Maria Bayard Dühring - Solid Mechanics

Chapter 7
Concluding remarks
The work presented in this Ph.D. thesis is a contribution to the continuously growing
research field of optimization of elastic and optical wave propagation. Three different
types of wave devices have been simulated and their performances have been
improved either by topology optimization or parameter studies of the geometry. The
first problem treated structures for sound reduction, the other was concerned with
the energy flow of optical waves in holey fibers, and finally the interaction between
surface acoustic waves and optical waves in waveguides was studied. By investigating
the waves propagating in the optimized structures, an increased understanding of
their physical behavior and the function of the devices were obtained. The acquired
knowledge could be employed to fabricate devices with improved efficiency.
It is explained, that even though the three investigated problems describe very
different physical phenomena, they can all be described in a similar way by second
order differential equations. The time dependency is eliminated as a harmonic time
variation can be assumed, and this simplifies the implementation, solving and optimization.
The high-level programming language Comsol Multiphysics was found
suitable for simulating the studied two-dimensional problems by the finite element
method. The implementation time can be reduced with this software, because the
differential equations are either predefined or can be specified in a straightforward
manner and the discretization, meshing and solving are automated. The code can
be extended with Matlab scripting such that studies of geometry parameters and
the call to the MMA optimization-algorithm can be performed. The program is
however not suited for solving bigger 3D problems due to high memory usage.
The method of topology optimization has successfully been applied to the three
types of wave problems. They are defined in a similar way and it was shown that a
generic formulation of the optimization problem was suitable for all the wave problems
with similar expressions for the objective functions and the interpolation functions.
By applying continuation methods and a close-type Heaviside morphologyfilter,
well defined designs with vanishing gray transition zones at the interfaces
between air and solid material were in general obtained. The optimized designs
guide and control the propagating waves such that objective function is optimized,
and they indicate how much the performance can be increased with unrestricted
design freedom. It is therefore concluded that the presented topology optimization
method works well for the three wave propagating problems. However, the
optimization problems are in general sensitive to factors as the initial guess, move
limit, tolerance, filter size and continuation method. So even though essentially the
same formulation of the topology optimization can be employed for the considered
problems, many different factors must be varied and tested in order to get suitable
55