0
Research Papers

An Innovative Layout Design Methodology for Stiffened Plate/Shell Structures by Material Increasing Criterion

[+] Author and Article Information
Baotong Li

e-mail: baotong.csu@stu.xjtu.edu.cn

Jun Hong

e-mail: jhong@mail.xjtu.edu.cn

Zhelin Wang

State Key Laboratory for Manufacturing Systems Engineering,
Xi’an Jiaotong University,
West Xianning Road 28th,
Xi’an 710049, China

Zhifeng Liu

School of Mechanical and Automotive Engineering,
Hefei University of Technology,
Tunxi Road 193rd,
Hefei 230009, China

1Corresponding author.

Manuscript received July 24, 2012; final manuscript received November 2, 2012; published online March 25, 2013. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 135(2), 021012 (Mar 25, 2013) (11 pages) Paper No: MATS-12-1176; doi: 10.1115/1.4023781 History: Received July 24, 2012; Revised November 02, 2012

The motivation of this paper is to develop a new and straightforward approach to provide a topology optimization solution for the layout design of stiffened plate/shell structures. Inspired by the similarities between the branching patterns in nature and stiffener layout patterns in engineering, a so-called material increasing design concept is first introduced to represent the topology configuration of the stiffened plate/shell structures. In addition, a well-founded mathematical explanation for the principles, properties, and mechanisms of adaptive growth behaviors of branching patterns in nature is derived from the Kuhn–Tucker conditions, leading to a novel optimality criterion which can serve engineering purposes for stiffener layout design. In this criterion, the common growth mechanism is described as an ideal ‘balanced point’ among individual branches in terms of their weight distribution. After characterizing the relationship between the growth behavior and mechanics self-adaptability, the reproduction of branching patterns in nature is implemented by a global coordinative model, which consists of several bottom programming models to find the optimal height distributions of individual branches and a top programming model to play a global coordinative role among them. The benefit and the advantages of the suggested method are illustrated with several 2D examples that are widely used in the recent research of topology optimization.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bendsoe, M. P., and Kikuchi, N., 1988, “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Comput. Methods Appl. Mech Eng., 71, pp. 197–224. [CrossRef]
Zhou, M., and Rozvany, G. I. N., 1991, “The COC Algorithm, Part II: Topological, Geometrical and Generalized Shape Optimization,” Comput. Methods Appl. Mech. Eng, 89, pp. 309–336. [CrossRef]
Yang, R. J., and Chuang, C. H., 1994, “Optimal Topology Design Using Linear Programming,” Comput. Struct., 52, pp. 265–275. [CrossRef]
Luo, J. H., and Gea, H. C., 1998, “A Systematic Topology Optimization Approach for Optimal Stiffener Design,” Struct. Optim., 16, pp. 280–288. [CrossRef]
Luo, J. H., and Gea, H. C., 1998, “Optimal Bead Orientation of 3D Shell/Plate Structures,” Finite. Elem. Anal. Des., 31, pp. 55–71. [CrossRef]
Krog, L. A., and Olhoff, N., 1999, “Optimum Topology and Reinforcement Design of Disk and Plate Structures With Multiple Stiffness and Eigenfrequency Objectives,” Comput. Struct., 72, pp. 535–563. [CrossRef]
Ansola, R., Canales, J., Tarrago, J. A., and Rasmussen, J., 2004, “Combined Shape and Reinforcement Layout Optimization of Shell Structures,” Struct. Multidiscip. Optim., 27, pp. 219–227. [CrossRef]
Cheng, H. C., Kikuchi, N., and Ma, Z. D., 1994, “An Improved Approach for Determining the Optimal Orientation of Orthotropic Material,” Struct. Optim., 8, pp. 101–112. [CrossRef]
Ha, Y., Kim, W., and Cho, S., 2006, “Design Sensitivity Analysis and Topology Optimization Method Applied to Stiffener Layout in Hull Structures,” J. Ship Res., 50(3), pp. 222–230.
