Problem 2
Generate appropriate constraint set for connecting the two elements.
To properly tie the two elements together, it is necessary to establish displacement relationships
between nodes 1, 2 and 3. Without constraints, node 3 is free to rotate without any resistance.
For horizontal and vertical translation, a simple linear interpolation can ensure node 3 will always be on
a line from node 1 to node 2. U and V refer to horizontal and vertical directions respectively.
The following variables are defined:
Constrain node 3 in the horizontal and vertical directions.
To tie the rotation of node 3 to the vertical and horizontal displacements of nodes 2 and 3 use the
following relationship:
This formula works very well for a small angle β, and shows good coorelation to up to 30 degrees. For an
angle of 30 degrees, plotting the subsequent displacements of nodes 1 and 2 and then calculating β
yields an angle of 28.476.
To develop the constraint set for this problem,assemble to fit the matrix equation:
Where Um is the dependent variable vector and Un is the independent variable
vector.
Problem 2 BLE
Problem 2 BLE