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In this paper the parametric design and functional optimisation of thin-walled structures made from plastics for food packaging is considered. These objects are produced in such vast numbers each year that one important task in the design of these objects is to minimise the amount of plastic used, subject to functional constraints, to reduce the costs of production and to conserve raw materials. By means of performing an automated optimisation on the possible shapes of the food containers, where the geometry is parametrised succinctly, a strategy to create the optimal design of the containers subject to a given set of functional constraints is demonstrated.

Metal foam is a relatively new and potentially revolutionary material that allows for components to be replaced with elements capable of large energy dissipation, or components to be stiffened with elements which will generate significant supplementary energy dissipation when buckling occurs. Metal foams provide a means to explore reconfiguring steel structures to mitigate cross-section buckling in many cases and dramatically increase energy dissipation in all cases. The microstructure of metal foams consists of solid and void phases. These voids have random shape and size. Therefore, randomness ,which is introduced into metal foams during the manufacturing processes, creating more uncertainty in the behavior of metal foams compared to solid steel. Therefore, studying uncertainty in the performance metrics of structures which have metal foams is more crucial than for conventional structures. Therefore, in this study, structural application of metal foams considering material and geometrical uncertainty is presented. This study applies the Sobol' decomposition of a function of many random variables to different problem in structural mechanics. First, the Sobol' decomposition itself is reviewed and extended to cover the case in which the input random variables have Gaussian distribution. Then two examples are given for a polynomial function of 3 random variables and the collapse load of a two story frame. In the structural example, the Sobol' decomposition is used to decompose the variance of the response, the collapse load, into contributions from the individual input variables. This decomposition reveals the relative importance of the individual member yield stresses in determining the collapse load of the frame. In applying the Sobol' decomposition to this structural problem the following issues are addressed: calculation of the components of the Sobol' decomposition by Monte Carlo simulation; the effect of input distribution on the Sobol' decomposition; convergence of estimates of the Sobol' decomposition with sample size using various sampling schemes; the possibility of model reduction guided by the results of the Sobol' decomposition. For the rest of the study the different structural applications of metal foam is investigated. In the first application, it is shown that metal foams have the potential to serve as hysteric dampers in the braces of braced building frames. Using metal foams in the structural braces decreases different dynamic responses such as roof drift, base shear and maximum moment in the columns. Optimum metal foam strengths are different for different earthquakes. In order to use metal foam in the structural braces, metal foams need to have stable cyclic response which might be achievable for metal foams with high relative density. The second application is to improve strength and ductility of a steel tube by filling it with steel foam. Steel tube beams and columns are able to provide significant strength for structures. They have an efficient shape with large second moment of inertia which leads to light elements with high bending strength. Steel foams with high strength to weight ratio are used to fill the steel tube to improves its mechanical behavior. The linear eigenvalue and plastic collapse finite element (FE) analysis are performed on steel foam filled tube under pure compression and three point bending simulation. It is shown that foam improves the maximum strength and the ability of energy absorption of the steel tubes significantly. Different configurations with different volume of steel foam and composite behavior are investigated. It is demonstrated that there are some optimum configurations with more efficient behavior. If composite action between steel foam and steel increases, the strength of the element will improve due to the change of the failure mode from local buckling to yielding. Moreover, the Sobol' decomposition is used to investigate uncertainty in the strength and ductility of the composite tube, including the sensitivity of the strength to input parameters such as the foam density, tube wall thickness, steel properties etc. Monte Carlo simulation is performed on aluminum foam filled tubes under three point bending conditions. The simulation method is nonlinear finite element analysis. Results show that the steel foam properties have a greater effect on ductility of the steel foam filled tube than its strength. Moreover, flexural strength is more sensitive to steel properties than to aluminum foam properties. Finally, the properties of hypothetical structural steel foam C-channels foamed are investigated via simulations. In thin-walled structural members, stability of the walls is the primary driver of structural limit states. Moreover, having a light weight is one of the main advantages of the thin-walled structural members. Therefore, thin-walled structural members made of steel foam exhibit improved strength while maintaining their low weight. Linear eigenvalue, finite strip method (FSM) and plastic collapse FE analysis is used to evaluate the strength and ductility of steel foam C-channels under uniform compression and bending. It is found that replacing steel walls of the C-channel with steel foam walls increases the local buckling resistance and decreases the global buckling resistance of the C-channel. By using the Sobol' decomposition, an optimum configuration for the variable density steel foam C-channel can be found. For high relative density, replacing solid steel of the lips and flange elements with steel foam increases the buckling strength. On the other hand, for low relative density replacing solid steel of the lips and flange elements with steel foam deceases the buckling strength. Moreover, it is shown that buckling strength of the steel foam C-channel is sensitive to the second order Sobol' indices. In summary, it is shown in this research that the metal foams have a great potential to improve different types of structural responses, and there are many promising application for metal foam in civil structures.

A study of a thin-walled curved rectangular box beam under torsion and out-of-plane bending is documented in this thesis. A new one-dimensional theory that takes into account warping and distortion in the beam cross-sections is the main focus. Existing available theories for thin-walled curved beams lack rigorous theoretical development, and most have ignored the effects of warping and distortion. A higher order theory including two additional degrees of freedom corresponding to warping and distortion was derived. The conventional three degrees of freedom model was compared with the new five degrees of freedom model. The variation of beam thickness to control and decrease the high distortion variable is investigated.

