PIECEWISE_LINEAR_PLASTICITY 5.2.3.3 Impact head
5.2.9 Convergence study
In order to achieve reliable results, determining appropriate mesh sizes (a minimum required number of elements) is important. An extremely coarse mesh would lead to a very short computational time but the solution would be very approximate. On the other hand, a very fine mesh would lead to increased accuracy of the solution at the expense of longer computational time. Consequently, a convergence study was necessary to be performed to find mesh size or mesh density which satisfactorily balances accuracy and computing resources. The convergence test was conducted by homogeneously halving the element size in each direction in each iteration. Figure 5-7a and Figure 5-7b present, respectively, the plot of initial peak impact forces and maximum global displacements at the impact point against average number of elements in 100 mm length in each direction based on the convergence study conducted on the numerical model simulating the fourth impact test series. The result of mesh convergence analysis suggested that the model with average elements’ length of 6 mm (i.e., the average element size of approximately 6 mm× 6 mm× 6 mm=216 mm3 for solid element and 6 mm× 6
Chapter 5: Development and Validation of Numerical Model 159 mm=36 mm2 for shell elements) provided the optimum solution as further increase in number
of elements had a marginal effect on the numerical results but led to a much longer calculation time.
(a) Initial peak impact force vs. average number of elements in 100 mm length in each direction
(b) Maximum displacement vs. average number of elements in 100 mm length in each direction
Figure 5-7: Convergence curve obtained based on performed mesh convergence study for the numerical model simulating the fourth impact test series
160 Chapter 5: Development and Validation of Numerical Model 5.3 Validation of Numerical Model
In order to evaluate the validity of the numerical model of the axially pre-loaded CFDST column under lateral impact loading, the results from the numerical simulations of the experimental impact testing were compared with those from the experimental testing data presented in Chapter 4. The collection and preparation methods of the testing data are presented in Section 3.9.
The comparisons were carried out for the time histories of the (i) velocity of the carriage, (ii) impact force, (iii) total reaction force, (iv) columns’ global displacement and (v) axial force as well as the permanent global and local buckling shapes of the columns. Table 5-9 summaries the numerical and experimental results in terms of key parameters (i.e., initial peak force (Fm), impact duration (ti), initial peak total reaction forces in tension (Rmt), initial peak total reaction forces in compression (Rmc), reaction force duration (tr), maximum deflection (δm), residual deflection (δr), depth of local buckling (Db) and length of local buckling (Lb)).
Table 5-9: Summary of comparison of numerical and experimental key results
Series 1 Series 2 Series 3 Series 4
Figure 5-8, Figure 5-9, Figure 5-10 and Figure 5-11compare the simulated and experimental impact carriage velocity-time histories for the first, second, third and fourth test series, respectively. It should be noted that only the initial impact velocity of the carriage (i.e., 7.8 m/sec) was input in the numerical model and the velocity profile was then predicted by the
Chapter 5: Development and Validation of Numerical Model 161 model. It can be seen from these figures that there is a good correlation between the simulated
and experimental time histories.
Figure 5-8: Comparison of simulated and experimental impact carriage velocity-time histories for test series 1
Figure 5-9: Comparison of simulated and experimental impact carriage velocity-time histories for test series 2
Figure 5-10: Comparison of simulated and experimental impact carriage velocity-time histories for test series 3
L/2 L/2
Impact Force
L/2 L/2
Impact Force
200 kN 200 kN
2L/3 L/3
Impact Force
200 kN 200 kN
162 Chapter 5: Development and Validation of Numerical Model Figure 5-11: Comparison of simulated and experimental impact carriage velocity-time
histories for test series 4
Figure 5-12 and Figure 5-13 compare the impact force-time histories obtained experimentally and numerically for third and fourth test series, correspondingly. A reasonably good agreement between the simulated and experimentally calculated time-histories can be observed.
The experimental impact force time-history featured four distinct phases (i.e., initial peak phase, vibration phase, plateau phase and unloading phase) all of which the numerical simulations of the tests were able to represent. Furthermore, it can be seen from Table 5-9 that the initial peak force and the impact duration predicted by the numerical model are reasonably accurate.
