Extract sub-model

The Model > Coordination tools > Extract sub-model feature allows a sub-model to be extracted from GSA, so that the sub-model can be investigated in more detail. There are two aspects to the sub-model: the elements that form the sub-model and the tasks that are to be associated with the sub-model.

The nodes that form the sub-model and the nodes that form the boundary between the sub-model and the remainder of the model are identified. A new model is then created for the sub-model. Nodes on the boundary are fully restrained. Properties are copied directly. Constraints and loading are updated to include only those associated with the sub-model. Tasks are updated based on the tasks selected for the sub-model.

Definition

Titles

The titles and job details to include in the new model

Sub-model and tasks

This selects the part of the model to be extracted, and the analysis tasks whose results are required. For dynamic tasks there are option for global versus local treatments See below.

Options

There are a number of options to guide the creation of the sub-model. The most significant is the option to trim rigid constraints that cross the boundary introduced by the sub-model.

Static analysis tasks

For static analysis tasks the displacements at the boundary nodes are extracted for each analysis case. These are then applied in a new load case as settlements, and the analysis cases updated to include these settlements.

Modal dynamic and Ritz analysis cases

For dynamic tasks there is the option of Local or Global response.

Local

If the mode is predominantly local it may be more appropriate to consider the boundary of the sub model as fixed and to carry out a modal analysis of the sub-model. In this case the model extraction is straightforward. In this case the analysis task is copied directly.

Global

It is not possible to carry out a sub-model modal analysis when the mode is global. In this case the modal results are used to create a set of static loads.

The modal analysis of the full model gives us eigenvalues and eigenvectors which satisfy:

$$K \varphi_{i}-\lambda_{i} M \varphi_{i}=0$$

This can be rearranged in the form

$$K \varphi_{i}=\lambda_{i} M \varphi_{i}$$

Which we can consider as a static (pseudo modal) analysis of

$$K \varphi_{i}=p_{i}$$

Where

$$p_{i}=\lambda_{i} M \varphi_{i}$$

When extracting the sub-model the frequency (eigenvalue) and mode shape (eigenvector) can be used to create a set of node loads:

$$\begin{gathered} { }^{n} p_{i}=\lambda_{i}{ }^{n} M^{n} \varphi_{i} \\ { }^{n} p_{i}=\left(2 \pi f_{i}\right)^{2} \cdot{ }^{n} M^{n} \varphi_{i} \end{gathered}$$

The modal task in the full model is mapped to a static task in the sub-model. As for the static analysis the displacements at the boundary nodes are used to determine settlements at the boundary nodes and the inertia loads are saved as node loads. The static analysis of these loads will then recover the mode shapes of the original model.

Response spectrum analysis

Response spectrum analysis is a combination of modal results scaled to match a given response spectrum. Extracting the modal results are static load cases means that the dynamic details are lost to the sub-model. To overcome this problem the response spectrum tasks are mapped to pseudo response spectrum tasks. A pseudo response spectrum task assumes that a static analysis case represents a mode shape. The dynamic details are supplied directly to the task in the form of frequency, modal mass and effective masses. When a response spectrum task is extracted from the full model these details are recovered from the modal analysis and included in the pseudo response spectrum analysis task.

Given a shape from a pseudo modal analysis the scaling for each mode $i$, for excitation in the $j$ direction is:

$$u_{i}=\Gamma_{i, j} \frac{a_{s p e c t r a l}}{\left(2 \pi f_{i}\right)_{2}} \varphi$$

Where

$$\Gamma_{i, j}=\sqrt{\frac{\mu_{i, j}}{\widetilde{m}}}$$

If the pseudo modal analysis is carried out using the static procedure above, and the frequency and participation factor are known from the primary model, then the modal contribution to the response spectrum analysis can be estimated. Thereafter the combination is just as for any normal modal analysis.