Part II Recent developments for the verification of component and assembly models
II.4 Calibration of the FE models
To be sure to get reliable results in the FE simulations and to ensure realistic results of the simulations, which are used to replace real test results, the numerical models have to be calibrated. For this purpose the influence of the shell type, element size, solver algorithm etc. on the simulation results have to be examined, and the results of the numerical simulations have to be compared with test results. It is the aim, to create robust FE models, that reproduce the load-displacement curves of real test results as exact as possible.
The first test results that were used to calibrate the FE model are based on the work of the university of Karlsruhe (see [40]; Table 6). In this study T-joints with RHS columns and RHS beams were tested. The specimen were fixed at the ends of the column and the loads were applied at the end of the beams. The displacements were measured at the point, where loads were applied, in direction of the loads. A principal sketch of the experimental setup is given in Figure 36.
Figure 36: Setup for T-joint with RHS members test to calibrate the FE models
The test M21, that was reproduced by FE modelling, has the following geometrical properties:
P
460 [mm]
1300
Figure 37: Geometrical properties of specimen M21
The dimensions of the RHS-profiles, according to the notations given in Figure 36, are:
Table 7: Geometrical properties of specimen M21
Joint member h [mm] b [mm] t [mm]
Column 140 140 8,8 Beam 100 100 4,0 The material properties are:
Table 8: Material properties of specimen M21 Joint member fy [N/mm²] fu [N/mm²] εf [-]
Column 335,7 528,9 0,2885
Beam 424,6 527,1 0,33375
where: fy is the yield strength fu is the ultimate strength
εf is the plastic strain at tensile failure
As the strain when the material reaches the ultimate tensile strength fu is not given, as an approximation different material laws for the beam and for the column are used, see Figure 38 and Figure 39. An initial stiffness of E=210000 N/mm² is assumed.
0 100 200 300 400 500 600
0 0,05 0,1 0,15 0,2 0,25 0,3
strain [-]
stress [N/mm²] Curve 1
Curve 2 Curve 3 Curve 4
Figure 38: Different approximations of the material law for the column of model M21
0 100 200 300 400 500 600
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35
strain [-]
stress [N/mm²]
Curve 5 Curve 6 Curve 7 Curve 8
Figure 39: Different approximations of the material law for the beam of model M21
8 node shell elements (S8R-elements in the ABAQUS-library) and 4 node shell elements (S4R- elements in the ABAQUS-library) with reduced integration were tested. The side length was varied between 8 and 4 mm.
By taking thicker shell elements with the width of 0,8a 2 , the welds are considered.
All displacements and loads are plane-symmetric. That means, that modelling only one half of the joint should lead to correct results, if the required boundary conditions are set.
As an example one model with an approximate shell element length of 8 mm is given in Figure 40.
Figure 40: FE model of test specimen M21
In Table 9 the main parameters for the different FE models of test M21 are summarized and the changes are marked. The σ-ε curves are in accordance with those given in see Figure 38 and Figure 39.
Table 9: Main parameters of the FE model M21 Model name Element type Approximate size
length [mm] σ-ε curve
column σ-ε curve beam
Further modifications
FEM 21-5 S8R 8 Curve 1 Curve 5 -
FEM 21-6 S4R 8 Curve 1 Curve 5 -
FEM 21-7 S4R 5 Curve 1 Curve 5 -
FEM 21-8 S8R 8 Curve 2 Curve 6 -
FEM 21-9 S8R 8 Curve 3 Curve 7 -
FEM 21-10 S4R 5 Curve 3 Curve 7 -
FEM 21-11 S4R 5 Curve 4 Curve 8 -
All simulations were computed geometrical non linear.
The comparison of the test results and the results of the numerical simulations of M21 is given in Figure 41, where P is the applied load, see Figure 37, and s is the deformation at the point of load introduction.
Figure 41: Comparison test results – FE simulations for specimen M21
The S8R element is an 8 node element, considering thick shell theory. The element S4R is used for thin shells. To avoid shear locking effects, S4R uses reduced integration when determining the stiffness matrix. The S4R results seem to fit better, and the refinement of the mesh has no significant influence on the load displacement curve. The system seems to be convergent.
With σ-ε curve 1 and 5 in the first models stiffness after yielding seems to be underestimated. To raise the gradient of the stress strain curve after yielding, and to describe the material behaviour more realistic, ε at the level of the ultimate stress was reduced, and a zero stiffness after reaching fu was assumed (see Figure 38, Figure 39). With this modifications the joint model produces sufficient results (see FEM 21-10). The initial stiffness and the behaviour of the joint in the non elastic range is close to the test result.
For FEM 21-11 the σ-ε curves were modified in a way, that the stiffness of the material after yielding is 1/50 of the initial E-modulus. This assumption overestimates the stiffness of the whole joint.
To check the results and to increase the knowledge about robust joint modelling, different other joints tested by the university of Karlsruhe [40] were modelled.
The measured properties of test specimen M10 are given in Table 10 and Table 11.
Table 10: Geometrical properties of specimen M10
Joint member h [mm] b [mm] t [mm]
Column 100 100 6,3 Beam 80 80 3,6
Table 11: Material properties of specimen M10 Joint member fy [N/mm²] fu [N/mm²] εf [-]
Column 242,5 353,1 0,3725
Beam 298,5 392,9 0,3706
where: fy is the yield strength fu is the ultimate strength
εf is the plastic strain at tensile failure
As there is again no exact information about the stress-strain curve, different material laws for the beam and for the column are tested, see Figure 42 and Figure 43.
