Rib Design for Kirchhoff's Plate Inspired by Venation Configuration

Abstract:

A new reinforcement distribution design method inspired by venation configuration is discussed in the paper. Learned from dicotyledonous venation, venation growing algorithm is proposed, minimization of strain energy and shear stress determine growth direction of the mainveins and subveins respectively. Vectorial equilibrium equation is used to calculate vein widths and adjust the orientation of vein cells slightly. Sensitivity number is used to measure the change in strain energy and shear stress when a vein cell grows, necessary equations are derived for bending Kirchhoffs plate. Several examples are design for venation-like rib distribution. The resultant rib layout by VGA is applicable and effective.

• Periodical: Journal of Biomimetics, Biomaterials and Tissue Engineering (Volume 16)
• Pages: 43-53
• DOI: https://doi.org/10.4028/www.scientific.net/JBBTE.16.43
• Online since: December 2012
• Authors: Kai Xue, Yong Xin Li, Wei Yuan Wang
• Keywords: Kirchhoffs Plate, Rib Layout, Sensitivity Number, Venation Growing Algorithm

References

[1] Y. X Li, K. Xue. Mechanics in Leaf Venation Morphogenesis and their Biomimetic Inspiration to Construct a 2-Dimensional Reinforcement Layout Model. J. Biomim., Biomat., Tiss. Eng., 2011, 10, 81-93.

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

[2] J. Chung, K. Lee. Optimal design of rib structures using the topology optimization technique. Proc. Instit. Mech. Eng. - Part C, J Mech. Eng. Sci., (1997), 211 (6), 425-37.

[3] L. A Krog, N. Olhoff. Optimum topology and reinforcement design of disk and plate structures with multiple stiffness and eigen frequency objectives. Computers and Structures, (1999), 72 (4-5), 535-63.

DOI: 10.1016/s0045-7949(98)00326-5

[4] Y. Couder, L. Pauchard, C. Allain, M. Adda Bedia, S. Douady. The leaf venation as formed in a tensorial field. Eur Phys J B (2002), 28 (2), 135-8.

DOI: 10.1140/epjb/e2002-00211-1

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

DOI: 10.1016/j.jtbi.2009.05.002

[6] S. Bohn, B. Andreotti, S. Douady, J. Munzinger, Y. Couder. Constitutive property of the local organization of leaf venation networks. Phys Rev E, (2002), 65 (6 pt 1), 061914-061925.

DOI: 10.1103/physreve.65.061914

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

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

[9] D. Nha Chu, Y. M Xie, A. Hira, G. P Steven. Evolutionary structural optimization for problems with stiffness constraints. Finite Elements in Analysis and Design, (1996), 21 (4), 239-51.

DOI: 10.1016/0168-874x(95)00043-s

[10] Q. Li, G. P Steven, Y. M Xie. Evolutionary structural optimization for stress minimization problems by discrete thickness design. Computers & Structures, (2000), 78 (6), 769-80.

DOI: 10.1016/s0045-7949(00)00057-2

[11] H. Kobayashi, M. Daimaruya, K. Kuribayashi. Venation pattern of butterbur leaf and its mechanical contribution. Journal Materials Science (2000), 49 (12), 1318-23.

DOI: 10.2472/jsms.49.1318

[12] Y. C Lam, S. Santhikumar. Automated Rib Location and Optimization for Plate Structures. Structural Multidisciplinary Optimization, (2003), 25 (1), 35-45.

DOI: 10.1007/s00158-002-0270-7

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

DOI: 10.1016/j.compstruc.2007.05.005