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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 lattices from combinatorial game theory: infinite casePublication . Carvalho, Alda; Santos, Carlos; Dias, Cátia; Coelho, Francisco; Neto, João P.; Nowakowski, Richard; Vinagre, SandraGiven a set of combinatorial games, the children are all those games that can be generated using as options the games of the original set. It is known that the partial order of the children of all games whose birthday is less than a fxed ordinal is a distributive lattice and also that the children of any set of games form a complete lat tice. We are interested in the converse. In a previous paper, we showed that for any fnite lattice there exists a fnite set of games such that the partial order of the chil dren, minus the top and bottom elements, is isomorphic to the original lattice. Here, the main part of the paper is to extend the result to infnite complete lattices. An original motivating question was to characterize those sets whose children generate distributive lattices. While we do not solve it, we show that if the process of taking children is iterated, eventually the corresponding lattice is distributive.
- Pisando Arte e Matemática em LisboaPublication . Carvalho, Alda; Santos, Carlos Pereira; Silva, Jorge Nuno; Teixeira, Ricardo Emanuel CunhaMotifs in one or two directions can be classified mathematically by the types of symmetries they possess, and that classification gives rise to seven frieze patterns and to seventeen wallpaper patterns. Rosettes are other type of patterns in which the repetition of the design occurs about a single point, within a limited region of the plane. Rosettes are either dihedral or cyclic, depending on the presence or absence of mirror symmetries. Many Portuguese pavements are beautiful artistic works: all the seven friezes, cyclic rosettes, dihedral rosettes and twelve of the seventeen types of wallpapers were detected in Lisbon. In this paper, we exemplify some of these artistic works, highlighting, in particular, the work in Rossio dos Olivais, carried out by Fernando Conduto. In 2014, the Ludus Association and the University of Lisbon published the Baralho de Simetrias - Calçadas de Lisboa, a deck of cards to disseminate this subject to the largest possible number of people. We also discuss that initiative.
- 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 static and dynamic response variability due to parametric uncertainty on fibre-reinforced compositesPublication . Carvalho, Alda; Silva, Tiago A. N.; Loja, M.A.R.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 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.
- A global optimization approach based on adaptive populationsPublication . Silva, Tiago A. N.; Loja, Amélia; Carvalho, Alda; Maia, Nuno M. M.; Barbosa, JoaquimThe solution of inverse problems based on experimental data is itself an important research issue. In this context and assuming that an experimental sample is available, rather than trying to find a specific deterministic solution for the inverse problem, one aims to determine the probabilistic distribution of the modelling parameters, based on the minimization of the dissimilarity between the empirical cumulative distribution function of an experimental solution and its simulation counterpart. The present paper presents na innovative framework, where Differential Evolution is extended in order to estimate not only an optimal set of modelling parameters, but to estimate their optimal probabilistic distributions. Additionally, the Adaptive Empirical Distributions optimization scheme is here introduced. Both schemes rely on the two samples Kolmogorov-Smirnov goodness-offit test in order to evaluate the resemblance between two empirical cumulative distribution functions. A numerical example is considered in order to assess the performance of the proposed strategies and validity of their solutions.
- Ordinal sums of impartial gamesPublication . Carvalho, Alda; Neto, João; Santos, CarlosIn an ordinal sum of two combinatorial games G and H, denoted by G : H, a player may move in either G (base) or H (subordinate), with the additional constraint that any move on G completely annihilates the component H. It is well-known that the ordinal sum does not depend on the form of its subordinate, but depends on the form of its base. In this work, we analyze g(G : H) where G and H are impartial forms, observing that the g-values are related to the concept of minimum excluded value of order k. As a case study, we introduce the ruleset OAK, a generalization of GREEN HACKENBUSH. By defining the operation gin sum, it is possible to determine the literal forms of the bases in polynomial time. (C) 2017 Elsevier B.V. All rights reserved.
- 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.
- Kinematics of a classical ballet base movement using a kinetic sensorPublication . Barbosa, Inês; Milho, João; Lourenço, Inês; Mota, Ana; Nascimento, Vanda Maria dos Santos; Carvalho, Alda; Carvalho, André; Portal, RicardoDance is an art form considered a language since it can sometimes reflect a population’s culture or even a celebration that accompanies humanity from its earliest times and which requires from performers a high physical and emotional dexterity. It is expected that the dancer performs rigorous and repetitive technical movements that often lead to painful injuries, resulting in 56% of classical ballet dancers will suffer from some type of musculoskeletal injury. Due to this high number of injuries, it is essential to study and analyse base movements for this type of dance in order to prevent injuries and to optimize the dancer's choreography and productivity. These movements are precedents of more complex movements. In this work, the study of a base dance movement, the Echappé Sauté, using biomechanical techniques is carried out to study the kinematics of the movement. For the data collection, three dancers voluntarily participated and the movements were capture using a 2nd Generation Kinect camera that allows the capture of 3D movement. The biomechanical analysis was performed using the IpiSoft software and a manual procedure was used to perform a 2D biomechanical analysis based on the assumption that the dance movements for this study occur only in one plane. The results were compared to show the adequacy of the use of the Kinetic sensor for 3D dance movement analysis. 7