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- Toward variability characterization and statistic models' constitution for the prediction of exponentially graded plates' static responsePublication . Rosa, Rafael da Silva Batista; Loja, M.A.R.; Carvalho, AldaFunctionally graded composite materials may constitute an advantageous alternative to engineering applications, allying a customized tailoring capability to its inherent continuous properties transition. However, these attractive characteristics must account for the uncertainty that affects these materials and their structures' physical quantities. Therefore, it is important to analyze how this uncertainty will modify the foreseen deterministic response of a structure that is built with these materials, identifying which of the parameters are responsible for a greater impact. To pursue this main objective, the material and geometrical parameters that characterize a plate made of an exponentially graded material are generated according to a random multivariate normal distribution, using the Latin hypercube sampling technique. Then, a set of finite element analyses based on the first-order shear deformation theory are performed to characterize the linear static responses of these plates, which are further correlated to the input parameters. This work also considers the constitution of statistic models in order to allow their use as alternative prediction models. The results show that for the plates that were analyzed, the uncertainty associated with the elasticity modulus of both phases is mainly responsible for the maximum transverse deflection variability. The effectiveness of the statistical models that are built are also shown.
- On the characterization of parametric uncertainty on FGM platesPublication . Damásio, Fábio R.; Silva, Tiago A. N.; Carvalho, Alda; Loja, AméliaComposite materials with their intrinsic tailor-made capabilities can be strong candidates to improve the mechanical performance of structures, either by partially or totally replacing other traditional materials. These easily tailored features can be thought not only in terms of the more often used fibre reinforced laminated composites but also in the context of particulate composites. In general, the mechanical performance of composite structures can be, intentionally or not, influenced through the manipulation of geometric properties, the selection of material’s phases and its disposition in the composite, as well as, the spatial distribution of reinforcement agents, such as fibres or particles. The uncertainty associated to all these diferente aspects can be considered as the main source of variability to the mechanical behaviour of a given structure. It is therefore important to characterize the relations between the geometric and material parameters and a set of some relevant structural responses. The quantification of uncertainty is often related to the experimental behaviour of a given structure, although it can also be assessed within the design perspective, where it is useful to understand and identify the parameters with a greater influence on the uncertainty associated to the model simulations. In the present work, one considers functionally graded plates, where different material and geometric characteristics are assumed to be uncertain. The mechanical behaviour of such plates is modelled using Lagrange- and Kriging-based finite element models, developed according to the assumptions of the first order shear deformation theory. A set of numerical results is presented and discussed in order to identify the most significant modelling parameters for the description of the output variability, in this case the maximum deflection.
- Assessing the influence of material and geometrical uncertainty on the mechanical behavior of functionally graded material platesPublication . Carvalho, Alda; Silva, Tiago; Loja, Amélia; Damásio, Fábio RaimundoComposite materials possessing a functional gradient are becoming strong candidates to enhance the performance of structures when severe operating conditions are a reality. These types of conditions may, for example, range from situations where a high thermal gradient is present to others where it is imperative to minimize abrupt stresses transitions between material interfaces. The manufacturing achievement of the gradients determined for a specific application may in practice face some limitations, which can be due, among other factors, to technological process constraints, eventual operating condition deterioration of production stages, or to nonconforming raw materials. Regardless of the origin of such limitations, the reality is that the uncertainty is always present to some extent; this is clearly reflected in the scattering of material and geometrical properties of these composites. The understanding that deterministic analyses are not enough to provide a complete prediction of the composite structures’ behavior emphasizes the crucial need to identify the effects that the variability in material and geometrical parameters will produce in the structural response.With the presentwork, one intends to study the influence of this variability in the static and free vibrations behavior of functionally graded plates. It is also an objective of this study to use regression models to predict these responses and to characterize the contribution of each model parameter to the explanation of the response variability. To this purpose, a set of numerical results is presented and discussed.
- Assessing static and dynamic response variability due to parametric uncertainty on fibre-reinforced compositesPublication . Carvalho, Alda; Silva, Tiago A. N.; Ramos Loja, M.A.Composite structures are known for their ability to be tailored according to specific operating requisites. Therefore, when modelling these types of structures or components, it is important to account for their response variability, which is mainly due to significant parametric uncertainty compared to traditional materials. The possibility of manufacturing a material according to certain needs provides greater flexibility in design but it also introduces additional sources of uncertainty. Regardless of the origin of the material and/or geometrical variabilities, they will influence the structural responses. Therefore, it is important to anticipate and quantify these uncertainties as much as possible. With the present work, we intend to assess the influence of uncertain material and geometrical parameters on the responses of composite structures. Behind this characterization, linear static and free vibration analyses are performed considering that several material properties, the thickness of each layer and the fibre orientation angles are deemed to be uncertain. In this study, multivariable linear regression models are used to model the maximum transverse deflection and fundamental frequency for a given set of plates, aiming at characterizing the contribution of each modelling parameter to the explanation of the response variability. A set of simulations and numerical results are presented and discussed.
- Assessing parametric uncertainty on fibre reinforced composite laminatesPublication . Carvalho, A.; Silva, T. A. N.; Loja, AméliaWhen modeling a composite structure it is important to take into account its greater exposition to parametric variability, when compared to other types of materials more traditionally used. The possibility to tailor composite materials according to specific requisites is simultaneously a source of additional variability, which origin may be associated to material and to geometrical characteristics. Regardless the origin of this variability, they will produce its effect in the structure response, thus it is very important to anticipate them and to quantify them as much as possible. With the present work, it is intended to assess and quantify the influence of geometrical parameters variabilities on the composite structural response. Behind this characterization, linear static analyses were performed, considering that the layers’ thicknesses and fibre orientation angles will be affected by uncertainty. A set of simulations and numerical results are presented and discussed.