Venation-Like Rib Layout Design in Plate under Bending Loads

Abstract:

This paper concerns a venation-like design method of rib layout and its application on some plates subjected to bending loads. Main topological characters of dicotyledonous venation and two determinative mechanical parameters in leaf venation morphogenesis theories are extracted, on the basis of those elicitations, a venation growing algorithm is proposed as an attempt at the proper layout of ribs in plate. Energy criterion and shear stress is specified as the factor orienting mainvein and subveins respectively. Vectorial equation equilibrium is used in reorganization to calculate widths and adjust vein cells slightly. Finite element method functions as background technique, under which several simple-shaped plates under bending loads are designed by venation growing algorithm. The resultant venation-like ribs offer multi-balanced improvements.

• Periodical: Journal of Biomimetics, Biomaterials and Tissue Engineering (Volume 13)
• Pages: 31-40
• DOI: https://doi.org/10.4028/www.scientific.net/JBBTE.13.31
• Online since: July 2012
• Authors: Kai Xue, Yong Xin Li, Wei Yuan Wang
• Keywords: Finite Element Method (FEM), Rib Layout, Shear Stress, Strain Energy, Vectorial Equilibrium, Venation

References

[1] J. Chung, K. Lee. Optimal design of rib structures using the topology optimization technique. Proceedings of the Institution of Mechanical Engineers, 211 C, 425-37, (1997).

DOI: 10.1243/0954406971521836

[2] D. Bojczuk and W. Szteleblak. Optimization of layout and shape of stiffeners in 2D structures. Computers and Structures; 86 (13-14), 1436-46, (2008).

DOI: 10.1016/j.compstruc.2007.05.005

[3] A. Kallassy, and J-L. Marcelin. Optimization of stiffened plates by genetic search. Struct Optim; 13 (2-3), 134-41, (1997).

DOI: 10.1007/bf01199232

[4] X. Ding, J. Lin, K. Yamazaki. Topology design optimization of stiffened thin-wall shell structures based on growth mechanism of root system. Chinese Journal of Mechanical Engineering; 4 (44), 201-5 (in Chinese), (2008).

DOI: 10.3901/jme.2008.04.201

[5] Y. X. Li, K. Xue. Mechanics in Leaf Venation Morphogenesis and their Biomimetic Inspiration to Construct a 2-Dimensional Reinforcement Layout Model. Journal of Biomimetics, Biomaterials, and Tissue Engineering; 10: 81-93, (2011).

DOI: 10.4028/www.scientific.net/jbbte.10.81

[6] C. Mattheck. Design in nature: Learning from trees. Berlin Heidelberg: Springer-Verlag, (1998).

[7] S. Bohn, B. Andreotti, S. Douady, J. Munzinger, Y. Couder. Constitutive property of the local organization of leaf venation networks. Phys Rev E 65, 061914-061925, (2002).

DOI: 10.1103/physreve.65.061914

[8] F. Corson, M. Adda-Bedia, A. Boudaoud. In silico leaf venation networks: growth and reorganization driven by mechanical forces. J. Theor. Biol. 259 (3), 440-8, (2009).

DOI: 10.1016/j.jtbi.2009.05.002

[9] A. Samanta, M. Mukhopadhyay. Finite element static analysis of stiffened shells. Appl. Mech. Engrg. 3(1), 55–87, (1998).

[10] A. Samanta, M. Mukhopadhyay. Free vibration analysis of stiffened shells by the finite element technique. European Journal of Mechanics A/Solids 23, 159-179, (2004).

DOI: 10.1016/j.euromechsol.2003.11.001

[11] S. Wang, L. Ren, Y. Liu, Z. Han, Y. Yang. Mechanical characteristics of typical plant leaves. J Bionic Eng.; 7 (3), 294-300, (2010).

DOI: 10.1016/s1672-6529(10)60253-3

[12] X. Ding, K. Yamazaki. Growth technique of stiffener layout pattern for plate and shell structures to achieve minimum compliance, Eng. Optimiz., 37 (3), 259-76, (2005).

DOI: 10.1080/0305215512331328231

[13] S. Zhang, J. Yang Jungang, W. Zhang. Evolutionary structural optimization for stiffener layout problem of plate structures. Modern Manufacturing Engineering; (4): 5-9, (2009).