Functions y=f(t)

Functions are quite useful to describe how some parameters evolve, over time for example. They can be used to prescribe displacements or to define hardening laws.

A piecewise linear function is defined one point at a time:

  fct = PieceWiseLinearFunction()
  fct.setData(abs1, ord1)
  fct.setData(abs2, ord2)
  ...

where

Remark: As can be seen above, the first and last segments are extrapolated if a value of the function is required outside its domain.

The CyclicPieceWiseLinearFunction allows to duplicate infinitely a PieceWiseLinearFunction.

2 constrains are applied on Data :

1. the first abcisse must be equal to 0.0 (abs1 = 0.0)
2. the cycle must be closed (ord1 = ordLast)

If a function is mathematically too complex to be defined with a PieceWiseLinearFunction, it can be defined analytically, with a PythonOneParameterFunction object.

def f(x):
    [function calculating y=f(x)]
    return y
fct1 = PythonOneParameterFunction(f)

For example, this is used to:

• Set the node density for a 1D mesher (1D Meshers (Curves)).
• define elaborated prescribed displacements (Prescribed Displacements).
• Define a hardening function with Python (General Points).

The ramp function:

  fct1 = PieceWiseLinearFunction()
  fct1.setData(0,0)
  fct1.setData(1,1)

can be also defined with a classical python function:

  def f(x):
      return x
  fct1 = PythonOneParameterFunction(f)

or, using python lambda function:

  f = lambda x: x
  fct1 = PythonOneParameterFunction(f)

The value can also be displayed for each estimation, and a more complex function can also be defined using all Python tools. For example, a load function can be first defined with a parabola, then with a straight line, the change between these two being controlled by an conditional structure.

  def f(a):
      val=0
      if(a‹0.5):
           val=a*a
      else:
           x=0.5*0.5;
           val=x+(a-0.5)/(1-0.5)*(1-x)
      print 'value=', val
      return val	
  fct1 = PythonOneParameterFunction(f)