0 50 100 150 200 250 300 350 400
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
strain [-]
stress [N/mm²]
Curve 1 Curve 2
Figure 42: Different approximations of the material law for the column of model M10
0 50 100 150 200 250 300 350 400 450
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
strain [-]
stress [N/mm²]
Curve 3 Curve 4
Figure 43: Different approximations of the material law for the beam of model M10
The main parameters of model M10and their variation are summarized in Table 12.
The load displacement curves and the comparison to the test result are given in Figure 44.
Table 12: Main parameters of the FE model M10 Model name Element type Approximate size
length [mm] σ-ε curve column
σ-ε curve beam
Further modifications
FEM 10-1 S8R 6 Curve 1 Curve 3 -
FEM 10-2 S4R 6 Curve 1 Curve 3 -
FEM 10-3 S4R 5 Curve 2 Curve 4 -
0
Figure 44: Comparison test results – FE simulations for specimen M10
The results of this comparison confirm the previous conclusion, that element type S8R is not adequate for such simulations. The simulation of FEM 10-1, where S8R is used, is aborted after 30 mm displacement. The simulation FEM 10-3 with the reduced ε 'at the level of ultimate strength (1/4 of the value in FEM 10-1 and FEM 10-2) fits very well. The initial stiffness and the load displacement curve after yielding is very close to the test result.
The calibration is repeated with test M78, taken from [40].
The measured properties of test specimen M78 are given in Table 13 and Table 14.
Table 13: Geometrical properties of specimen M78
Joint member h [mm] b [mm] t [mm]
Column 180 180 14,2 Beam 100 100 6,3
Table 14: Material properties of specimen M78 Joint member fy [N/mm²] fu [N/mm²] εf [-]
In this model a stress-strain curve with a reduced ε at the ultimate strength level (∼1/4 of εf) is used directly, because of the results of the former tests.
The used curves for the column and for the beam are given in Figure 45 and Figure 46.
0
Figure 45: Material law for the column of model M78
0
Figure 46: Material law for the beam of model M78
The main parameters of model M78and their variation are summarized in Table 15.
The load displacement curves and the comparison to the test result are given in Figure 47.
Table 15: Main parameters of the FE model M78 Model name Element type Approximate size
length [mm] σ-ε curve
Figure 47: Comparison test results – FE simulations for specimen M78
The results of this simulation confirm again, that S4R elements work well, even if the walls of the RHS profiles are thick (14,2 mm). The mesh refinement has no significant influence and the boundary conditions are set correctly, so that the results of the model, where only one plane symmetric part is modelled to increase the efficiency of the simulation, lead to correct results (see Figure 48 and Figure 49).
Considering all the simulations of the test one arrives at the conclusion that using the ABAOQUS 4-node elements S4R with a material behaviour close to the stress strain curve of the real material leads to sufficient results.
With this knowledge further test results are rechecked by using S4R elements when generating the models with the tool described in section II.3.
Figure 48: Test specimen FEM 78-2 under load
Figure 49: Test specimen FEM 78-4 under load
The next test, that are reproduced by FE simulation are part of the work presented by Y.
Makino, Y. Kurobane, J.C. Paul, Y. Orita and K. Hiraishi in 1991 (see [37] and Table 4).
In this tests X- and T-joints were examined under normal- and bending loads of the beam. The column was always a CHS-profile with different geometrical properties, while the profile types of the beams were diversified.
The joint that was reproduced by FE modelling was a X-joint with horizontal gusset plates under tension and compression. The geometrical properties of the joints are given in Figure 50 and Figure 51.
Figure 50: Dimensions of test specimen XP-1-C-1
Figure 51: Dimensions of test specimen XP-1-T-1
For this test specimen there is no information about the measured material properties available.
Because of this lack of information a bi-linear stress strain curve with a theoretical value of 488 N/mm² for fy is used for the simulation of test XP-1-C-1 and XP-1-T-1. This value is obtained from an expression given in [37].
Loads and displacements of the specimen are double symmetric, so that only a quarter of the structure had to be generated. The mesh for the simulation of test XP-1-C-1 is given in Figure 52.
Figure 52: Mesh of test specimen FEM XP1-Compression
The load displacement curve of the specimen under compression is given in Figure 53.
0 50 100 150 200 250 300 350 400 450
0 5 10 15 20 25 30
s [mm]
P [kN]
Test results
FEM XP1-Compression
Figure 53: Load displacement curves of X-joint XP1-C-1 under compression (FEM and test results)
With regard to the ultimate resistance the FE model doesn't fit exact with the test results. But as said above, there is poor information about the material behaviour. The buckling of the CHS profile, can be identified in the FE simulation. The deformed specimen is given in Figure 54.
Figure 54: FEM XP1-C-1 under compression loads
The results of the same joint configuration under tension loads are given in Figure 55.
0 100 200 300 400 500 600 700 800
0 5 10 15 20 25
s [mm]
P [kN]
Test results
FEM XP1-Tension
Figure 55: Load displacement curves of X-joint XP1-T-1 under tension (FEM and test results)
After analysing all FE simulations carefully, the results lead to the conclusion, that real test results can be reproduced by FE modelling in a sufficient way. If there is enough information about the material behaviour and the test setup, the load displacement curves derived from numerical simulations are nearly identical with those ones measured at real tests.
Effects like buckling and yielding can be simulated, and the computation runs reliable, if the ABAQUS shell elements S4R are used. In its final version the FE model generator uses for all required joint configurations shell elements S4R. The size length has to be specified adequate.
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