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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.

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Figures

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Fig. 1

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

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Fig. 2

Parametric oriented analysis model of the branching pattern

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Fig. 3

Convergence process and corresponding strain energy contours at different loading cases

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Fig. 4

Simulation strategy for reproducing the adaptive growth process

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Fig. 5

Decomposition-coordination programming model for the material increasing operation

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Fig. 6

Flow chart of the adaptive growth process

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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