As mentioned in Section 3.7.5.4, the overloading of the 200 g accelerometer in the first two series (i.e., CFDST1A, CFDST2B, CFDST2B and CFDST2C tests) resulted in loss of acceleration data in these tests. Additionally, the velocity results from the string potentiometer as well as proximity sensor could not be used to calculate the acceleration of the carriage as they did not have sufficient resolution. Consequently, the impact force, calculated based on known value of the carriage acceleration and impact mass, could not be determined and compared with the numerical results in the first two series. However, given the good correction between the simulated and experimental impact force-time histories in the third and fourth test series as well as velocity-time histories in all test series, the numerical model can be expected to provide a reasonably good prediction of impact force-time history.
400 kN 400 kN
L/2 L/2
Impact Force
Chapter 5: Development and Validation of Numerical Model 163 Figure 5-12: Comparison of simulated and experimental impact force-time histories for test
series 3
Figure 5-13: Comparison of simulated and experimental impact force-time histories for test series 4
Figure 5-14, Figure 5-15, Figure 5-16 and Figure 5-17 show the comparison between the total reaction force-time histories obtained numerically and experimentally for the first, second, third and fourth test series, respectively. It is clear from these figures that there is a good agreement between the simulated and experimental results in terms of the general trend of the time history curves. As seen from Table 5-9, the numerical model was able to predict the initial peak total reaction forces in tension, initial peak total reaction forces in compression and reaction force duration with a good level of accuracy.
2L/3 L/3
Impact Force
200 kN 200 kN
400 kN 400 kN
L/2 L/2
Impact Force
164 Chapter 5: Development and Validation of Numerical Model Figure 5-14: Comparison of simulated and experimental total reaction force-time histories
for test series 1
Figure 5-15: Comparison of simulated and experimental total reaction force-time histories for test series 2
Figure 5-16: Comparison of simulated and experimental total reaction force-time histories for test series 3
L/2 L/2
Impact Force
L/2 L/2
Impact Force
200 kN 200 kN
2L/3 L/3
Impact Force
200 kN 200 kN
Chapter 5: Development and Validation of Numerical Model 165 Figure 5-17: Comparison of simulated and experimental total reaction force-time histories
for test series 4
The comparison of the numerically and experimentally obtained CFDST columns’ global displacement-time histories at the impact point for the first, second, third and fourth test series are presented in Figure 5-18, Figure 5-19, Figure 5-20 and Figure 5-21, respectively. It can be seen that there is a good correlation between the numerical and experimental results in terms of the general trend of the curves. Additionally, comparison of results in terms of maximum and residual deflections, summarised in Table 5-9 and presented in these figures confirm that numerical model can estimate both values with a good level of accuracy.
Figure 5-18: Comparison of simulated and experimental global displacement-time histories at impact point for test series 1
L/2 L/2
Impact Force
400 kN 400 kN
L/2 L/2
Impact Force
166 Chapter 5: Development and Validation of Numerical Model Figure 5-19: Comparison of simulated and experimental global displacement-time histories
at impact point for test series 2
Figure 5-20: Comparison of simulated and experimental global displacement-time histories at impact point for test series 3
Figure 5-21: Comparison of simulated and experimental global displacement-time histories at impact point for test series 4
L/2 L/2
Impact Force
200 kN 200 kN
2L/3 L/3 Impact Force
200 kN 200 kN
400 kN 400 kN
L/2 L/2
Impact Force
Chapter 5: Development and Validation of Numerical Model 167 Figure 5-22, Figure 5-23 and Figure 5-24 show the experimental and numerical time histories
of the axial force for second, third and fourth test series, respectively. It is evident that there is a reasonably good agreement between the two sets of results in terms of the trend of the time-history curves.
