Numerical simulation of neutral axis in transverse bending of tree trunk

Xu Pengfei; Zhang Houjiang; Xin Zhenbo; Yuan Jiangyu

doi:10.12171/j.1000-1522.20240073

Journal of Beijing Forestry University > 2024 > 46(8): 1-14. > DOI: 10.12171/j.1000-1522.20240073

Xu Pengfei, Zhang Houjiang, Xin Zhenbo, Yuan Jiangyu. Numerical simulation of neutral axis in transverse bending of tree trunk[J]. Journal of Beijing Forestry University, 2024, 46(8): 1-14. DOI: 10.12171/j.1000-1522.20240073

Citation:

PDF (3827 KB)

Numerical simulation of neutral axis in transverse bending of tree trunk

Xu Pengfei^{1, 2,},
Zhang Houjiang^{1, 2, ,},
Xin Zhenbo³,
Yuan Jiangyu⁴

1.
School of Technology, Beijing Forestry University, Beijing 100083, China
2.
Joint International Research Institute of Wood Nondestructive Testing and Evaluation, Beijing Forestry University, Beijing 100083, China
3.
College of Mechanical & Electronic Engineering, Shandong Agricultural University, Taian 271018, Shandong, China
4.
Administration Office of the Ming Tombs in Changping District, Beijing 102213, China

More Information

Received Date: March 14, 2024
Revised Date: June 26, 2024
Accepted Date: August 11, 2024
Available Online: August 12, 2024

Graphical Abstract

Abstract

Abstract

Objective
In order to assess the wind load safety of trees, the transverse force bending of trees under wind force was studied to determine the effect of factors such as trunk cross-sectional shape, tree ring, and defects on the neutral axis of trunk bending.
Method
In this study, the Euler-Bernoulli beam assumption was used to deduce a generalized formula for the slope of neutral axis. Then, trunk models were designed with three types of contours (circle, ellipse, and random), two internal structures (multi-layer concentric structure and circular defects). And different moduli of elasticity were used to simulate variations in material properties. Finally, numerical simulations were performed, the results of numerical simulations were analyzed and predicted using the random forest model, and the relative contribution of each factor was identified.
Result
In tree-ring models, the probability that the distance from mass center to form center of the tunk cross-section was less than 4 mm exceeded 97%, and the importance affecting the distance was ratio of the elasticity modulus of the early wood to the late wood > tree-ring number > ratio of the eccentricity distance to the basal circle radius > cross-section roundness. The deflection angles (from the actual neutral axis to the neutral axis of uniform section) were all less than 0.5°, and more than 97% of the total number was less than 0.08°. The importance affecting the slope angle of neutral axis in trunk bending was load azimuth > cross-section roundness > ratio of the eccentricity distance to the basal circle radius > tree-ring number > ratio of the elasticity modulus of the early wood to the late wood. In the circular defect model, there was about 80% of all cases where the distance from mass center to form center was less than 5 mm, about 15% of all cases between 5−15 mm, and about 5% of all cases greater than 15 mm. The importance affecting the distance was the defect radius > ratio of the elasticity modulus of the trunk with defects to the normal trunk > ratio of the eccentricity distance to the basal circle radius > cross-section roundness. More than 90% of all cases had a deflection angle less than 1°, but in some extreme cases, the deflection angle may reach 50°. The importance affecting the slope angle was load azimuth > cross-section roundness > ratio of the eccentricity distance to the basal circle radius > the defect radius > ratio of the elasticity modulus of the trunk with defects to the normal trunk.
Conclusion
Tree-ring have a small effect on bending neutral axis of a tree trunk, while defects and cross-section shapes have a large effect on it. In the calculation and detection of trunk stress, the tree-ring can be ignored, but the cross-section shape and defects inside a trunk need to be taken into account.
- bending,
- risk assessment,
- numerical simulation,
- distance from mass center to form center,
- slope angle of bending neutral axis

FullText(HTML)

References (18)

