Optimization is a decision making process to solve problems in a number of fields including engineering mechanics. Bio-inspired optimization algorithms, including genetic algorithm (GA), have been studied for many years. There is a large literature on applying the GA to mechanics problems. However, disadvantages of the GA include the high computational cost and the inability to get the global optimal solution that can be found by using a honeybee-inspired optimization algorithm, called the New Nest-Site Selection (NeSS). We use the NeSS to find optimal parameters for three mechanics problems by following the three processes: screening, identifying relationships, and optimization. The screening process identifies significant parameters from a set of input parameters of interest. Then, relationships between the significant input parameters and responses are established. Finally, the optimization process searches for an optimal solution to achieve objectives of a problem. For the first two problems, we use the NeSS algorithm in conjunction with a third order shear and normal deformable plate theory (TSNDT), the finite element method (FEM), a one-step stress recovery scheme (SRS) and the Tsai-Wu failure criterion to find the stacking sequence of composite laminates and the topology and materials for doubly curved sandwich shells to maximize the first failure load. It is followed by the progressive failure analysis to determine the ultimate failure load. For the sandwich shell, we use the maximum transverse shear stress criterion for delineating failure of the core, and also study simultaneously maximizing the first failure load and minimizing the mass subject to certain constraints. For composite laminates, it is found that the first failure load for an optimally designed stacking sequence exceeds that for the typical [0°/90°]₅ laminate by about 36%. Moreover, the design for the optimal first failure load need not have the maximum ultimate load. For clamped laminates and sandwich shells, the ultimate load is about 50% higher than the first failure load. However, for simply supported edges the ultimate load is generally only about 10% higher than the first failure load. For the atmospheric spray process, we employ the NeSS algorithm to find optimal values of four process input parameters, namely the argon flow rate, the hydrogen flow rate, the powder feed rate and the current, that result in the desired mean particle temperature and the mean particle velocity when they reach the substrate. These optimal values give the desired mean particle temperature and the mean particle velocity within 5% of their target values. / Ph. D. / An optimization process iteratively searches for the best solution from all feasible solutions in the search space that satisfy prespecified criteria. Optimization problems consist of sets of parameters, constraints, and objective functions. Here we use a honeybee-inspired optimization algorithm, called the New Nest-Site Selection (NeSS), to find optimal parameters for three mechanics problems. In the first problem, we optimize the design of an assembly of layers of unidirectional fiber-reinforced materials called composite laminates. Because of their high specific strength and directional-dependent stiffness as compared to those of metals, the composite laminates are being increasingly used in aerospace and automotive industries. After having analyzed deformations of a composite laminate, a failure criterion is used to determine if any point in the structure has failed. The minimum load for which the failure criterion is satisfied at a point is called the first ply failure load. Here we determine the fiber orientation angle in each layer of a rectangular laminate deformed statically by transverse loads applied on the top surface that maximizes the first ply failure load. Subsequently, the load is incrementally increased for the optimally designed laminate and the strength of the failed elements is degraded till the structure cannot support any additional load. The maximum load a structure can support is called the ultimate load. It is found that for a laminate with all edges clamped, the ultimate load can be 40% more than the first ply failure load. We extend the above work to design an optimal geometry and an optimal combination of materials of the facesheets and the core that simultaneously maximizes the first failure load, minimizes the weight of a doubly curved sandwich shell, and satisfies pre-specified constraints. The doubly curved sandwich structure of interest here is comprised of two thin parallel unidirectional fiber-reinforced facesheets bonded to and enclosing a relatively thick mid-layer made of a material softer and lighter than that of the facesheets. The sandwich structures are widely used in aircraft, marine, automobile, and civilian infrastructures. It is found that optimal designs for doubly curved sandwich shells strongly depend upon how the shell edges are supported, and shells designed for the maximum first failure load need not have the maximum ultimate load. An atmospheric plasma spray process (APSP) has been successfully used to coat components for gas turbines, airframe, engines and drive trains, and silicon chips. In the APSP, coating powder is injected into the plasma, which is a mixture of ionized gases such as argon, hydrogen, and helium, through a powder port generally oriented perpendicular to the plasma jet axis. Through interactions with the plasma jet, the particles are accelerated, heated and partially melted before they strike the substrate and are deposited on it to form a coating. It is believed that the coating properties and its quality depend on the particles’ temperature and velocity when they hit the substrate. Here we determine optimum values of four input parameters, namely, the argon flow rate, the hydrogen flow rate, the current, and the powder feed rate to achieve the desirable mean particles’ temperature and the mean particles’ velocity. It is found that the four processes input parameters can be optimized to attain particles’ characteristics within 5% of their prespecified desired values.

