999.0983]CrossRefGoogle Scholar
  11. Weber, J., Penn, J., 1995. Creation and Rendering of Realistic Trees. Proceedings of the SIGGRAPH’95 Annual Conference. ACM Press, New York, p.119–127.Google Scholar
  12. Williamson, C.H.K., Govardhan, R., 2004. Vortex-induced vibrations. Annual Review of Fluid Mechanics, 36(1):413–455. [doi:10.1146/annurev.fluid.36.050802.122128]MathSciNetCrossRefzbMATHGoogle Scholar
  13. Wood Handbook, 1999. Wood as an Engineering Material. USDA Forest Products Laboratory, Madison, Wisconsin.Google Scholar
  14. Zienkiewicz, O.C., Taylor, R.L., 1991. The Finite Element Method. McGraw-Hill, New York.zbMATHGoogle Scholar

Copyright information

© Zhejiang University and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringZhejiang UniversityHangzhouChina
  2. 2.School of EngineeringZhejiang Forestry UniversityHangzhouChina

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