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Assessing static and dynamic response variability due to parametric uncertainty on fibre-reinforced composites

Publication . 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.

2018-02-01Journal article

Open access

Ordinal sums of impartial games

Publication . Carvalho, Alda; Neto, João; Santos, Carlos

In 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.

2018-07-10Journal article

Restricted access

Assessing static and dynamic response variability due to parametric uncertainty on fibre-reinforced composites

Publication . Carvalho, Alda; Silva, Tiago A. N.; Loja, M.A.R.

2018-02-01Journal article

Open access

Adaptive empirical distributions in the framework of inverse problems

Publication . Silva, Tiago; Loja, Amélia; Carvalho, Alda; Maia, Nuno. M.; Barbosa, Joaquim

This article presents an innovative framework regarding an inverse problem. One presents the extension of a global optimization algorithm to estimate not only an optimal set of modeling parameters, but also their optimal distributions. Regarding its characteristics, differential evolution algorithm is used to demonstrate this extension, although other population-based algorithms may be considered. The adaptive empirical distributions algorithm is here introduced for the same purpose. Both schemes rely on the minimization of the dissimilarity between the empirical cumulative distribution functions of two data sets, using a goodness-of-fit test to evaluate their resemblance.

2017Journal article

Restricted access

Toward variability characterization and statistic models' constitution for the prediction of exponentially graded plates' static response

Publication . Rosa, Rafael da Silva Batista; Loja, M.A.R.; Carvalho, Alda

Functionally 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.

2018-10-13Journal article

Open access