References

[1]	陶嗣巍, 赵东. 树木几何结构快速建模的研究[J]. 北京林业大学学报, 2013, 35(2): 97−101. Tao S W, Zhao D. Rapid parametric modeling of geometry structure for trees[J]. Journal of Beijing Forestry University, 2013, 35(2): 97−101.
[2]	Wu Y, Shao Z. Measurement and mechanical analysis of the strains–stresses induced by tree-pulling experiments in tree stems[J]. Trees, 2016, 30(3): 675−684. doi: 10.1007/s00468-015-1310-4
[3]	吴贻军, 姚剑飞, 吴俊, 等. 基于abaqus有限元法的空洞树干强度分析[J]. 西北林学院学报, 2022, 37(3): 205−210. doi: 10.3969/j.issn.1001-7461.2022.03.28 Wu Y J, Yao J F, Wu J, et al. Strength analysis of cavity tree trunks by finite element method based on abaqus[J]. Journal of Northwest Forestry University, 2022, 37(3): 205−210. doi: 10.3969/j.issn.1001-7461.2022.03.28
[4]	张鳌, 冀晓东, 丛旭, 等. 基于线性滤波法的单株林木抗风有限元模拟[J]. 北京林业大学学报, 2016, 38(2): 1−9. Zhang A, Ji X D, Cong X, et al. Finite element modeling of wind resistance of single trees based on linear filtering method[J]. Journal of Beijing Forestry University, 2016, 38(2): 1−9.
[5]	尤磊. 基于点云数据的树干干形测量[D]. 北京:中国林业科学研究院, 2016. You L. Stem form measurement based on point cloud data[D]. Beijing: Chinese Academy of Forestry, 2016.
[6]	李秀莲, 邵楠. 非对称截面梁的弯曲正应力分析[J]. 青海大学学报(自然科学版), 2010, 28(1): 67−72. Li X L, Shao N. The analysis on the bending normal stress of a non-symmetric section beam[J]. Journal of Qinghai University (Natural Science), 2010, 28(1): 67−72.
[7]	于永柱, 管成, 张厚江, 等. 古建筑墙体木柱缺陷对其安全性影响数值模拟研究[J]. 北京林业大学学报, 2022, 44(1): 132−145. doi: 10.12171/j.1000-1522.20210341 Yu Y Z, Guan C, Zhang H J, et al. Numerical simulation on the influence of wall wood column defects on the safety of ancient building[J]. Journal of Beijing Forestry University, 2022, 44(1): 132−145. doi: 10.12171/j.1000-1522.20210341
[8]	欧自娜, 张厚江, 管成. 古建筑七架梁缺陷安全性影响数值模拟研究[J]. 北京林业大学学报, 2020, 42(4): 142−154. doi: 10.12171/j.1000-1522.20190328 Ou Z N, Zhang H J, Guan C. Numerical simulation of the safety influence of defects on qijia-beams of ancient timber building[J]. Journal of Beijing Forestry University, 2020, 42(4): 142−154. doi: 10.12171/j.1000-1522.20190328
[9]	刘丰禄, 姜芳, 张建中, 等. 落叶松生材12个弹性常数的试验研究[J]. 西北林学院学报, 2015, 30(6): 227−231. doi: 10.3969/j.issn.1001-7461.2015.06.41 Liu F L, Jiang F, Zhang J Z, et al. Twelve elastic constant values of larch forest[J]. Journal of Northwest Forestry University, 2015, 30(6): 227−231. doi: 10.3969/j.issn.1001-7461.2015.06.41
[10]	王振刚. 含损伤梁结构的刚度及变形分析[D]. 西安: 西安理工大学, 2020. Wang Z G. Analysis of stiffness and deformation of beam structure with damage[D]. Xi’an: Xi’an University of Technology, 2020.
[11]	吴晓, 杨立军. 双模量泡沫铝芯夹层梁的弯曲计算分析[J]. 应用力学学报, 2015, 32(6): 922−927. Wu X, Yang L J. Bending calculation and analysis of bimodulous aluminum foam corelaminated beam[J]. Chinese Journal of Applied Mechanics, 2015, 32(6): 922−927.
[12]	姚文娟, 叶志明. 不同模量理论弹性支承连续梁及框架[J]. 力学与实践, 2004, 26(4): 37−41. doi: 10.3969/j.issn.1000-0879.2004.04.011 Yao W J, Ye Z M. The elastic supported continuous beam and frame of different modulus[J]. Mechanics in Engineering, 2004, 26(4): 37−41. doi: 10.3969/j.issn.1000-0879.2004.04.011
[13]	Mattheck C. Wood: the internal optimization of trees[J]. Arboricultural Journal, 1995, 19(2): 97−110. doi: 10.1080/03071375.1995.9747051
[14]	Krauss A, Moliński W, Kúdela J, et al. Differences in the mechanical properties of early and latewood within individual annual rings in dominant pine tree (Pinus sylvestris)[J]. Wood Res-Slovakia, 2011, 56(1): 1−12.
[15]	葛晓雯. 腐朽对杨树木材及活立木干基截面弯曲特性的影响[D]. 哈尔滨: 东北林业大学, 2017. Ge X W. Effects of decay on section bending properties of poplar wood and trunks of standing trees[D]. Harbin: Northeast Forestry University, 2017.
[16]	郭莹洁, 赵荣军, 钟永, 等. 基于早晚材的兴安落叶松成熟材力学模型——顺纹抗拉弹性模量[J]. 林业科学, 2014, 50(9): 118−123. Guo Y J, Zhao R J, Zhong Y, et al. Mechanical models of Larix gmelinii mature clear wood based on the properties of earlywood and latewood: longitudinal modulus of elastic[J]. Scientia Silvae Sinicae, 2014, 50(9): 118−123.
[17]	徐金梅. 祁连山青海云杉木材性质对气候变化的响应[D]. 北京: 中国林业科学研究院, 2012. Xu J M. Response of wood properties in tree rings of Picea crassifolia in Oiliang Mountains to climate change[D]. Beijing: Chinese Academy of Forestry, 2012.
[18]	余雁. 人工林杉木管胞的纵向力学性质及其主要影响因子研究[D]. 北京: 中国林业科学研究院, 2003. Yu Y. Longitudinal mechanical properties and its main influencing factors of tracheids of Chinese fir from plantation [D]. Beijing: Chinese Academy of Forestry, 2003.

