A ‘boundary layer’ finite element for thin multi-strake conical shells
File(s)
Accepted version
Author(s)
Boyez, A
Sadowski, AJ
Izzuddin, BA
Type
Journal Article
Abstract
Multi-strake cylindrical and conical shells of revolution are complex but commonplace industrial structures which are composed of multipl
e segments of varying wall thickness. They find application as tanks, silos, circular hollow sections, aerospace structures and wind turbine
support towers, amongst others. The modelling of such structures with classical finite elements interpolated using low order polynomial shape functions presents a particular challenge, because many elements must be sacrificed solely in order to accurately represent the regions of
local compatibility bending, so-called ‘boundary layers’, near shell boundaries, changes of wall thickness and at other discontinuities. Partitioning schemes must be applied to localise mesh refinement within the boundary layers and avoid excessive model runtimes, a particular concern in incremental nonlinear analyses of large models where matrix systems are handled repeatedly. In a previous paper, the authors introduced a novel axisymmetric cylindrical shell finite element
that was enriched with transcendental shape functions to capture the bending boundary layer exactly, permitting significant economies in the el
ement and degrees of freedom count, mesh design and model generation effort. One element is sufficient per wall strake. This paper extends this work to conical geometries, where axisymmetric elements enriched with Bessel functions accurately capture the bending boundary layer for both ‘shallow’ and ‘steep’ conical strakes, which are characterised by interacting and independent boundary layers, respectively. The bending shape functions are integrated numerica
lly, with several integration schemes investigated for accuracy and efficiency. The potential of the element is illustrated through a stress analysis of a real 22-strake metal wind turbine support tower under self-weight. The work is part of a wider project to design a general thre
e-dimensional ‘boundary layer’ element.
e segments of varying wall thickness. They find application as tanks, silos, circular hollow sections, aerospace structures and wind turbine
support towers, amongst others. The modelling of such structures with classical finite elements interpolated using low order polynomial shape functions presents a particular challenge, because many elements must be sacrificed solely in order to accurately represent the regions of
local compatibility bending, so-called ‘boundary layers’, near shell boundaries, changes of wall thickness and at other discontinuities. Partitioning schemes must be applied to localise mesh refinement within the boundary layers and avoid excessive model runtimes, a particular concern in incremental nonlinear analyses of large models where matrix systems are handled repeatedly. In a previous paper, the authors introduced a novel axisymmetric cylindrical shell finite element
that was enriched with transcendental shape functions to capture the bending boundary layer exactly, permitting significant economies in the el
ement and degrees of freedom count, mesh design and model generation effort. One element is sufficient per wall strake. This paper extends this work to conical geometries, where axisymmetric elements enriched with Bessel functions accurately capture the bending boundary layer for both ‘shallow’ and ‘steep’ conical strakes, which are characterised by interacting and independent boundary layers, respectively. The bending shape functions are integrated numerica
lly, with several integration schemes investigated for accuracy and efficiency. The potential of the element is illustrated through a stress analysis of a real 22-strake metal wind turbine support tower under self-weight. The work is part of a wider project to design a general thre
e-dimensional ‘boundary layer’ element.
Date Issued
2018-09-01
Date Acceptance
2018-05-18
Citation
Thin-Walled Structures, 2018, 130, pp.535-549
ISSN
0263-8231
Publisher
Elsevier
Start Page
535
End Page
549
Journal / Book Title
Thin-Walled Structures
Volume
130
Copyright Statement
© 2018 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.
Subjects
Science & Technology
Technology
Engineering, Civil
Engineering
Conical shell
Thin axisymmetric shell
Bending boundary layer
Bessel functions
Finite element method
EXACT STIFFNESS MATRIX
WIND TURBINES
FATIGUE LOADS
GENERATION
THICKNESS
DESIGN
0901 Aerospace Engineering
0905 Civil Engineering
0913 Mechanical Engineering
Civil Engineering
Publication Status
Published
Date Publish Online
2018-07-04