## Interface

Flex2D consists of two views: 1. A "Loads" view, and 2. A "Flexure" view. You can choose any of these views by either clicking the tabs on top of the window, using the "Modules" menu, or typing ⌘1 or ⌘2 for the "Loads" or the "Flexure" view respectively.

Flex2D is a "Document based application". You can open as many documents as you want.

### The "Loads" view

In the "Loads" view (Figure 4) you can enter and visualize the loads. You can add or remove loads by either clicking the "Add" or "Delete" buttons, choosing the Add or Delete submenus in the Loads menu, or typing ⌘= (add) or ⌘- (delete). For a description of the parameters needed for defining a load see the conventions section.

Figure 4. The "Loads" view

When entering the loads, you can undo (Undo submenu in the Edit menu or ⌘z) or redo (Redo submenu in the Edit menu or ⇧⌘z) changes.

You will notice that the program by default automatically draws the loads if they have been entered correctly (see the conventions section). This behavior can be changed in the Preferences panel. If the "Automatically draw loads" checkbox is unselected in the Preferences Panel, the "Draw" button, and the "Draw" submenu under the "Loads" menu, will be enabled. Loads can then be drawn by either clicking the "Draw" button, choosing the "Draw" submenu, or typing ⇧⌘d.

Adding loads from the pasteboard or a text file:

If you find annoying to enter loads in the application's table, you can add the loads from the pasteboard or using a text file. Open a text editor or a spreadsheet program (e.g. Excel). Enter the loads as in Flex2D. If in a text editor, use spaces, commas, or tabs to separate the entries of a load, and the return key to start a new load. When finished, you can either copy the contents of the file and paste them in to the Loads table, or save the file as a text file (plain text document). Then you can drag the text file into the Loads table. If entered correctly, the loads will be added to the Loads table. Dragging and dropping a file only works with a text file (plain text document).

Flexing the profile:

Once you have entered the loads, you can flex the profile by either clicking the "Flex" button, choosing the Flex submenu in the Units menu, or typing ⇧⌘f. The program will automatically switch to the "Flexure" view and show the deformed profile.

Notice that Flex2D does not automatically update the "Flexure" view according to changes in the "Loads" view. To update the Flexure view you need to flex the profile (i.e. click the flex button).

You can save the loads data by either choosing the Save submenu in the File menu, or typing ⌘s. The program will then create a file with extension flex2d.

#### The "Flexure" view

Before applying the loads, the "Flexure" view is not very exciting. It shows just a blank graph and a table without data. When you flex the profile (click the flex button, or choose the flex submenu), the program automatically chooses the "Flexure" view. Both, the deformed topography (by default black) and the displacement profile (by default red) are shown in a graph and in a table (Figure 5). The table rows for the maximum (basin axis) and minimum (forebulge) deflection are shown in red and blue respectively.

Figure 5. The "Flexure" view

You can toggle on and off the topography and deflection curves using the buttons below the table. You can move the mouse over the flexure graph to see its coordinates.

### Setting Parameters and Editing Plots

You can set the model parameters, edit the graphs, or change the properties of lines using the "Inspector" panel ( "Inspector" submenu in the Tools menu, or key combination ⇧⌘i). The model parameters can be set in the "Parameters" view, the plots can be edited in the "Plot " view, and the properties of lines can be edited in the "Lines" view of the Inspector (Figure 6).

Figure 6. The Inspector panel and its views. Parameters view (upper left). Plot view (upper right). Lines view (lower left).

In the Parameters view, you can set the type of solution: Infinite or semi-infinite beam. The infinite beam solution uses an elastic beam that extends infinitely along the x axis (positive and negative x values). The semi-infinite beam has a free end at x = 0, and extends infinitely in the positive x direction. When the semi-infinite beam solution is selected, loads with x coordinates lower than zero are not considered in the computation. Flex2D uses by default the infinite beam solution.

