Visual Instruction of Shape Function and Interpolation

  

Basic usage of the function

Described in this section is the basic usage of the function which includes forming and displaying the interpolation model, and also view transformation and rendering options for better visualization.

Starting the function

The following few steps are necessary to start displaying shape functions and their derivatives.

 

1) Create elements with shape function to be examined.

Generate mesh with elements of the shape and the order for which the desired shape function is employed.
 

2) Assign element properties.

Only elements assigned with element properties are valid for displaying their shape functions.
 

3) Select ¡°Shape Function¡± item from ¡°Stiffness¡± submenu of menu.

¡°Shape Function¡± window appears on the screen, and menu is attached to the menu bar.

Ending the function

The function is terminated by closing ¡°Shape Function¡± window. Clicking the close box of the window will close the window. The function may also be terminated by starting any other menu function. menu also disappears from the menu bar as the function terminates.

Forming the interpolation model

The shape functions and their derivatives may be displayed either for a single element independently or for two or more elements in combination. The formation of element(s) for shape function is termed here as ¡°Interpolation model.¡± An interpolation model is formed simply by selecting one or more element(s) from the mesh displayed on the main window. Elements may be added or removed from the interpolation model by selecting or unselecting the elements using shift click, even if the shape function or the derivative of the model is already displayed.

Setting the rendering mode

There are 3 different modes of rendering the shape function: wireframe, shading and contouring. The mode can be set by choosing the corresponding item from menu.

 

¡°Display by Wireframe¡± : Choose this item to render the shape function in wireframe. The grid lines of the interpolation model are drawn with hidden line removal.
  ¡°Display by Shading¡± : Choose this item to render the shape function in shading. The interpolation model is rendered by smooth shading.
  ¡°Display by Contour¡± : Choose this item to render the shape function by contour. The interpolation model is re p resented by contour line. This rendering option is useful especially for examining the inter- element continuity of the shape function derivatives.

There appears check mark in front of the menu item set for the rendering mode.

< Modes of rendering the interpolation mode >

Turning on or off supplementary lines in rendering

Supplementary lines may be added to therer rendered image of the interpolation model to improve its visual clarity. Choose the following items from menu to turn on or off the corresponding supplementary lines.

  ¡°Show Base Plane Edges¡± : A base plane is the plane formed by the actual elements of the interpolation model. Edges of the base plane are displayed if this menu item has check mark in front.
  ¡°Show Model Edges¡± : Edges of the interpolation model are displayed if this menu item has check mark.
 

¡°Show Node Legs¡± : Node leg is a line drawn from a node of the interpolation model to the base plane. Node legs are displayed if this menu item has check mark in front.

<Supplementary lines for the interpolation model >

Enlarging or reducing the value scale

The shape function or its derivative is expressed graphically as the height of the interpolation model over the base plane. The value scale implies the height re p resenting unit value of the shape function or its derivatives. If the scale is larger, the interpolation model is represented as a more steep surface.

The value scale can be adjusted. The scale is enlarged by choosing "Enlarge Scale" item, and reduced by choosing ¡°Reduce Scale¡± item from menu.

< Adjusting value scale >

Increasing or decreasing the grid lines of interpolation model

If the rendering mode is set as ¡°Display by Wireframe,¡± the interpolation model is represented by a number of grid lines. If necessary for better visualization, the number of grid lines can be adjusted. The number of grid lines increases, if ¡°Increase Grid Lines¡± item is selected from menu, and decreases, if ¡°Decrease Grid Lines¡± item is selected.

< Adjusting grid density >

Transforming the view of the interpolation model

The interpolation model is initially displayed on ¡°Shape Function¡± window, with the same view transformation as that of the main window. The model is centered on the window. This view may be rotated, zoomed, or panned for better visualization. These view transformations can be achieved in the same way as transformation of the finite element mesh on the main window. However, the view transformation affects only the ¡°Shape Function¡± window, but not the main window, while "Shape Function" window is opened.

Rotation: Rotate the virtual track ball on the tool palette as shown left.

Zooming in/out: Adjust the zoom dial or click the zoom button .
Panning: Use option drag to pan the image on "Shape Function" window. In other words, press option key and click a point in the window(Windows: click with right mouse button). Then, the cursor turns into .

Drag the mouse with button pressed. The entire image on the window moves following the cursor. The movement ends and the shape of the cursor returns to , when the mouse button is released.

For more detailed description on the use of the tool palette, refer to the "View Control" section in Chapter 2.

Scrolling, resizing and zooming the window

The contents of ¡°Shape Function¡± window can be scrolled using horizontal or vertical scroll bars. The window may be resized or zoomed if necessary, by dragging the resize box or clicking the zoom box of the window.