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Research Papers: Structures and Safety Reliability

A Three-Dimensional Curved Beam Element for Helical Components Modeling

[+] Author and Article Information
Rodrigo Provasi

University of São Paulo,
Department of Structural and
Geotechnical Engineering,
Avenida Professor Almeida Prado,
Trav. 2, No. 83,
São Paulo, SP 05508-900, Brazil
e-mail: provasi@usp.br

Clóvis de Arruda Martins

University of São Paulo,
Department of Mechanical Engineering,
Avenida Professor Mello Moraes,
No. 2231,
São Paulo, SP 05508-900, Brazil
e-mail: cmartins@usp.br

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received December 16, 2013; final manuscript received June 26, 2014; published online July 16, 2014. Assoc. Editor: Daniel T. Valentine.

J. Offshore Mech. Arct. Eng 136(4), 041601 (Jul 16, 2014) (7 pages) Paper No: OMAE-13-1121; doi: 10.1115/1.4027956 History: Received December 16, 2013; Revised June 26, 2014

The structural behavior of flexible pipes and umbilical cables is difficult to model due to their complex construction that includes components of different materials, shapes, and functions. Also, it is difficult to model due to the nonlinear interaction between those components, which includes contacts, gaps, and friction. To model a flexible pipe or umbilical cable, one can rely on analytical or numerical approaches. Analytical models need a large set of simplifying hypotheses. Numerical models, like classical finite elements models, require large meshes and have great difficulties to converge. But one can take profit of the particular characteristics of a specific component and develop a custom-made finite element that represents its structural behavior, a so-called finite macro-element. Adopting this approach, in a previous work, it was developed a cylindrical macro-element with orthotropic behavior, to model the plastic layers of a flexible pipe or umbilical cable. This paper presents a three-dimensional (3D) curved beam element, built to model a helical metallic component, which takes into account the effects of curvature and tortuosity of that kind of component. This is accomplished by using a strong coupling between displacements and assuming that the twist and shear strains vary linearly within the element, to avoid the shear lock phenomenon. The complete formulation of this element is presented. Results obtained with this formulation are also presented and compared to those obtained by a classical finite element modeling tool, with good agreement.

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References

Provasi, R., and Martins, C. A., 2009, “A Finite Macro-Element for Cylindrical Layer Modeling,” ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering, Shanghai, China, June 6–11, pp. 429–438.
Provasi, R., and Martins, C. A., 2013, “A Finite Macro-Element for Orthotropic Cylindrical Layer Modeling,” ASME J. Offshore Mech. Arct. Eng., 135(3), p. 031401. [CrossRef]
Provasi, R., and Martins, C. A., 2011, “A Three-Dimensional Curved Beam Element for Helical Components Modeling,” ASME 2010 30th International Conference on Ocean, Offshore and Arctic Engineering, Rotterdam, The Netherlands, June 19–24, pp. 101–109.
Provasi, R., and Martins, C. A., 2013, “A Rigid Connection Element for Macro-Elements With Different Node Displacement Natures,” 23rd International Offshore (Ocean) and Polar Engineering Conference, ISOPE2013, Anchorage, AK, June 30–July 5, pp. 222–226.
Provasi, R., and Martins, C. A., 2013, “A Contact Element for Macro-Elements With Different Node Displacement Natures,” 23rd International Offshore (Ocean) and Polar Engineering Conference, ISOPE2013, Anchorage, AK, June 30–July 5, pp. 227–233.
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Figures

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Fig. 1

Element schematics and associated coordinate system (Frenet triad)

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Fig. 2

Coordinate systems relations

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Fig. 3

Displacement comparisons and mesh convergence

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Fig. 4

Presented model versus Ansys for external radius and axial coordinate z = 429.6 mm

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