In the Parameters view, you can also specify the model parameters: i. The parameters of the elastic lithosphere: Young Modulus, Poisson's ratio, and elastic thickness. ii. The density of the foundation, and iii. The x interval at which the deflection is computed. The density of the foundation is the difference between the density of the mantle and the density of the material filling the basin. You can set this value to simulate: i. No material filling the resultant depression, ii. water filling the resultant depression, or iii. sediments filling the resultant depression (see conventions section). By default the density of the foundation is the density of the mantle: 3300 kg/m3. This corresponds to the case of no material filling the basin.

The elastic thickness can be set to constant or variable. By default Flex2D uses a constant elastic thickness. If you chooose the constant elastic thickness option (Figure 6, upper left), you can enter the elastic thickness in the corresponding text field. If you choose the variable elastic thickness option, you will be able to edit the elastic thickness along the profile by clicking the "Edit" button (Figure 6, upper left). This will open a sheet where you can enter the elastic thickness along the profile by either: (i) clicking on the graph, (ii) entering points along the profile in the table to the left of the graph, or (iii) dropping in the table a text file with 2 columns corresponding to the x locations and values of Et (Figure 7). The graph and the table are linked, so any change you make in the graph is reflected in the table, and vice versa. You can use the graph to roughly enter the variation of elastic thickness, and then edit the entries in the table to exactly fit the desired elastic thickness profile. Alternatively as said above, you can make a text file with the location (1st column) and values of Et (2nd column) and drop this file into the table. That is easier if there are many points with Et values along the profile.

Figure 7. The sheet used to enter the elastic thickness variation along the profile.

The equations for the deflection of elastic, infinite and semi-infinite beams of constant thickness are from Hetenyi (1946). The equations for the deflection of elastic, infinite and semi-infinite beams of variable thickness are from Bodine (1981). For the same constant elastic thickness and same load distribution, the Hetenyi and Bodine solutions are quite close although they don't give exactly the same results. This is because Hetenyi's solution is analytical while Bodine's is numerical (based on finite differences), and also because in Hetenyi's solution, loads are entered as columns, while in Bodine's solution, loads change continuously along the profile. The last difference will be less marked as the width of the columns is reduced. A short description of the equations is given in the formulas section.

The use of the Inspector is straightforward. It is a great way to see the effect of changing model parameters. Input the loads, flex the profile, open the Inspector and in its Parameters view change the elastic thickness for example. The program will automatically update the flexure graph and table for the new elastic thickness.

The Inspector can also be used to change the extent (horizontal or vertical) of the model. Change the values of the Xmin, Xmax, Ymin, and Ymax fields in the Plot view of the Inspector. The program will automatically update the graphs and tables according to the new values. If using the semi-infinite solution, please notice that you won't be able to set the minimum x coordinate of the plots below x = 0.

Editing your graphs for publications or presentations is very easy. Try experimenting with both the "Plot" and "Lines" views of the inspector. Notice that you can choose the line (loads, topography or deflection) to be modified using the first pop-up button in the Lines view of the Inspector.

Changes in the Inspector affect the selected document and vice versa. The settings in the Inspector are saved to flex2d files so these files open with the same settings they had when they were saved. flex2d files contain, however, only the Input loads and the Inspector settings. After opening a flex2d file, you will have to flex the profile (press the flex button) to see results in the flexure view.

### Saving Plots

You can save the plots produced by Flex2D as pdf. Just choose the Save Plot as PDF submenu in the File menu.

### Dragging and Copy/Paste

You can drag plots to vector programs (e.g. Illustrator, Intaglio), and the content of the tables to text editors and spreadsheet programs (e.g. TextWrangler, Excel). You can also drag these elements to the Finder to make a pdf of a plot, or a text clipping of the selected data. You can also copy and paste table data (e.g. to Excel) using the copy (⌘c) and paste (⌘v) submenus.

Figure 8. Dragging plot to text edit

### Preferences Panel

You can set whether or not the program draws the loads automatically or open a new document at launch, through the Preferences panel (Figure 9).

Figure 9. The preferences panel