Figure 5-22: Comparison of simulated and experimental axial force-time histories for test series 2
Figure 5-23: Comparison of simulated and experimental axial force-time-time histories for test series 3
L/2 L/2 Impact force
2L/3 L/3 Impact Force
200 kN 200 kN
168 Chapter 5: Development and Validation of Numerical Model Figure 5-24: Comparison of simulated and experimental axial force-time histories for test
series 4
During the impact tests the axial pre-loading did not remain entirely constant and a degree of long term drop was observed due to the shortening of the impacted columns. The final and permanent drop in the axial load was greater in columns with higher axial pre-loading.
Comparing the experimental results with those predicted by the numerical model confirm that the numerical model was able to successfully simulate the action of the disc-springs and tension-rods of the axial pre-loading frame, using the elastic spring systems, as well as the response of the CFDST columns. Greater long term drop for the columns with higher axial pre-loading was also predicted by the numerical model.
The experimental and simulated post-impact permanent global deformation of the CFDST columns in test series 1, test series 2, test series 3 and test series 4 are compared in Figure 5-25, Figure 5-26, Figure 5-27 and Figure 5-28, respectively. The global permanent deformation shape of CFDST columns observed in the finite element model appears to conform well to the experimental results.
The contours of effective plastic strains in the outer steel tubes presented in Figure 5-25, Figure 5-26, Figure 5-27 and Figure 5-28 show that plastic deformation only appears in the impact zone, the impact side of which is the location of local bucking. Whilst Figure 5-29 shows the typical post-impact permanent local bucking shape of CFDST columns observed experimentally and numerically, Figure 5-30, Figure 5-31, Figure 5-32 and Figure 5-33 present the comparison between the simulated and experimental profiles of post-impact permanent
400 kN 400 kN
L/2 L/2 Impact Force
Chapter 5: Development and Validation of Numerical Model 169 local buckling for the first, second, third and fourth test series, respectively. As observed from
Figure 5-30, Figure 5-31, Figure 5-32, Figure 5-33 and Table 5-9, there is a good agreement between the experimental and numerical results in terms of length and depth of local buckling of CFDST columns.
(a) Experimental result: Post-impact column global deformation shape
(b) FEM result: Post-impact column global deformation shape
(c) FEM result: Countors of effective plastic strain - Side view of outer tube
(d) FEM result: Countors of effective plastic strain - Plan view of outer tube (impact side)
Figure 5-25: Comparison of simulated and experimental post-impact CFDST column’s global deformation shape in test series 1
CFDST1A
Impact side of impact zone
Non-impact side of impact zone
170 Chapter 5: Development and Validation of Numerical Model (a) Experimental results: Post-impact columns’ global deformation shape
(b) FEM result: Post-impact column global deformation shape
(c) FEM result: Countors of effective plastic strain - Side view of outer tube
(d) FEM result: Countors of effective plastic strain - Plan view of outer tube (impact side) Figure 5-26: Comparison of simulated and experimental post-impact CFDST columns’
global deformation shape in test series 2
CFDST2A
CFDST2B
CFDST2C
Chapter 5: Development and Validation of Numerical Model 171 (a) Experimental results: Post-impact columns’ global deformation shape
(b) FEM result: Post-impact column global deformation shape
(c) FEM result: Countors of effective plastic strain - Side view of outer tube
(d) FEM result: Countors of effective plastic strain - Plan view of outer tube (impact side) Figure 5-27: Comparison of simulated and experimental post-impact CFDST columns’
global deformation shape in test series 3
CFDST3A
CFDST3B
172 Chapter 5: Development and Validation of Numerical Model (a) Experimental results: Post-impact columns’ global deformation shape
(b) FEM result: Post-impact column global deformation shape
(c) FEM result: Countors of effective plastic strain - Side view of outer tube
(d) FEM result: Countors of effective plastic strain - Plan view of outer tube (impact side) Figure 5-28: Comparison of simulated and experimental post-impact CFDST columns’
global deformation shape in test series 4
CFDST4A
CFDST4B
Chapter 5: Development and Validation of Numerical Model 173
(a) Experimental result (b) FEM result
Figure 5-29: Comparison of simulated and experimental post-impact CFDST column local buckling shape in CFDST4A test
Figure 5-30: Comparison of simulated and experimental post-impact CFDST column local deformation profiles in test series 1
Figure 5-31: Comparison of simulated and experimental post-impact CFDST columns’ local deformation profiles in test series 2
Local buckling
L/2 L/2
Impact Force
200 kN 200 kN
L/2 L/2
Impact Force
174 Chapter 5: Development and Validation of Numerical Model Figure 5-32: Comparison of simulated and experimental post-impact CFDST columns’ local
deformation profiles in test series 3
Figure 5-33: Comparison of simulated and experimental post-impact CFDST columns’ local deformation profiles in test series 4
Investigation of the columns carried out after the impact events showed that the reaction plates had undergone permanent bending deformation in all tests as the columns buckled globally.
