Users:General FEM Analysis/Elements Reference/Shell NURBS KL
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Contents |
General Description
This element is based on the Phd Thesis of J.Kiendl. The element formulation is well tested for static and dynamic linear and nonlinear analysis. Stresses for nonlinear case need to be corrected.
Example of a Complete Input Block
EL-PROP 1 : SHELL_NURBS_KL MAT= EL-MAT 1 !material property THICKNESS = 1.0 COUPLING = EL-PROP 6 !BRep coupling element to handle C^0 continuity inside the patch !STABILIZATION = EL-PROP 7 !Stabilization element for improving condition number NEJA = NURBS !DIP or FULL !Method for handling the integration for trimmed elements(use NURBS) INT_TYPE_SHELL_NURBS_KL = USER !or FULL or OPTIMAL !FULL means p+1 and q+1;OPTIML uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3 ! GAUSS_U = 4 !# of quadratur points in u-dir in case of INT_TYPE = USER ! GAUSS_V = 4 !# of quadratur points in u-dir in case of INT_TYPE = USER
Element Type
- This element provides a geometrically nonlinear, isogeometric spatial Bernoulli beam[1].
- Torsion without warping is included
- The element formulation can handle arbitrary orientations of the cross section along the beam.
Degrees of Freedom
The element uses three translatoric degrees of freedom (Disp_X, Disp_Y, Disp_Z) and a rotational degree of freedom (Rot_Tan) at each control point.
Parameter Description
| Compulsory Parameters | ||
| Parameter | Values, Default(*) | Description |
|---|---|---|
| MAT | EL-MAT int | Linking to a material input block |
| INT_TYPE_BEAM_3D_NURBS_KLRod | FULL, USER | Control of integration type.
|
| CROSS SECTION | DIAMETER = float | circular cross section defined ba the diameter. A = d^2π/4, Iy = Iz = d^4π/32, It= d^4π/32 |
| HEIGHT = float WIDTH = float |
rectangular cross section defined by height and width. A = h*w, Iy = h^3*w/12 Iz = h*w^3/12 It= min(h,w)^3*max(h,w)/3 | |
| AREA = float IY = float IZ = float IT = float |
cross section defined directly | |
| AXIS | AXIS float1 float2 float3 float4 | Definition of the cross sectional principal axis. Second axis is perpendicual to first and tangent of the curve. float1 is the position on the curve and float - float4 the direction (x,y,z). Base vectors are normalized and linearly interpolated for postions inbetween the defined ones. Axes for start and end knot of the NURBS curve are mandatory. |
| Optional Parameters | ||
| Parameter | Values, Default(*) | Description |
| GAUSS_U | GAUSS_U = int | Number of Gauss point per element. Must only to be defined when INT_TYPE_BEAM_3D_NURBS_KLRod = USER |
Example of a Complete Input Block
EL-PROP 1 : BEAM_3D_NURBS_KLRod MAT= EL-MAT 1 DIAMETER=1.0 !or: HEIGHT=1.0 WIDTH=1.0 or: AREA=1.0000e+008 IY=1.0000e+008 IZ=1.0000e+008 IT=1.0000e+008 INT_TYPE_BEAM_3D_NURBS_KLRod = FULL !or: INT_TYPE_BEAM_3D_NURBS_KLRod = USER GAUSS_U = 3 ! U n1 n2 n3 AXIS 0.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000 AXIS 1.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000
Element Loading
The Beam_3D_NURBS_KLRod element is able to carry the following loads:
- dead load
- snow load
- pressure load
- moment
Benchmarks
The main benchmark file in the Carat++-repository is
- '../examples/benchmark_examples/isogeometric/iga_kl_rod_nln/cbm_iga_kl_rod_nln.txt'.
It is further used in:
- '../examples/benchmark_examples/isogeometric/iga_formfinding_4point_with_trusses/cbm_4PointSailwTrusses.txt'
References
- ↑ A. M. Bauer, M. Breitenberger, B. Philipp, R. Wüchner, K.-U. Bletzinger: „Nonlinear isogeometric spatial Bernoulli beam“, in „Computer methods in applied mechanics and engineering“, Vol. 303, 2016, Seiten 101-127 http://dx.doi.org/10.1016/j.cma.2015.12.027
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