Indiana University-Purdue University Indianapolis (IUPUI) / Topology optimization allows designers to obtain lightweight structures considering the binary distribution of a solid material. The introduction of cellular material models in topology optimization allows designers to achieve significant weight reductions in structural applications. However, the traditional topology optimization method is challenged by the use of cellular materials. Furthermore, increased material savings and performance can be achieved if the material and the structure topologies are concurrently designed. Hence, multi-scale topology optimization methodologies are introduced to fulfill this goal. The objective of this investigation is to discuss and compare the design methodologies to obtaining optimal macro-scale structures and the corresponding optimal meso-scale material designs in continuum design domains. These approaches make use of homogenization theory to establish communication bridges between both material and structural scales. The periodicity constraint makes such cellular materials manufacturable while relaxing the periodicity constraint to achieve major improvements of structural performance. Penalization methods are used to obtain binary solutions in both scales. The proposed methodologies are demonstrated in the design of stiff structure and compliant mechanism synthesis. The multiscale results are compared with the traditional structural-level designs in the context of Pareto solutions, demonstrating benefits of ultra-lightweight configurations. Errors involved in the mult-scale topology optimization procedure are also discussed. Errors are mainly classified as mesh refinement errors and homogenization errors. Comparisons between the multi-level designs and uni-level designs of solid structures, structures using periodic cellular materials and non-periodic cellular materials are provided. Error quantifications also indicate the superiority of using non-periodic cellular materials rather than periodic cellular materials.

Indiana University-Purdue University Indianapolis (IUPUI) / Our ability to engineer materials is limited by our capacity to tailor the material’s microstructure morphology and predict resulting properties. The insufficient knowledge on microstructure-property relationship is due to complexity and randomness in all materials at different scales. The objective of this research is to establish a design optimization methodology for microstructured materials. The material design problem is stated as finding the optimum microstructure to maximize the desired performance satisfying material processing constrains. This problem has been solved in this thesis by means of numerical techniques through four main steps: microstructure characterization, model reconstruction, property evaluation, and optimization. Two methods of microstructure characterizations have been investigated along with the advantages and disadvantages of each method. The first microstructure characterization method is a statistical method which utilizes correlation functions to extract the microstructural information. Algorithms for calculating these correlations functions have been developed and optimized based on their computational cost using MATLAB software. The second microstructure characterization method is physical characterization which works based on evaluation of physical features in microstructured domain. These features have been measured by means of MATLAB codes. Three model reconstruction techniques are proposed based on these characterization methods and employed to generate material models for further evaluation. The first reconstructing algorithm uses statistical functions to reconstruct the statistical equivalent model through simulating annealing optimization method. The second algorithm uses cellular automaton concepts to simulate the grain growth utilizing physical descriptors, and the third one generates elliptical inclusions in a material matrix using physical characteristic of microstructure. The finite element method is used to analysis the mechanical behavior of material models. Several material samples with different microstructural characteristics have been generated to model the micro-scale design domain of AZ31 magnesium alloy and magnesium matrix composite with silicon carbide fibers. Then, surrogate models have been created based on these samples to approximate the entire design domain and demonstrate the sensitivity of the desired mechanical property to two independent microstructural features. Finally, the optimum microstructure characteristics of material samples for fracture strength maximization have been obtained.

[pt] Estruturas treliçadas espaciais são arranjos geométricos de barras amplamente utilizados em coberturas de edificações. Diversos fatores favorecem o seu uso, tais como a capacidade de vencer grandes vãos e a facilidade em assumir diversas formas. A busca pela geometria ótima é um objetivo importante no projeto de estruturas, onde o interesse principal é minimizar o custo da estrutura. O objetivo deste trabalho é apresentar um sistema computacional capaz de minimizar o peso de estruturas treliçadas cuja geometria é definida por curvas de Bézier. Portanto, os pontos de controle das curvas de Bézier são utilizados como variáveis de projeto. As áreas das seções transversais das barras e a altura da treliça também são consideradas como variáveis de projeto e restrições sobre a tensão de escoamento e a tensão crítica de Euler são impostas no problema de otimização. A estrutura é analisada por meio do método dos elementos finitos considerando a hipótese do comportamento linear físico e geométrico. Os algoritmos de otimização usados neste trabalho utilizam o gradiente da função objetivo e das restrições em relação às variáveis de projeto. O sistema computacional desenvolvido neste trabalho foi escrito em linguagem MATLAB e conta com uma integração com o SAP2000 por meio da OAPI (Open Application Programming Interface). Os resultados numéricos obtidos demonstram a eficiência e a aplicabilidade deste sistema. / [en] Spatial truss structures are geometrical arrangements of bars widely used in building roofs. Several factors favor their use, such as the ability to overcome large spans and the capability of assuming a variety of configurations. The search for optimal geometry is an important goal in the design of structures, where the main interest is to minimize the cost of the structure. The objective of this work is to present a computational system capable of minimizing the weight of truss structures whose geometry is defined by Bézier curves. Therefore, the control points of the Bézier curves are used as design variables. The cross-sectional areas of the bars and the truss height are also considered as design variables and constraints on the yield stress and Euler critical stress are imposed on the optimization problem. The structure is analyzed using truss elements considering the physical and geometric linear behavior. The optimization algorithms used in this work require the gradient of the objective function and constraints with respect to the design variables. The computational system developed in this work was written in MATLAB and has an integration with SAP2000 through the OAPI (Open Application Programming Interface). The obtained numerical results demonstrate the efficiency and applicability of the developed system.

El objetivo de esta Tesis es el diseño de algoritmos robustos y flexibles que permitan automatizar el diseño óptimo de los pórticos de hormigón armado habitualmente empleados en edificación y extraer conclusiones generales sobre las estructuras optimizadas. El trabajo define un esquema general para la optimización monoobjetivo (coste económico) y multiobjetivo de estas estructuras que es aplicado a pórticos planos con un máximo de 153 variables. Entre ellas figuran seis calidades diferentes de hormigón. Para minimizar el coste económico se prueban cinco métodos heurísticos: una Estrategia de Saltos Múltiples Aleatorios (RW), el Gradiente First Best (FB), la Cristalización Simulada (SA), la Aceptación por Umbrales (TA) y los Algoritmos Genéticos (GA). Estas técnicas se utilizan en una primera fase para optimizar un pórtico de dos vanos y cuatro plantas sometido a acciones verticales y horizontables. La versión desarrollada de SA proporciona el diseño de mayor calidad, cuyo coste es de 3473.06 . Los mejores proyectos obtenidos mediante las variantes creadas de TA, FB, GA y RW tienen costes mínimos superiores en un 0.52%, 5.74%, 8.69% y un 124.6% respectivamente. Por estos motivos se elige SA para, en una segunda fase, optimizar económicamente otros pórticos de dos vanos y dos, seis y ocho plantas. Los resultados obtenidos permiten proponer reglas para el predimensionamiento de las estructuras optimizadas y automatizar la elección de los parámetros del algoritmo SA, lo que evita largos procesos de ensayo y error. Se comprueba que los estados límites habitualmente empleados en el diseño de esta tipología estructural son también suficientes para comprobar la seguridad de las estructuras optimizadas. Asimismo se investiga la repercusión económica del empleo de un único tipo de hormigón (un HA-25 con resistencia de proyecto a compresión igual a 25 MPa) y de la utilización de vigas planas en lugar de descolgadas. En el caso del pórtico de ocho plantas, el uso exclusivo / Payá Zaforteza, IJ. (2007). Optimización heuristica de pórticos de edificación de hormigón armado [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/4161