Rais, R. M., and Lokits, J., 2007, “Reinforcement Layout and Sizing Optimization of Composite Submarine Sail Structures,” Struct. Multidiscip. Optim., 34, pp. 75–90. [CrossRef]
Chang, C. J., Zheng, B., and Gea, H. C., 2008, “Automated Design of Thin-Walled Packaging Structures,” Struct. Multidiscip. Optim., 35, pp. 601–608. [CrossRef]
Wang, Q., Liu, Z. Z., and Gea, H. C., 2011, “New Topology Optimization Method for Wing Leading-Edge Rib,” J. Aircr., 48, pp. 1741–1748. [CrossRef]
Brown, J. H., and West, G. B., 2000, Scaling in Biology, Oxford University Press, Oxford, New York.
Yoseph, B. C., Liu, Z. Z., and Gea, H. C., 2006, “Biomimetics—Using Nature to Inspire Human Innovation,” Bioinspir. Biomim., 1, pp. 1–12. [CrossRef] [PubMed]
Vincent, J. F. V., 2006, “Making a Mechanical Organism Being the Fourth in a Series of Essays on the Materials of Nature,” J. Bionic. Eng., 3, pp. 43–58. [CrossRef]
Bhushan, B., 2006, “Biomimetics: Lessons From Nature—an Overview,” Philos. Trans. R. Soc. London, Ser. A., 367(1893), pp. 1445–1486. [CrossRef]
Markus, M., Thomas, S., Olga, S., and Heinrich, P., 2006, “Biomimetics and Technical Textiles: Solving Engineering Problems With the Help of Nature’s Wisdom,” Am. J. Bot., 93, pp. 1455–1465. [CrossRef] [PubMed]
Honda, H., 1971, “Description of the Form of Trees by the Parameters of the Tree-LIke Body: Effects of the Branching Angle and the Branch Length on the Shape of Tree-Like Body,” J. Theor. Biol., 31, pp. 331–338. [CrossRef] [PubMed]
Fisher, J. B., and Honda, H., 1977, “Computer Simulation of Branching Pattern and Geometry in Terminalia (Combretaceae), a Tropical Tree,” Bot. Gaz., 138, pp. 377–384. [CrossRef]
Schreiner, W., Karch, R., Neumann, M., Neumann, F., Szawlowski, P., and Roedler, S., 2005, “Optimized Arterial Trees Supplying Hollow Organs,” Med. Eng. Phys., 28, pp. 416–429. [CrossRef] [PubMed]
Wang, Z., Zhao, M., and Yu, Q., 2001, “Modeling of Branching Structure of Plants,” J. Theor. Biol., 209, pp. 383–394. [CrossRef] [PubMed]
Ding, X. H., and Yamazaki, K., 2004, “Stiffener Layout Design for Plate Structures by Growing and Branching Tree Model (Application to Vibration-Proof Design),” Struct. Multidiscip. Optim., 26, pp. 99–110. [CrossRef]
Ding, X. H., and Yamazaki, K., 2007, “Constructal Design of Cooling Channel in Heat Transfer System by Utilizing Optimality of Branch Systems in Nature,” ASME Trans. J. Heat Transfer, 129, pp. 245–255. [CrossRef]
Chen, S., 1992, Some Modern Design Methods of Precise and Complex Structures, Beijing University of Aeronautics and Astronautics Press, Beijing.
Chen, S., 2008, Analysis, Synthesis and Optimization of Engineering Structural Systems, China Science Culture, Hong Kong.
Ansys, 2005, ANSYS “10.0 User’s Manual,” Ansys, Inc., Canonsburg, PA.

Figures

Grahic Jump Location
Fig. 1

The branching patterns of leaf veins: (a) Calathea makoyana leaf; (b) Coleus blumei leaf; and (c) Monstera deliciosa leaf

Grahic Jump Location
Fig. 2

Parametric oriented analysis model of the branching pattern

Grahic Jump Location
Fig. 3

Convergence process and corresponding strain energy contours at different loading cases

Grahic Jump Location
Fig. 4

Simulation strategy for reproducing the adaptive growth process

Grahic Jump Location
Fig. 5

Decomposition-coordination programming model for the material increasing operation

Grahic Jump Location
Fig. 6

Flow chart of the adaptive growth process

Grahic Jump Location
Fig. 7

Growth processes and corresponding optimal material distribution (loading case 1)

Grahic Jump Location
Fig. 8

Growth processes and corresponding optimal material distribution (loading case 2)

Grahic Jump Location
Fig. 9

Growth processes and corresponding optimal material distribution (loading case 3)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In