CAE-Companion-2018-2019

-120000. -220000. -320000.

966.7 800.0 633.3 466.7 300.0 133.3

20.00 12.50 5.00

Theory WISSEN CAE

more effective because it converges much better in the nonlinear iterations of the time steps, larger time steps can be employed, and the method remains stable when the Newmark and alpha generalized methods become unstable (unless sufficient damping is introduced). The above observations are demonstrated in the solutions given in Figures 4 to 10. TIME 10.02500 X Y Z NODAL CONTACT STATUS TIME 10.02500 STICKING SLIPPING CLOSED

RESPONSE GRAPH

4.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

3.

2.

*10 -3

1.

0.

X-DISPLACEMENT, FLANGE

1000100. 005. 10010. 10015. 10020. 10025. 10030. 10035. 10040. *10 -3 -1.

OPEN DEAD

rigid wall

TIME

Y

Y

TIME 10.02500

TIME 10.02500

DISP MAG 100.0

Z

X

Z

X

VELOCITY TIME 10.02500

fluid

Potential based fluid elements

Elastic shell elements

shell

FE_PRESSURE RST CALC TIME 10.02500

35.21

ACCELERATION MAGNITUDE TIME 10.02500

sudden fluid flux

180000. 80000. -20000. -120000. -220000. -320000.

35.00 27.50 20.00 12.50 5.00

966.7 800.0 633.3 466.7 300.0 133.3

contact

contact

shell

clamped

TIME 10.02500

X

RESPONSE GRAPH

4.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

Y Z

clamped

3.

1000100. 005. 10010. 10015. 10020. 10025. 10030. 10035. 10040. *10 -3 -1. Figure 5: Predicted response using Newmark method, no damping (δ = 0.5, α = 0.25) 0. 1. 2. *10 -3 X-DISPLACEMENT, FLANGE Y

NODAL CONTACT STATUS TIME 10.02500

Figure 4: Schematic of the shell-fluid problem considered; results shown in Figures 5 - 8 Figure 4 shows the model considered, which consists of an elastic shell fully clamped at its base and a fluid surrounding it contained by an exterior rigid wall. Shell elements and subsonic potential based fluid elements are used to represent the media. The shell structure consists of two parts with frictional contact conditions between them. The model is subjected to a sudden fluid flux representing a pipe break. The resulting shock waves cause the internal parts of the model that are in contact to rapidly change status. For the im- plicit dynamic analysis of such problems usually the Newmark time integration is used. However, when contact conditions are included between internal parts, the contact surfaces re- peatedly stick and slip, which results in rapid pressure pulses in the fluid. As a consequence, high frequency vibrations are observed. These high frequency oscillations are spurious in the Newmark method solution and growwith time. After a while, the solution becomes obviously very erroneous and may even diverge. The results using the Newmark method without damping are shown in Figure 5. Note the highly oscillatory response of the flange, the non-smooth contact status between the internal parts and the parasitic pressure distribution. To overcome this problem, different techniques can be used, such as adding physical damping to the model (e.g. Rayleigh damping). In this case the damping will only be applied to the structure and the question is howmuch damping to introduce when physically it is negligible. Alternatively, the Newmark method can be used to introduce numerical damp- ing. This reduces the numerical oscillations, but also reduces the physical response which should be solved for, and the question is howmuch numerical damping to introduce in order to obtain acceptable results. TIME 10.02500 X Y Z FE_PRESSURE RST CALC TIME 10.02500 180000. 80000. -20000. -120000. -220000. -320000. VELOCITY TIME 10.02500 36.12 35.00 27.50 20.00 12.50 5.00 TIME 10.02500 X Y Z NODAL CONTACT STATUS TIME 10.02500 STICKING SLIPPING CLOSED OPEN DEAD

STICKING SLIPPING CLOSED

TIME 10.02500

DISP MAG 100.0

OPEN DEAD

Z

X

TIME

Figures 6 and 7 show that while the presence of physical damping or numerical damping improves the results using the Newmark method, to suppress all oscillations, the damp- ing must be increased to high levels, which is not desirable. However, when using the Bathe method, no numerical parameter had to be adjusted and no artificial physical damp- ing was introduced in the model, see Figure 8. The results achieved in this analysis led to the subsequent use of the Bathe method in the analyses of large finite element models. ACCELERATION MAGNITUDE TIME 10.02500 966.7 800.0 633.3 466.7 300.0 133.3

RESPONSE GRAPH

8.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

6.

4.

*10 -3

2.

0.

X-DISPLACEMENT, FLANGE

-2.

1000.

1001.

1002.

1003.

1004.

1005.

*10 -2

TIME

Y

Y

TIME 10.02500

TIME 10.02500

DISP MAG 100.0

Z

X

Z

X

VELOCITY TIME 10.02500

FE_PRESSURE RST CALC TIME 10.02500

36.12

ACCELERATION MAGNITUDE TIME 10.02500

180000. 80000. -20000. -120000. -220000. -320000.

35.00 27.50 20.00 12.50 5.00

966.7 800.0 633.3 466.7 300.0 133.3

TIME 10.02500

X

RESPONSE GRAPH

8.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

Y Z

6.

0. Figure 6: Predicted response using Newmark method with Rayleigh damping, with C = 0.001 2. 4. *10 -3 X-DISPLACEMENT, FLANGE

NODAL CONTACT STATUS TIME 10.02500

STICKING SLIPPING CLOSED

-2.

OPEN DEAD

1000.

1001.

1002.

1003.

1004.

1005.

*10 -2

TIME

87