1. Description#
1.1. General description#
The structure is a square reinforced concrete gantry with a \(10m\) side and \(2m\) high, the 4 posts of which are connected at their base to a raft of the same size and resting on a carpet of ground springs.
The base and the roof are represented in shell elements of the Q4GG type. Only the self can be non-linear (law of behavior GLRC_DAMAGE) and it is subject to variable pressure over time.
The objective of this type of study is to deal with the rapid dynamic part of the response in Europlexus, and then switch to Code_Aster (implicitly) for the induced upheaval phase, whose duration is too long to allow a resolution in a reasonable time while remaining explicit in Europlexus.
In post-processing, we will analyze the movements, acceleration and the oscillator response spectrum (SRO) at point \(\mathit{PP2}\) which is in the middle of the upper slab.
1.2. Material properties#
The slabs are reinforced concrete and the posts are steel.
Material |
Concrete |
Steel |
Young’s module |
\({E}_{b}\mathrm{=}\mathrm{42824,5}\mathit{MPa}\) |
|
Poisson’s ratio |
\({\nu }_{b}\mathrm{=}0\) |
|
Density |
\({m}_{b}\mathrm{=}2500\mathit{Kg}\mathrm{/}{m}^{3}\) |
|
D_ SIGM_EPSI |
0 |
0 |
SYT |
|
Not applicable |
SYC |
|
Not applicable |
SY |
Not applicable |
\({5.10}^{7}\mathit{MPa}\) |
The linear part of the slabs is affected by the linear characteristics of the concrete defined above.
The complementary part is characterized by a behavior of type GLRC_DAMAGE., whose concrete phase and steel reinforcements also have the above characteristics.
The specific parameters of law GLRC_DAMAGE are specified with the DEFI_GLRC operator.
BETON |
NAPPE |
||
EPAIS |
1.3 |
OMX |
\(\mathrm{5,027}{.10}^{-3}\) |
GAMMA |
0 |
OMY |
\(\mathrm{5,027}{.10}^{-3}\) |
QP1 |
0.152 |
RX |
0.877 |
QP2 |
0.152 |
RY |
0.877 |
OMT |
\({5.10}^{-3}\) |
||
EAT |
\({2.10}^{11}\) |
||
C1N1=C1N2=C1N3 =C2N1=C2N2=C2N3 |
\(\mathrm{87,3}{.10}^{6}\) |
||
C 1M1 =C1M2=C1M3 =C1M3 =C2 M 1=C2M2=C2M3 |
\(\mathrm{14,8}{.10}^{6}\) |
||
1.3. Boundary conditions and loading#
The pressure imposed on the upper slab follows this pattern over time:
Pressure
0.0171
0.001
0.017
Time (s)
The base rests on a carpet of ground springs (type K_ TR_D_N) defined with the RIGI_PARASOL AFFE_CARA_ELEM keyword. The six components of the overall input stiffness are equal to:
\(\begin{array}{c}\mathit{Kx}\mathrm{=}\mathrm{0,13572}{.10}^{12}\mathit{Pa}\\ \mathit{Ky}\mathrm{=}\mathrm{0,13428}{.10}^{12}\mathit{Pa}\\ \mathit{Kz}\mathrm{=}\mathrm{0,13467}{.10}^{12}\mathit{Pa}\\ \mathit{Krx}\mathrm{=}\mathrm{0,24722}{.10}^{15}\mathit{Pa}\\ \mathit{Kry}\mathrm{=}\mathrm{0,22386}{.10}^{15}\mathit{Pa}\\ \mathit{Krz}\mathrm{=}\mathrm{0,30600}{.10}^{15}\mathit{Pa}\end{array}\)
1.4. Limitations imposed by time CPU#
For reasons purely related to a short CPU time for this test case, we will deliberately shorten the total duration that will be simulated numerically during the transitory resolution. This will also induce a moment of switching between the codes that will be located too « early »: the initial regime of rapid dynamic response will not have been transformed into an overall shake-up mode. The test case will therefore have the disadvantage of switching from one diagram to another at an unfavorable moment when the nonlinearities will still be in the propagation phase, which should not be the case for a real industrial study where the shaking phase treated implicitly should remain linear.
Logically, the switch should therefore occur after the imposed pressure returns to 0 (late enough to be in a shaky state), so after \(\mathrm{0,0171}s\). Since condition CFL requires an explicit time step of the order of \(5\mu s\), the number of time steps would be prohibitive for a test case. In order to reduce time CPU, we place the switch much earlier, around \(\mathrm{0,007}s\), so when the pressure imposed is at its maximum plateau. By default, the time step will be \(50\mu s\).
1.5. Strategy for switching Europlexus to Code_Aster#
In this chapter we will discuss two issues:
the rereading and construction of fields to go from the Europlexus resolution (via CALC_EUROPLEXUS) to DYNA_NON_LINE: we will validate this step by comparing explicit calculations (we stick to the schema in the same amount of time between the codes),
the switch from an explicit schema to an implicit schema.
1.5.1. Construction of fields for the pursuit#
The model includes a linear zone and a non-linear zone. On the linear zone, the fields that we will recover at the last moment calculated with Europlexus are the kinematic fields, so only fields at the nodes. The constraints will be recalculated in*Code_Aster*.
On the non-linear zone, two fields must be linked to the additional Gauss points for the constraint and the internal variables related to the material law used: GLRC_DAMAGE. The non-linear zone only includes elements of the Q4GG type on triangular or quadrangular cells.
All fields generated by Europlexus will be re-read from a MED file.
For the continuation with DYNA_NON_LINE (or MACRO_BASCULE_SCHEMA), the following fields are defined as initial state: displacement, speed, acceleration, constraint (throughout the model) and internal variables.
1.5.2. Schema toggle#
We continue the transitional resolution, following Europlexus, in Code_Aster by starting by taking a few steps with the explicit diagram of centered differences, with a lumped mass matrix, in order to remain in the same hypotheses as the Europlexus calculation. Then the transition to an implicit resolution takes place with a specific rebalancing phase within the MACRO_BASCULE_SCHEMA operator. The transitory resolution therefore ends implicitly with a consistent mass matrix and for a time step ten times greater than in explicit.