3D Displacement Based Beam With Torsion and Warping
Number of Nodes: 2
Number of DoFs: 7 (Translation, Translation, Translation, Rotation, Rotation, Rotation, Warping)
References
Syntax
element B31OS (1) (2) (3) (4) (5) [6] [7]
# (1) int, unique element tag
# (2) int, node i
# (3) int, node j
# (4) int, section tag
# (5) int, orientation tag
# [6] int, number of integration points, default: 6
# [7] int, nonlinear geometry switch, default: false
Remarks
The Lobatto integration is used by default. The number of integration points ranges from 3 to 20.
Please check for its definition.
To use the corotational formulation for nonlinearity, please attach a corotational transformation .
The reference also introduced a circumvention of membrane locking. It is implemented in this element. The Hermite shape function is used for the interpolation of Ï•.
A 3D OS section is required for this element.
The Alemdar's thesis contains a few typos. The following expressions are confirmed to be correct and used in the implementation.
Eq. 7.12 (Eq. 7.63)
Eq. 7.41
Eq. 7.69
Use S to record section forces. Each section contains six force components, namely axial force, bending moment about major axis, bending moment about minor axis, Wagner stress resultant, bi-moment and St. Venant torsion.
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If five integration points are used, the output file contains 6×5=30 columns.
At element level, the implementation transforms global nodal quantities to local elemental quantities, namely,
uniform axial
strong axis bending near node
strong axis bending far node
weak axis bending near node
weak axis bending far node
torsion near node
torsion far node
warping near node
warping far node
Those quantities are further interpolated to sectional quantities, namely,