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Design and Analysis

Finite Element Study on the Optimization of an Orthotropic Composite Toroidal Shell

[+] Author and Article Information
Matthew J. Vick

Department of Aerospace and Mechanical Engineering,  University of Oklahoma, 865 Asp Avenue, Felgar Hall, Room 237, Norman, OK 73019matthew.j.vick-1@ou.edu

Kurt Gramoll

Department of Aerospace and Mechanical Engineering,  University of Oklahoma, 865 Asp Avenue, Felgar Hall, Room 237, Norman, OK 73019gramoll@ou.edu

J. Pressure Vessel Technol 134(5), 051201 (Aug 27, 2012) (7 pages) doi:10.1115/1.4005873 History: Received February 05, 2011; Revised December 21, 2011; Published August 27, 2012

In this research, an analysis technique is developed to model orthotropic composite toroids and optimize the fiber layup, accounting for the natural variation in thickness due to fiber stacking. The behavior of toroids is difficult to model using membrane shell theories due to a singularity in the strain-displacement relations occurring at the toroid crest that yields discontinuous displacement results. A technique is developed here where the constitutive properties of multilayered toroidal shells are determined using lamination theory, and the toroid strains and line loads are determined using finite element analysis. The toroid strains are rotated into the fiber directions, allowing the fiber stress and transverse stress distributions to be determined for each layer. The fiber layup is modified heuristically until an optimum is found. An optimum is reached when the maximum fiber and transverse direction stresses of each shell layer are equal, minimizing wasted fibers and excess weight. Test cases are analyzed to verify the accuracy of the finite element model and an example composite toroid with Kevlar/epoxy material properties is optimized. The analysis technique developed here can decrease the time and cost associated with the development of orthotropic toroidal pressure vessels, resulting in lighter, cheaper, and more optimal structures. The models developed can be expanded to include a steel liner and a broader range of fiber winding patterns.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Circular toroid geometry: (a) section view; (b) top view; and (c) global view

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Figure 2

Thickness variation with meridional position (normalized with respect to crest thickness, tc )

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Figure 3

Laminate fiber orientations

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Figure 4

Isotropic, constant thickness toroid: (a) toroid displacement comparison; (b) FEA normalized line forces (EC and PI results identical)

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Figure 5

Isotropic, variable thickness toroid: (a) planar strains; (b) normalized line forces (EC and PI results identical)

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Figure 6

Orthotropic, variable thickness toroid: (a) planar strains; (b) normalized line forces (EC and PI results identical)

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Figure 7

Heuristic optimization process

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Figure 8

Fiber layup orientations

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Figure 9

Maximum layer stresses with respect to angle ply orientation: (a) fiber direction; (b) transverse direction

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Figure 10

Ratio of maximum to minimum layer stresses with respect to angle-ply orientation: (a) fiber direction; (b) transverse direction

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