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Research Papers: Design Automation

Optimal Design of Panel Reinforcements With Ribs Made of Plates

[+] Author and Article Information
Shanglong Zhang

Structural Optimization Laboratory,
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: shanglong.zhang@uconn.edu

Julián A. Norato

Structural Optimization Laboratory,
Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: norato@engr.uconn.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 26, 2016; final manuscript received May 23, 2017; published online June 26, 2017. Assoc. Editor: Samy Missoum.

J. Mech. Des 139(8), 081403 (Jun 26, 2017) (11 pages) Paper No: MD-16-1792; doi: 10.1115/1.4036999 History: Received November 26, 2016; Revised May 23, 2017

The stiffness of plate structures can be significantly improved by adding reinforcing ribs. In this paper, we are concerned with the stiffening of panels using ribs made of constant-thickness plates. These ribs are common in, for example, the reinforcement of ship hulls, aircraft wings, pressure vessels, and storage tanks. Here, we present a method for optimally designing the locations and dimensions of rectangular ribs to reinforce a panel. The work presented here is an extension to our previous work to design structures made solely of discrete plate elements. The most important feature of our method is that the explicit geometry representation provides a direct translation to a computer-aided design (CAD) model, thereby producing reinforcement designs that conform to available plate cutting and joining processes. The main contributions of this paper are the introduction of two important design and manufacturing constraints for the optimal rib layout problem. One is a constraint on the minimum separation between any two ribs to guarantee adequate weld gun access. The other is a constraint that guarantees that ribs do not interfere with holes in the panel. These holes may be needed to, for example, route components or provide access, such as a manhole. We present numerical examples of our method under different types of loadings to demonstrate its applicability.

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Figures

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Fig. 1

Geometry projection

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Fig. 2

Rib parameterization (rotation angle and size variable αq not depicted). The dashed rectangle is the medial surface of the rib.

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Fig. 3

Fixed panel with a circular void region

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Fig. 7

Initial design. The scale of a rib corresponds to the value of its size variable αq.

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Fig. 4

Panel under cantilever loading

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Fig. 5

Panel under torsion loading

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Fig. 8

Optimal design of cantilever under point bending load: (a) ribs design (scale indicates ζ(αq)) and (b) 0.5 isosurface of effective density ρ̃

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Fig. 10

Free-form topology optimization for panel reinforcement under bending. Optimal design has compliance of Θ = 0.162 and volume fraction vf = 0.45. The topology corresponds to the 0.5 isosurface of the optimal topology.

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Fig. 11

Optimal design of cantilever under distributed bending load: (a) ribs design (the scale indicates ζ(αq)) and (b) 0.5 isosurface of effective density ρ̃

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Fig. 12

Optimal design of torsion loading: (a) ribs design (the scale indicates ζ(αq)) and (b) 0.5 isosurface of effective density ρ̃

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Fig. 9

Convergence history for the optimization of bending loading. The bottom figures show the history of constraints, where the dash line in second figure represents v* and dot line in the third figure represents the true maximum auxiliary density. Likewise, the dot line in the fourth represents the maximum projection density within and above the hole.

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Fig. 14

Free-form topology optimization for panel under torsion. Optimal design has compliance of Θ = 0.277 and volume fraction vf = 0.45. The topology corresponds to the 0.5 isosurface of the optimal topology. A quarter of the structure is removed from the visualization to better show that the reinforcement is hollow.

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Fig. 15

Optimal design of cantilever loading with separation constraint s*= 0.3: (a) ribs design (the scale indicates ζ(αq)) and (b) 0.5 isosurface of effective density ρ̃

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Fig. 16

The effect of the penalization power s in Eq. (13) on optimal ribs design under torsion loading: (a) s = 2, (b) s = 3, and (c) s = 4. The top row shows rib designs plotted with penalized size variables ζ(αq), while the bottom row shows the rib designs plotted with raw size variables αq.

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Fig. 17

The effect of initial size variables on optimal ribs design under torsion loading. The initial designs are plotted on the top while the corresponding optimal designs are plotted on the bottom (the scale indicates ζ(αq)): (a) α = 0.5, (b) α = 0.75, and (c) α = 1.

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Fig. 18

The effect of initial designs on optimal ribs design under torsion loading. The initial designs are plotted on the top while the corresponding optimal designs are plotted on the bottom (the scale indicates ζ(αq)): (a) initial design 1 and (b) initial design 2.

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Fig. 13

Convergence history for the optimization of torsion loading. The bottom figures show the history of constraints, where the dash line in second figure represents v* and dot line in the third figure represents the true maximum auxiliary density. Likewise, the dot line in the fourth represents the maximum projection density within and above the hole.

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