Response History Analysis of An Elastic Coupled Wall¶
In this page, we perform eigen analysis and response history analysis of an elastic coupled wall model.
The wall model is a simplified version of the example shown in section 7.2 of this paper: 10.1016/j.engstruct.2020.110760.
The model can be downloaded.
Model Brief¶
The geometry is summarized in the following figure.
Definitions of nodes, elements, materials, boundary conditions are stored in node.supan
and element.supan
. Use
proper commands to load files.
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Eigen Analysis¶
Before performing the eigen analysis, the system is double-checked to be symmetric. In fact, as eigen analysis is normally conducted on elastic structures, which are most likely to be symmetric, it is in general not problematic as long as elasto-plastic behavior is not involved.
Now we define a Frequency
step to compute ten eigenvalues of the generalized eigen problem.
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Invoke analysis and check the eigenvalues.
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The output is shown as follows.
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Thus, the period of the first mode can be computed as
Response History Analysis¶
Ground Motion¶
We use one of the recordings of 2011 Christchurch Earthquake, the original raw recording can be obtained from
this page. Please
check NZStrongMotion for more details. The chosen record has a
tag of 20110221_235142_LPCC
, the PGA is \(\(8.91~\mathrm{m/s^2}\)\).
After downloading the processed recording file, the following command can be used to define the amplitude.
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The acceleration is applied to the structure, note NZStrongMotion
produces normalized (dimensionless) amplitudes, to
apply an accelerogram of target PGA, the corresponding magnitude shall be adjusted to be equal to that PGA. In this
example, we assign a PGA of \(\(0.4g\)\).
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Damping Model¶
The Lee’s damping model is chosen as an illustration. Knowing that \(\(\omega_1=\sqrt{367.59}=19.17~\mathrm{rad/s}\)\), we assign a single basic function at \(\(\omega_1\)\) with \(\(5\%\)\) damping ratio.
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Other Settings¶
We define a dynamic step and perform the analysis with the time step of \(\(0.005~\mathrm{s}\)\) for \(\(60~\mathrm{s}\)\).
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Some Stats¶
This example consists of \(\(83\)\) nodes, equivalent to \(\(249\)\) DoFs. With one basic function used in the damping model, the size of matrix solved is about \(\(500\times500\)\). On recent machines, the response history analysis can be done within one minute. The solving time increases almost linearly with an increasing number of basic functions used in the damping model.
Result¶
We show roof displacement history to close this example.