FEM ConstraintDisplacement/pl

Description
Creates a FEM constraint for a prescribed displacement of a selected object for a specified degree of freedom.

Usage

 * 1) Either press the button   or select the menu.
 * 2) In the 3D view select the object the constraint should be applied to, which can be a vertex (corner), edge, or face.
 * 3) Press the  button.
 * 4) Uncheck Unspecified to activate the necessary fields for edition.
 * 5) Set the values or  specify a formula for the displacements.

General
For the solver Elmer it is possible to  define the displacement as a formula. In this case the solver sets the displacement according to the given formula variable.

Take for example the case that we want to perform a transient analysis. For every time step the displacement $$d$$ should be increased by 6 mm:

$$\quad d(t)=0.006\cdot t $$

enter this in the Formula field:

This code has the following syntax:
 * the prefix Variable specifies that the displacement is not a constant but a variable
 * the variable is the current time
 * the displacement values are returned as Real (floating point) values
 * MATC is a prefix for the Elmer solver indicating that the following code is a formula
 * tx is always the name of the variable in MATC formulas, no matter that tx in our case is actually t

Rotations
Elmer only uses the Displacement * fields of the constraint. To define rotations, we need a formula.

If for example a face should be rotated according to this condition:

$$\quad \begin{align} d_{x}(t)= & \left(\cos(\phi)-1\right)x-\sin(\phi)y\\ d_{y}(t)= & \left(\cos(\phi)-1\right)y+\sin(\phi)x \end{align} $$

then we need to enter for Displacement x

and for Displacement y

This code has the following syntax:
 * we have 4 variables, the time and all possible coordinates (x, y z)
 * tx is a vector, tx(0) refers to the first variable, the time, while tx(1) refers to the first coordinate x
 * pi denotes $$\pi$$ and was added so that after $$t=1\rm\, s$$ a rotation of 180° is performed