The thesis passed with and Excellent Cum Laude today, 3rd February 2015, in the Universitat Politecnica de Catalunya.

I would like to thank both my mentors Prof. Jaume Roset (UPC) and Prof. Vojko Kilar (University of Ljubjana), and all those that were with me all along...

Following is the abstract of the thesis:

# Abstract

This thesis explores a very well
understood area of physics: computational structural dynamics. The
aim is to stretch its boundaries by merging it with another very well
established discipline such as structural design and optimization. In
the recent past both of them have made significant advances, often
unaware one of each other for different reasons. It is the aim of
this thesis to serve as a bridging tool between the realms of physics
and engineering.

The work in divided in three parts:
variational mechanics, structural optimization and implementation.

The initial part deals with
deterministic variational mechanics. Two chapters are dedicated to
probe the applicability of energy functionals in the structural
analysis. First, by mapping the state of the art regarding the vast
field of numerical methods for structural dynamics; second, by using
those functionals as a tool to compare the methods. It is shown how,
once the methods are grouped according to the kind of differential
equations they integrate, it is easy to establish a framework for
benchmarking. Moreover, if this comparison is made using balance of
energy the only parameter needed to observe is a relatively easy to
obtain scalar value.

The second part, where structural
optimization is treated, has also two chapters. In the first one the
non-deterministic tools employed by structural designers are
presented and examined. An important distinction between tools for
optimization and tools for analysis is highlighted. In the following
chapter, a framework for the objective characterization of structural
systems is developed. This characterization is made on the basis of
the thermodynamics and energetic characteristics of the system.
Finally, it is successfully applied to drive a sample simulated
annealing algorithm.

In the third part the resulting code
employed in the numerical experiments is shown and explained. This
code was developed by means of a visual programming environment and
allows for the fast implementation of programs within a consolidated
CAD application. It was used to interconnect simultaneously with
other applications to seamlessly share simulation data and process
it. Those applications were, respectively, a spreadsheet and a
general purpose finite element.