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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 Cross-Section Coordinates.

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 Model

Add and connect the blocks to represent the dome. Include a Solver Configuration block so that you can visualize the solid in Mechanics Explorer during the modeling process.

  1. Drag these blocks into a new model.

    LibraryBlockQuantity
    Body ElementsSolid1
    Simscape™ UtilitiesSolver Configuration1

  2. Connect the blocks as shown.

  3. In the Solid block dialog box, specify these parameters.

    ParameterValue
    Geometry > ShapeSelect Revolution
    Geometry > Cross-SectionEnter CS. Specify units of cm.
    Graphic > Visual Properties > ColorEnter RGB

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

Specify Parameter Values

In the subsystem mask, initialize the solid parameters. Then, in the subsystem dialog box, specify their values.

  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 three edit boxes into the Parameters group and specify these parameters.

    PromptName
    RadiusR
    Wall ThicknessT
    ColorRGB

  3. In the Initialization tab of the Mask Editor, enter the initialization code for the xsection variable.

    % 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 these parameters.

    ParameterValue
    Radius (in)1
    Wall Thickness (in)0.1
    Color [R G B][0.85 0.45 0]

Visualize Model

You can now visualize the dome that you modeled. To do this, on the Simulink® menu bar, select Simulation > Update Diagram. Mechanics Explorer opens with a 3-D display of your model. Rotate, pan, and zoom to explore.

Try modifying the dome geometry. To do this, in the subsystem dialog box, change the dimension parameter values. Then, update the model. The figure shows some examples.

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