[1]	Jiang Wenjie, Yang Qinsong, Li Guolei, Yao Fei, Shao Zhanhai, Liu Wen. Effects of storage substances and endogenous hormones on seed germination and seedling formation of Quercus variabilis[J]. Journal of Beijing Forestry University, 2024, 46(1): 19-26. DOI: 10.12171/j.1000-1522.20220207
[2]	Liu Ningwei, Wang Lu, Zhang Zhiyong, Zhang Shuhang, Zhang Qing, Wang Guangpeng, Qin Ling, Cao Qingqin. Analysis of inherited tendency of fruit characteristics in F1 group of reciprocal crossing between ‘Yanshanzaofeng’ and ‘Yanjing’ in Castanea mollissima[J]. Journal of Beijing Forestry University, 2021, 43(5): 75-85. DOI: 10.12171/j.1000-1522.20200312
[3]	Deng Wenhong, Zhao Xinrui, Zhang Junqi, Guo Huihong. Determination of plant hormones in plant tissues by UPLC-MS/MS[J]. Journal of Beijing Forestry University, 2019, 41(8): 154-160. DOI: 10.13332/j.1000-1522.20190052
[4]	CAO Yong-qing, YAO Xiao-hua, REN Hua-dong, WANG Kai-liang.. Changes in contents of endogenous hormones and main mineral elements in oil-tea camellia fruit during maturation.[J]. Journal of Beijing Forestry University, 2015, 37(11): 76-81. DOI: 10.13332/j.1000-1522.20140407
[5]	ZHANG Ling-yun, WANG Xiao-yi, CAO Yi-bo.. Soluble sugar content and key enzyme activity and the relationship between sugar metabolism and lipid accumulation in developing fruit of Camellia oleifera.[J]. Journal of Beijing Forestry University, 2013, 35(4): 55-60.
[6]	CHEN Li-pei, YANG Bo, SHEN Yong-bao. Endogenous hormone content of endosperm of Pinus tabuliformis seeds during initial germinating stage[J]. Journal of Beijing Forestry University, 2012, 34(6): 30-33.
[7]	WANG Xiao-ling, ZHAO Zhong, QUAN Jin-e. Effects of planting time on endogenous hormones and oxidase in tetraploid Robinia pseudoacacia softwood cuttings.[J]. Journal of Beijing Forestry University, 2011, 33(6): 102-106.
[8]	SUN Wei, LI Chong-hui, WANG Liang-sheng, DAI Si-lan. Accumulation and variation of anthocyanins in blue flowers of Senecio cruentus at different flowering stages[J]. Journal of Beijing Forestry University, 2010, 32(3): 128-134.
[9]	QIAN Hua, LIU Yan, ZHENG Yong-ping, YU Ji-ying, FAN Wen-feng. Effects of applying 6-BA on the Nobiletype Dendrobium flower bud differentiation and changes of hormones.[J]. Journal of Beijing Forestry University, 2009, 31(6): 27-31.
[10]	KONG De-zheng, JIN Dan-dan, HE Song-lin, YANG Qiu-sheng, LIU Yi-ping.. Anatomy and changes in endogenous hormones during flower bud differentiation in Nelumbo nucifera[J]. Journal of Beijing Forestry University, 2009, 31(3): 42-45.

Cited By

Cited by

Periodical cited type(1)

虞夏霓，刘偲，陈步先，包新德，关鑫，林金国. 砂光处理对翅荚木表面特性影响研究. 林产工业. 2024(06): 14-19 .

Other cited types(1)

Get Citation

PDF

XML

Article views (298) PDF downloads (43) Cited by(2)

Turn off MathJax

Article Contents

Abstract

References

Numerical simulation of neutral axis in transverse bending of tree trunk