This is an advanced model example showing how
can be implemented and modeled with FEATool. The model has been
developed and kindly shared to us by Prof. Shintaro Yamasaki at the
Department of Mechanical Engineering of Osaka University .
In contrast to standard simulations where the domain and geometry is
known, in topology optimization the problem is reversed and asks what
the best shape is for a set of constraints. In the following a
material in a plane stress condition fixed to the left wall is being
pulled down from the lower right edge, and the question is where to
optimally allocate material within the rectangle.
To solve this problem the custom PDE equations
have been used. One for the plane stress structural mechanics problem,
one for the material fraction per cell, and two additional equations
for the design variable and node wise filtered material
distribution. As this model features very advanced customization and
usage it will not be described in further detail but the interested
reader can inspect the linked source code.
The images and video below show how the material distribution looks
like after a few iterations. One can clearly see how the optimal shape
eventually takes on the form of a triangular truss.
A MATLAB m-script for the topology optimization model example can be
downloaded from the link below. The model depends and requires the
linear programming solver which is available with the
MATLAB optimization toolbox.
 Kawamoto, A., Matsumori, T., Yamasaki, S. et
al., Heaviside projection based topology optimization by a
PDE-filtered scalar function. Structural and Multidisciplinary
Optimization., Volume 44, Issue 1, pp 19-24, Springer-Verlag, 2011.