4. B, C, D, E models

4.1. Boundary conditions and loads

The acceleration condition is a function of time:

\({A}_{0}.\mathrm{sin}(2\pi .\mathit{f.t})\) with \(f=5\mathit{Hz};{A}_{0}=1.0m/{s}^{2}\) for 4 periods i.e. \(t\in [0,\mathrm{0.8sec}]\)

then

\(0\) for \(t\in [\mathrm{0.8sec},\mathrm{3.2sec}]\)

In command DYNA_NON_LINE the time diagram is: for modeling B type NEWMARK (average acceleration).

In command DYNA_VIBRA the time diagram is: for C modeling type EULER, for modeling D type RK54, for modeling E type RK32.

4.2. Tested sizes and results

The quantities tested are displacement and effort.

The displacement and force functions are extracted from the results and subtracted from the displacement and force functions obtained by a method of integrating the problem external to Code_Aster. These new functions are normalized by the maximum value of either movements or efforts. The quantity tested is the maximum deviation.

This gives for the trip:

\(\mathit{Grandeur}\mathit{testée}=\frac{\mathit{Max}[{\mathit{Depl}}_{\mathit{Externe}}(\mathit{Temps})–{\mathit{Depl}}_{\text{Code\_Aster}}(\mathit{Temps})]}{\mathit{Max}[{\mathit{Depl}}_{\mathit{Externe}}(\mathit{Temps})]}\)

Tolerances are by default.

Figure 4.2-a : Responses (displacement over time) calculated by an external method and by Code_Aster with the commands DYNA_NON_LINEet **** DYNA_VIBRA. **

Figure 4.2-b : Responses (strength as a function of time), calculated by an external method and by Code_Aster with the commands DYNA_NON_LINEet DYNA_VIBRA.

Figure 4.2-c : Responses (Force as a function of displacement), calculated by an external method and by Code_Aster with the commands DYNA_NON_LINEet DYNA_VIBRA.