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Twisted Cantilever Beam |
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Twisted Cantilever Beam |
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Twisted Cantilever Beam |
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Twisted Cantilever Beam |
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Length = 12.0; Width = 1.1; Depth = 0.32; E = 29.0E6; Poisson’s ratio = 0.22; Loading = unit forces at tip.
This is a twisted cantilever beam solved with solid and shell elements. A model is made with each element's type to investigate the effect of distorted elements with a high aspect ratio.
Six types of elements are used for this problem. They are tria-shell, quad-shell, and hexa-solid elements, each with 1st and 2nd order. Two loading cases are used for each model; in-plane bending, transverse bending. For both load cases, unit loads are applied in a consistent fashion over all of the nodes at the tip of the beam.
Theoretical solutions for the deflections at the tip, computed by beam theory, are as follows.
Load Type |
Component |
Value |
in-plane bending |
UY |
0.001754 |
transverse bending |
UZ |
0.005424 |
All results are normalized with the target value.
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In-plane Bending |
Transverse Bending |
QUAD4 |
0.988 |
0.992 |
QUAD8 |
1.014 |
1.062 |
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TRI3 |
0.839 |
0.984 |
TRI6 |
1.161 |
1.215 |
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HEX8 |
0.986 |
1.005 |
HEX20 |
1.017 |
1.052 |
<install_directory>/demos/hwsolvers/optistruct/CBhex.fem
<install_directory>/demos/hwsolvers/optistruct/CBpent1.fem
<install_directory>/demos/hwsolvers/optistruct/CBpen2.fem
<install_directory>/demos/hwsolvers/optistruct/CBquad.fem
<install_directory>/demos/hwsolvers/optistruct/cbquad2.fem
<install_directory>/demos/hwsolvers/optistruct/cbquad4.fem
<install_directory>/demos/hwsolvers/optistruct/CBtri1.fem
<install_directory>/demos/hwsolvers/optistruct/CBtri2.fem
MacNeal, R.H., and Harder, R.L., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Elements in Analysis and Design, 1 (1985) 3-20.