# Documentation

## Model Dome

### Model Overview

You can model a solid of revolution with a round cross-section. One example is the circular dome. In this example, you specify the cross-section coordinates of a circular dome using the MATLAB® `cos` and `sin` functions. For an example that shows you how to model a cone-shaped solid, see Model Cone.

### Modeling Approach

To represent the dome geometry, first identify its cross-section shape. This is the 2-D shape that SimMechanics revolves to obtain the 3-D dome. You can then specify the cross-section coordinates in the Solid block dialog box. These coordinates must satisfy certain restrictions. See Revolution and General Extrusion Shapes.

The dome has a quarter-circle cross-sectional shape. The figure shows this shape.

The [0 0] cross-section coordinate identifies the reference frame origin for this solid. To place the solid reference frame at the dome base center, you specify the coordinates so that the [0 0] coordinate coincides with the base center. By parameterizing the cross-section coordinates in terms of the relevant dome dimensions, you can quickly change the dome dimensions without having to reenter the cross-section coordinates. The figure shows the parameterized cross-section coordinate points.

To define the dome cross-section, first define two angle arrays—one in counterclockwise order, running from 0–90°; the other in a clockwise order running from 90–0°. You can then use the first array to define the outer cross-section coordinates, and the second array to define the inner cross-section coordinates. You do that using the MATLAB `cos` and `sin` functions.

### Build Solid Model

1. At the MATLAB command prompt, enter `smnew`. A new SimMechanics™ model opens with some commonly used blocks. Delete all but the Solid block.

2. In the Solid block dialog box, specify the following parameters. You later initialize the different MATLAB variables in a subsystem mask.

ParameterSelect or Enter
Geometry > Shape`Revolution`
Geometry > Cross-Section`CS`, units of `cm`
Inertia > Density`Rho`
Graphic > Visual Properties > Color`RGB`

3. Select the Solid block and generate a subsystem, e.g., by pressing Ctrl+G.

### Define Solid Properties

1. Select the Subsystem block and create a subsystem mask, e.g., by pressing Ctrl+M.

2. In the Parameters & Dialog tab of the Mask Editor, drag four Edit boxes into the Parameters group and specify these parameters.

PromptName
`Base Radius``R`
`Wall Thickness``T`
`Density``Rho`
`Color``RGB`

3. In the Initialization tab of the Mask Editor, define the cross-section coordinates and assign them to the MATLAB variable `CS`:

```% Circular dome outer coordinates: Alpha = (0:0.01:pi/2)'; OuterCS = R*[cos(Alpha), sin(Alpha)]; % Circular dome inner coordinates: Beta = (pi/2:-0.01:0)'; InnerCS = (R-T)*[cos(Beta), sin(Beta)]; CS = [OuterCS; InnerCS];```

4. In the Subsystem block dialog box, specify the numerical values of the solid properties. The table shows some values that you can enter.

ParameterEnter
Base Radius`1`
Wall Thickness`0.1`
Density`2700`
Color`[0.85 0.45 0]`

### Visualize Solid Model

You can now visualize the dome solid. To do this, look under the Subsystem mask—e.g., by selecting the Subsystem block and pressing Ctrl+U—and open the Solid block dialog box. The solid visualization pane shows the solid that you modeled.

Parameterizing the solid dimensions in terms of MATLAB variables enables you to modify the solid shape without having to redefine its cross-section coordinates. You can change the solid size and proportions simply by changing their values in the Subsystem block dialog box. The figure shows some examples.