Figure 5-34 shows the comparison of the permanent bending deformation of the reaction plates observed experimentally and predicted numerically for CFDST1A, CFDST2C, CFDST3B and CFDST4B tests as representative of first, second, third and fourth test series, respectively. It can be seen from this figure that numerical model was able to predict the bending deformation of the reactions plates reasonably.
2L/3 L/3
Impact Force
200 kN 200 kN
400 kN 400 kN
L/2 L/2
Impact Force
Chapter 5: Development and Validation of Numerical Model 175
(a) Experimental result (b) FEM result
(a) Experimental result (b) FEM result
(a) Experimental result (b) FEM result
(a) Experimental result (b) FEM result
Figure 5-34: Comparison of simulated and experimental post-impact ram-side reaction plates’ deformation shape
CFDST1A
CFDST2C
CFDST3B
CFDST4B
176 Chapter 5: Development and Validation of Numerical Model 5.4 Concluding Remarks
This chapter presented the details of finite element models developed to simulate the lateral impact tests conducted on axially pre-loaded CFDST columns. Additionally, it presented the comparison of the results emanating from the numerical simulations of the experimental impact testing with the experimental testing data to assess the validity of the numerical models.
The explicit dynamic nonlinear finite element code LS-DYNA was employed as a platform for developing the numerical model based upon its success in the literature for accurately modelling impact response of various composite structures.
The numerical model of the impact test comprised of fourteen main components which were the impact head of carriage, specimen’s outer steel tube, specimen’s inner steel tube, specimen’s concrete core, two steel end plates of the specimens, two steel reaction plates, two steel end caps, two steel base plates of load cells and two sets of axial linear springs, which represented the actions of the disc-springs and tension-rods in the tests and hence replicating the experiments in terms of the change in the axial load. The model incorporated concrete confinement, strain rate effects of steel and concrete, contact between the steel tubes and concrete and dynamic relaxation for pre-loading, which is a relatively recent method for applying a pre-loading in the explicit solver.
Convergence studies were performed to find mesh size or density which satisfactorily balance accuracy and computing resources. This numerical model was developed to simulate the experimental impact tests described in Chapter 4. The numerical results were hence compared with the experimental results to evaluate its validity. The comparison was in terms of the velocity-time history of carriage, impact force-time history, total reaction force-time history, global displacement-time history and axial force-time history of CFDST columns and columns’
global and local buckling shapes at the end of impact event. Overall, the predicted results showed a good agreement with those of the experiments. The good correlation of time histories and columns’ permanent global and local deformation shape, as well as the relatively small differences in the results for the key parameters (i.e., initial peak force, impact duration, initial peak total reaction forces in tension, initial peak total reaction forces in compression, the reaction force duration, maximum deflection, residual deflection, depth of local buckling and length of local buckling) showed that the numerical model was able to represent the lateral
Chapter 5: Development and Validation of Numerical Model 177 impact behaviour of the axially pre-loaded CFDST columns with a good level of accuracy and
can be used as a viable alternative to experimental testing in the analysis and design process of CFDST columns. This numerical model can hence be used with confidence to carry out the parametric study as well as the comparative study which will be presented in chapter 6 and chapter 7, respectively.