Variational mechanics and stochastic methods applied to structural design
Authors:   , Andujar Moreno Rabindranath 
Published: October 2023

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.
La presente tesis explora un area de la fisica ampliamente establecida: dinamica computacional de estructuras. El proposito es expandir los limites de la misma mediante la combinacion con otra disciplina como es el diseño y la optimizacion estructurales. Recientemente, ambas han experimentado avances significativos que, frecuentemente, han ocurrido de forma ajena una de la otra. Esta tesis busca servir de nexo entre el campo de la fisica y la ingenieria. El trabajo esta dividido en tres partes: mecanica variacional, optimizacion estructural e implementacion de una aplicacion de software para su uso en la practica real. La parte inicial trata la mecanica variacional desde el punto de vista determinista. Se dedican dos capitulos a demostrar la aplicabilidad de los funcionales energeticos en el analisis estructural. Primero, se hace un recorrido por el estado del arte de los metodos numericos para dinamica estructural; posteriormente, se emplean estos funcionales para comparar dichos metodos de forma objetiva y eficaz. Se demuestra como, una vez que los metodos han quedado agrupados de acuerdo al tipo de ecuaciones diferenciales que resuelven (ordinarias, parciales o algebraicas), es facil crear un marco de referencia para su evaluacion. Al hacerse la comparacion mediante equilibrio energetico el resultado es un valor escalar cuyo manejo es relativamente facil de interpretar. La segunda parte, donde se trata la optimizacion estructural, abarca tambien dos capitulos. En el primero se presentan y examinan las herramientas no deterministas utilizadas por los diseñadores estructurales y se pone de relevancia la importante distincion entre las herramientas de analisis y las de optimizacion. A continuacion, se desarrolla un marco para la caracterizacion objetiva de sistemas estructurales elaborado sobre la base de la mecanica estadistica y las caracteristicas energeticas de las estructuras. Finalmente, el marco se combina con un algoritmo de "Simulated Annealing" para la optimizacion de estructuras. En la tercera parte de la tesis el codigo resultante empleado en los experimentos numericos de los capitulos anteriores queda explicado. Este codigo, desarrollado mediante herramientas de programacion visual, permite la rapida implementacion de aplicaciones dentro de un entorno de CAD. para su posterior aplicacion a problemas reales.