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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e-mail: matthew.j.vick-1@ou.edu
e-mail: gramoll@ou.edu
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October 2012
Design And Analysis
Finite Element Study on the Optimization of an Orthotropic Composite Toroidal Shell
Matthew J. Vick,
Matthew J. Vick
Department of Aerospace and Mechanical Engineering,
e-mail: matthew.j.vick-1@ou.edu
University of Oklahoma
, 865 Asp Avenue, Felgar Hall, Room 237, Norman, OK 73019
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Kurt Gramoll
Kurt Gramoll
Department of Aerospace and Mechanical Engineering,
e-mail: gramoll@ou.edu
University of Oklahoma
, 865 Asp Avenue, Felgar Hall, Room 237, Norman, OK 73019
Search for other works by this author on:
Matthew J. Vick
Department of Aerospace and Mechanical Engineering,
University of Oklahoma
, 865 Asp Avenue, Felgar Hall, Room 237, Norman, OK 73019e-mail: matthew.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 73019e-mail: gramoll@ou.edu
J. Pressure Vessel Technol. Oct 2012, 134(5): 051201 (7 pages)
Published Online: August 27, 2012
Article history
Received:
February 5, 2011
Revised:
December 21, 2011
Published:
August 27, 2012
Citation
Vick, M. J., and Gramoll, K. (August 27, 2012). "Finite Element Study on the Optimization of an Orthotropic Composite Toroidal Shell." ASME. J. Pressure Vessel Technol. October 2012; 134(5): 051201. https://doi.org/10.1115/1.4005873
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