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La presencia inadvertida de daños en elementos estructurales representa un aspecto crítico en la seguridad de los mismos. Tales fallas pueden causar irregularidades de funcionamiento e incluso conducir al colapso catastrófico. Por ese motivo, la detección de daños en forma temprana es de fundamental importancia. Un tipo de falla que puede pasar peligrosamente inadvertida es aquélla producida por fatiga, ya que resulta muy difícil de detectar a simple vista. Si bien existen técnicas adecuadas para la detección localizada, la aplicación de las mismas puede resultar impráctica en base a la dificultad en la revisión de estructuras complejas, que inclusive pueden pre-sentar sectores inaccesibles. En consecuencia, se han investi-gado otro tipo de procedimientos de carácter más global, entre los que ha adquirido gran importancia la identificación basada en la respuesta dinámica. Esencialmente, este método se basa en la comparación entre valores teóricos y experimenta-les de parámetros dinámicos de estructuras dañadas. Las incógnitas del mencionado problema corresponden a las magni-tudes asociadas al daño (localización, intensidad). Por lo tan-to, a los valores más próximos a los reales les corresponderá una mínima desviación entre los valores teóricos y experimen-tales. Este tipo de técnica inversa hace uso de un modelo teó-rico de la estructura dañada. En esta tesis se presenta un nuevo modelo unidimensional que permite reproducir el comportamiento estructural de vigas de pared delgada con presencia de fisuras debidas a fatiga. En dicho modelo, se admite la posibilidad de considerar el efecto no lineal de cerra-miento parcial de fisura o breathing. El modelo asocia un enfoque de daño estructural por fisura basado en conceptos de mecánica de fracturas, que se desarrolla íntegramente en este trabajo, con una teoría de vigas de pared delgada recien-temente desarrollada para el caso de vigas intactas. Esta teo-ría debe ser extendida para considerar la presencia de fisuras. La premisa global de la teoría es que la presencia de una fisu-ra genera una reducción localizada en la rigidez de la viga. El modelo unidimensional de viga de pared delgada dañada es aplicable a vigas construidas con materiales isótropos, ortótro-pos y compuestos con laminación cross-ply simétrica o espe-cialmente ortótropa. Considera además flexibilidad por corte debido a flexión y alabeo. Los parámetros asociados a las fisuras son identificados mediante la minimización de una fun-ción objetivo, que se define en términos de diferencias norma-lizadas entre valores de indicadores de fisura obtenidos experi-mentalmente y calculados con el modelo viga. Como indica-dores de daño estructural se consideran los desplazamientos producidos por excitación forzada y también las frecuencias de vibración natural. En orden de resolver el problema inverso, se emplea el algoritmo de optimización Evolución Diferencial. / The unnoticed presence of damage in structural elements represents a critical issue in their security. Such flaws may generate malfunctions and even leading to catastrophic collapse. Thus, early detection of damage represents a topic of fundamental importance. A kind of flaw that can be dange-rously unnoticed is that one produced by fatigue, in terms of the difficulty to detect it with the naked eye. Although there are adequate techniques for local detection, their application may result impractical based on the difficulty represented by complex structures, which can have inaccessible parts. Consequently, other procedures of more global character have been topic of research. Among them, identification ba-sed on dynamic response has acquired major importance. Essentially, this method is based on comparisons among theo-retical and experimental values of dynamic parameters related to damaged structures. The unknowns of the mentioned problem correspond to the magnitudes associated to damage (location, severity). Thus, a minimal deviation among theore-tical and experimental results will correspond to the values closer to real ones. This kind of inverse technique makes use of a theoretical model of the damaged structure. In this the-sis, a new one-dimensional model is presented, which allows replicating the structural behavior of thin-walled beams with the presence of cracks generated by fatigue. In this model, the possibility of considering the nonlinear effect of crack partial closure or breathing is allowed. The model associates a structural damage approach based on fracture mechanics concepts, developed entirely in this work, with a recently developed thin-walled beam theory for the case of intact beams. This theory must be extended in order to consider the presence of cracks. The global premise of the theory is that the presence of a crack generates a localized reduction on the beam stiffness. The one-dimensional thin-walled da-maged beam model is applicable to beams made of isotropic material beams, orthotropic materials and composite materials with symmetric cross-ply or specially orthotropic stacking sequences. In addition, shear flexibility debt to flexure and warping is considered. Damage parameters associated to cracks are identified by means of the minimization of a target function, defined in terms of normalized differences among values of damage indicators obtained experimentally and calculated with the beam model. As indicators of structural damage, displacements debt to forced excitation and also frequencies of natural vibration are considered. In order to solve the inverse problem, the optimization algorithm Differential Evolution is employed.

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Yes / Here the design and functional optimisation of thermoformed thin-walled structures made from plastics is considered. Such objects are created in great numbers especially in the food packaging industry. In fact these objects are produced in such vast numbers each year, that one important task in the design of these objects is the minimisation of the amount of plastic used, subject to functional constraints. In this paper a procedure for achieving this is described, which involves the automatic optimisation of the mold shape taking into account the strength of the final object and its thickness distribution, thus reducing the need to perform inefficient and expensive `trial and error¿ experimentation using physical prototypes. An efficient technique for parameterising geometry is utilised here, enabling to create a wide variety of possible mold shapes on which appropriate analysis can be performed. The results of the analysis are used within an automatic optimisation routine enabling to find a design which satisfies user requirements. Thus, the paper describes a rational means for the automatic optimal design of composite thermoformed thin-walled structures.