The cantilever beam model

The cantilever beam model describes the vertical deviation of a diving board created by a child diver. It is a widely-use OpenTURNS use case.

We consider a cantilever beam defined by its Young’s modulus E, its length L and its section modulus I. One end of the cantilever beam is built in a wall and we apply a concentrated bending load F at the other end of the beam, resulting in a deviation Y.

The mechanical equation ruling the deviation writes:

$Y = \frac{FL^3}{3EI}$

This model is implemented in Modelica language:

model deviation
  output Real y;
  input Real E (start=3.0e7);
  input Real F (start=3.0e4);
  input Real L (start=250);
  input Real I (start=400);
equation
  y=(F*L^3)/(3.0*E*I);
end deviation;

Note

This model is time-independent: the simulation start and final times do not matter.

We focus on the effect of the E, F, L and I on the deviation Y. Hence four input variables and one time-independent output.