This thesis considered the design of new and improved foldcore sandwich panels suitable for high-performance energy absorption applications. This was achieved by utilising origami geometry design techniques to alter foldcore structures such that they possessed different mechanical behaviours and failure modes. The major findings of this thesis were in three areas as follows. First, a modified planar foldcore geometry was developed by introducing sub-folds into a standard foldcore pattern. The new geometry, deemed the indented foldcore, successfully triggered a high-order failure mode known as a travelling hinge line failure mode. This was found to have a much higher energy absorption than the plate buckling failure mode seen in an unmodified foldcore structure. A comprehensive numerical, theoretical, and experimental analysis was conducted on the indented core, which included the development of a new foldcore prototyping method that utilised 3D printed moulds. It was shown that compared to available commercial honeycomb cores, the indented foldcore had an improved uniformity of energy absorption, but weaker overall peak and crushing stresses. Second, rigid origami design principles were used to develop extended foldcore geometries. New parametrisations were presented for three patterns, to complete a set of Miura-derivative geometries termed first-level derivatives. The first-level derivative parametrisations were then combined to create complex, piecewise geometries, with compatible faceted sandwich face geometry also developed. Finally, a method to generate rigid-foldable, curved-crease geometry from Miura-derivative straight-crease geometry was presented. All geometry was validated with physical prototypes and was compiled into a MATLAB Toolbox. Third, the performance of these extended foldcore geometries under impact loadings was investigated. An investigation of curved-crease foldcores showed that they were stronger than straight-crease foldcores, and at certain configurations can potentially match the strength, energy-absorption under quasi-static impact loads, and out-of-plane stiffness of a honeycomb core. A brief investigation of foldcores under low-velocity impact loadings showed that curved-crease foldcores, unlike straight-crease foldcores, strengthened under dynamic loadings, however not to the same extent as honeycomb. Finally, an investigation of single-curved foldcore sandwich shells was conducted. It was seen that foldcore shells could not match the energy-absorption capability of an over-expanded honeycomb shell, but certain core types did exhibit other attributes that might be exploitable with future research, including superior initial strength and superior uniformity of response.

[pt] As cascas cilíndricas possuem aplicações em diversas áreas da engenharia. Nas últimas décadas tem se observado o surgimento de novos materiais e suas técnicas de produção, levando a novas aplicações em estruturas de cascas. Dentre estas, as cascas sanduíche e cascas com gradação funcional têm levado, em muitas aplicações, a um melhor desempenho estrutural associado a uma redução de peso. Este trabalho tem como objetivo estudar as frequências naturais e as cargas críticas de cascas sanduíche com faces de metal e núcleo de espuma metálica e cascas com gradação funcional, onde as características da espuma metálica variam ao longo da espessura levando a uma estrutura similar à da casca sanduíche. Esses resultados são comparados com aqueles de cascas isotrópicas homogêneas. Para tanto, é utilizada a teoria linear de Donnell, que é uma das mais empregadas para análise de cascas. Primeiramente, derivam-se as equações de movimento assim como as equações de equilíbrio crítico. Utilizando as soluções analíticas para uma casca simplesmente apoiada, obtêm-se as matrizes de massa, de rigidez e de rigidez geométrica, possibilitando o cálculo das frequências naturais e cargas críticas da casca sob compressão axial e pressão lateral. Através de uma análise paramétrica, os resultados mostram a influência da geometria da casca, da variação do material ao longo da espessura, do cisalhamento no núcleo e dos termos de inércia nas cargas críticas e frequências naturais. Os resultados também ressaltam a influência do núcleo de espuma metálica no aumento da capacidade de carga e redução de peso das cascas sanduíche e com gradação funcional. / [en] Cylindrical shells are used in several areas of engineering fields. In the last decades has been observed the emergence of new materials and their production techniques, leading to new applications in shell structures. Among these, the sandwich shells and shell with functionally graded materials have led, in many applications, to a better structural performance associated to a reduction of weight. This work aims to study the natural frequencies and the critical loads of sandwich shells with metal faces and metal foam core and functionally graded shells, where the characteristics of the metallic foam vary throughout the thickness leading to a structure similar to that of the sandwich shell. These results are compared with those of homogeneous isotropic shells. For this, the linear theory of Donnell, which is one of the most used for shell analysis, is here used. First, the equations of motion as well as the critical equilibrium equations are derived. Using the analytical solutions for a simply supported shell, the mass, stiffness and geometric stiffness matrices are obtained, allowing the calculation of the natural frequencies and critical loads of the shell under axial compression and lateral pressure. Through a parametric analysis, the results show the influence of the shell geometry, material variation along the shell thickness, shear deformation of the core and the inertia terms on the critical loads and natural frequencies. The results also highlight the influence of the metallic foam core in increasing the load bearing capacity and reducing the weight of the sandwich and functionally graded shells.